DI Awesome Collection

1.3 Marks

Saira, Mumtaz and Zeenat have a ball, a pen and a pencil, and each girl hasjust one object in hand. Among the following statements, only one is true andthe other two are false.

Saira has a ball.I.Mumtaz does not have the ball.II.Zeenat does not have the pen.III.

Who has the ball?

1) Saira

2) Mumtaz

3) Zeenat

4) Indeterminate

Solution:Case I: Assume statement I is true.

In such a case, statements II and III have to be false.

Thus, if Saira has the ball, Mumtaz cannot have the ball.

This makes statement II true as well, which is not possible.

Thus, statement I cannot be true.

Case II: Assume statement II is true.

In such a case, statements I and III have to be false.

If Mumtaz does not have the ball, then one of Saira or Zeenat has to have theball.

Since statement I is false, Saira does not have the ball.

Since Saira does not have the ball, Zeenat has to have the ball.

Thus, Zeenat cannot have the pen.

Thus, this makes statement III true, which is not possible.

Thus, statement II cannot be true.

Section I

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Thus, only statement III is true.

Thus, Zeenat who does not have the pen, has either the ball or the pencil.

Since statement II is false, Mumtaz has to have the ball.

Hence, Zeenat has the pencil and Saira has the pen.

Hence, option 2.

2.3 Marks

Albert, David, Jerome and Tommy were plucking mangoes in a grove to earnsome pocket money during the summer holidays. Their earnings were directlyrelated to the number of mangoes plucked and had the following relationship:

Jerome got less money than Tommy. Jerome and Tommy together got thesame amount at Albert and David taken together. Albert and Tommy togethergot less than David and Jerome taken together.

Who earned the most pocket money? Who plucked the least number ofmangoes?

1) David, Jerome

2) David, Albert

3) Jerome, Tommy

4) Jerome, Albert

Solution:Let the money with Jerome, Tommy, David and Albert be J, T, D and Arespectively.

(1) Jerome got less money than Tommy.

J < T ... (i)

(2) Jerome and Tommy together got the same amount at Albert and Davidtaken together.

J + T = A + D ... (ii)

Albert and Tommy together got less than David and Jerome taken together.

A + T < D + J ... (iii)

Adding (ii) and (iii), you get J + A + 2T < A + 2D + J

∴ 2T < 2D


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∴ T < D ... (iv)

From (i) and (iv), you get J < T < D

Subtracting (iii) from (ii), you get J – A > A – J

∴ 2J > 2A

∴ J > A ... (v)

The final order is A < J < T < D

Thus, Albert plucked the least number of mangoes and David earned themost pocket money.

Hence, option 2.

Group Question

Answer the following questions based on the information given below.

Kya-Kya is an obscure island which is inhabited by two types of people: the ‘Yes’type and the ‘No’ type. Natives of the ‘Yes’ type ask only those questions whichhave the right answer as ‘Yes’, while those of the ‘No’ type ask only thosequestions which have the right answer as ‘No’. For example: The ‘Yes’ type peoplewill ask questions like “Is 2 plus 2 equal to 4?” while the ‘No’ type will askquestions like “Is 2 plus 2 equal to five?” The following questions are based onyour visit to the island of Kya-Kya.

3.3 Marks

If an islander asks, “Do I belong to the ‘No’ type?”, which of the followingis correct?

1) He is a ‘No’.

2) He is a ‘Yes’.

3) It is impossible for him to have asked such a question.

4) His type cannot be identified.

Solution:Since there are only two types of people on this island, the person hasto belong to one of the two types.

Case I: Assume that the person belongs to the ‘Yes’ type.

If the above assumption is true, the answer to the question should be‘Yes’ (as per the definition of the type) but the actual answer to the


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question will be ‘No’.

Thus, a person of the ‘Yes’ type can never ask this question.

Case II: Assume that the person belongs to the ‘No’ type.

If the above assumption is true, the answer to the question should be‘No’ (as per the definition of the type) but the actual answer to thequestion will be ‘Yes’.

Thus, a person of the ‘No’ type can never ask this question.

Since these are the only type of people on this island, no one from theisland can ask this question.

Thus, it is impossible for the islander to have asked this question.

Hence, option 3.

4.3 Marks

Ram and Laxman are brothers from the island. Laxman asks you, “Is atleast one from our pair of the ‘No’ type?” You can conclude that:

1) Ram is ‘No’, Laxman is ‘Yes’.

2) Both are ‘Yes’.

3) Ram is ‘Yes’, Laxman is ‘No’.

4) Both are ‘No’.

Solution:There are 4 cases possible here, 2 where both brothers are of the sametype and 2 where both brothers are of different types.

Case I : Both brothers are of the type ‘Yes’.

If both brothers are of the type ‘Yes’, the answer to Laxman's question(as per the definition of the type) should be ‘Yes’ while the actualanswer will be ‘No’.

Thus, both brothers cannot be of the type ‘Yes’.

Case II : Both brothers are of the type ‘No’.

If both brothers are of the type ‘No’, the answer to Laxman's question(as per the definition of the type) should be ‘No’ while the actual answerwill be ‘Yes’.


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Thus, both brothers cannot be of the type ‘No’.

Hence, options 2 and 4 can be eliminated.

Case III: Laxman is the ‘No’ type and Ram is the ‘Yes’ type.

If Laxman is of the ‘No’ type, the answer to his question (as per thedefinition of the type) should be ‘No’ while the actual answer will be‘Yes’.

Thus, Laxman cannot be of the ‘No’ type.

Hence, option 3 can be eliminated. Case IV: Laxman is the ‘Yes’ type and Ram is the ‘No’ type.

If Laxman is of the ‘Yes’ type, the answer to his question (as per thedefinition of the type) should be ‘Yes’ while the actual answer will alsobe ‘Yes’ (because Ram is of the ‘No’ type).

Thus, Laxman is the ‘Yes’ type and Ram is the ‘No’ type.

Hence, option 1.

5.3 Marks

You are approached by one of the islanders and asked, “Am I ofthe ‘Yes’ type?” You can infer that …

1) he is a ‘No’ type.

2) he is a ‘Yes’ type.

3) such a question is impossible to ask.

4) no conclusion is possible.

Solution:The islander can either be a ‘Yes’ type person or a ‘No’ type person.

Case I: The islander is a ‘Yes’ type person.

For such a person, the answer to the question will be ‘Yes’ as per thedefinition of the type and the actual answer will also be ‘Yes’.

Thus, the person could be a ‘Yes’ type person.

Case II: The islander is a ‘No’ type person.

For such a person, the answer to the question will be ‘No’ as per the


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definition of the type and the actual answer will also be ‘No’.

Thus, the person could be a ‘No’ type person.

Thus, the person could be any islander whose type cannot bedetermined.

Hence, no conclusion is possible.

Hence, option 4.

6.3 Marks

Each of three friends knows whether the other two have passed or failed in anexamination, but does not know his own result. The teacher comes and says,“At least one student has failed”. If all three friends still do not know their ownresults which of the following is true?

1) One student has failed.

2) Two students have failed.

3) Two or more students have failed.

4) All three have failed.

Solution:

Let the three students be A, B and C.

Their results can have 8 possibilities as shown in the table above.

It is known that even after the teacher says “At least one student has failed”,no one knows his result.

Consider that exactly one student has failed.

This is seen in cases IV, VI and VII.


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In case IV, A knows that B and C have passed, but doesn't know his ownresult.

Now, if the teacher says that at least one student has failed, it becomes clearto A that he is the one who has failed.

Thus, A knows his result now, which is contradictory with the information inthe question.

Thus, only A cannot fail.

Using a similar logic, only B or only C cannot fail.

Thus, only one student cannot fail.

Hence, option 1 can be eliminated.

Now consider that exactly two students have failed.

This is seen in cases II, III and V.

In case II, C knows that A and B have failed, but doesn't know his own result.

Now, if the teacher says that at least one student has failed, it may mean thatA and B have failed while C has passed, or that all three have failed.

Thus, C still does not know his result.

This can be proved for case III and V as well.

In general, it is possible that exactly two students failed.

Finally, consider that all three students failed (as seen in case I).

Every person knows that the other two students failed. Now, if the teacher says that at least one student has failed, it may meanthat two have failed while the third has passed, or that all three have failed.

Thus, it is possible that all three students have failed.

Thus, two or more students have failed.

Hence, option 3.

7.3 Marks

Amar, Akbar and Anthony come from the same public school in theHimalayas. Every boy in that school either fishes for trout or plays Frisbee. Allfishermen like snow while no Frisbee player likes rain. Amar dislikes whatever


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Akbar likes and likes whatever Akbar dislikes. Akbar likes rain and snow.Anthony likes whatever the other two like. Who is a fisherman but not aFrisbee player?

1) Amar

2) Akbar

3) Anthony

4) More than one of the three boys

Solution:All fishermen like snow while no Frisbee player likes rain.

Akbar likes rain and snow.

Therefore, Akbar is a fisherman but not a Frisbee player.

Amar dislikes both rain and snow.

Therefore, Amar is a Frisbee player but not a fisherman.

Since Anthony likes what the other two like, he cannot like anything. This isbecause Amar dislikes rain and snow.

Therefore, Anthony is also a Frisbee player but not a fisherman.

Thus, only Akbar is a fisherman but not a Frisbee player.

Hence, option 2.

Group Question


A leading socialite decided to organise a dinner and invited some of her friends.Only the host and hostess were sitting at opposite ends of a rectangular table,with three people on each side. The seating arrangement was such thatevery person had at least on person of the opposite sex next to him/her. Maqboolis opposite Shoba, who is not the hostess. Ratan has a woman on his right and issitting opposite a woman. Monisha is sitting to the hostess’s right, next toDhirubhai. One person is seated between Madhuri and Urmila, who is not thehostess. The men were Maqbool, Ratan, Dhirubhai and Jackie, while the womenwere Madhuri, Urmila, Shoba and Monisha.

8.3 Marks

Jackie must be ...

the host.I.


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seated to Shoba’s right.II.seated opposite Urmila.III.

1) I only

2) III only

3) I and II only

4) II and III only

Solution:

Neither Shoba nor Urmila is the hostess. Also, Monisha is sitting to theright of the hostess.

Thus, only Madhuri can be the hostess.

Thus, if one starts from Madhuri, Monisha is to her immediate right andDhirubhai is to Monisha's right.

Also, there is one person between Madhuri and Urmila.

Thus, Urmila has to be at the second place from left, starting fromMadhuri. This means that Urmila and Dhirubhai sit opposite each other.

Now, Shoba and Maqbool sit opposite each other. The only place wheretwo seats opposite each other are available is to the immediate right andleft of the host.

This means that Maqbool cannot be the host. Also, one of Ratan andJackie has to be the host.

Thus, there is one empty seat between Dhirubhai and the host (who is amale).

Since every person must have at least one person of the opposite sexnext to him/her, the person between Dhirubhai and the host cannot be amale.


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Since the only female left is Shoba, she has to be to the immediate rightof Dhirubhai and Maqbool is opposite her (i.e. to the immediate rightof the host).

Since Ratan has a woman to his right, he cannot be the host (due toMaqbool on his right).

Therefore, Jackie is the host and Ratan is between Madhuri and Urmila.

Thus, the final arrangement is as shown in the figure above.

Statement I is true as Jackie is the host.

Statement II is also true as Jackie is to Shoba's right.

Statement III is false as Dhirubhai, and not Jackie, is seated oppositeUrmila.

Thus, only statements I and II are true.

Hence, option 3.

9.3 Marks

Which of the following persons is definitely not seated next to a personof the same sex?

1) Maqbool

2) Madhuri

3) Jackie

4) Shoba

Solution:From the arrangement obtained in the solution to the first question, itcan be seen that Shoba is sitting between two men (Jackie andDhirubhai).

Thus, Shoba is not seated next to a person of the same sex.

Hence, option 4.

10.3 Marks

If Ratan had exchanged seats with the person four places to his left,which of the following would have been true after the exchange?

No one was seated between two persons of the opposite sex. (e.g. no man wasseated between two women)

I.


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One side of the table consisted entirely of persons of the same sex.II.Either the host or the hostess changed seats.III.

1) I only

2) II only

3) I and II only

4) II and III only

Solution:Consider the final arrangement obtained in the solution to the firstquestion.

If Ratan had exchange seats with the person four places to his left, hewould have had to change places with Shoba.

No one else would need to change places.

Thus, neither the host nor the hostess would have changed their place.

Thus, statement III is false.


The side to Madhuri's right would have consisted of Monisha, Dhirubhaiand Ratan i.e. female, male and male.

The side to Madhuri's left would have consisted of Shoba, Urmila andMaqbool i.e. female, female and male.

Thus, no side of the table would consist of people from the same sex.

Thus, statement II is false.


As per the new arrangement, Shoba and Ratan would be seatedbetween two people of the same sex.

No one would have been seated between two people of the oppositesex.

Thus, statement I is true.

Hence, option 1.


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11.3 Marks

If each person is placed directly opposite his/her spouse, which of thefollowing pairs must be married?

1) Ratan and Monisha

2) Madhuri and Dhirubhai

3) Urmila and Jackie

4) Ratan and Madhuri

Solution:Refer to the final arrangement obtained in the solution to the firstquestion.

Among the pairs given in the answer options, only Ratan and Monishaare seated opposite each other.

Hence, Ratan and Monisha must be married.

Hence, option 1.

Group Question


Five of India’s leading models are posing for a photograph promoting “y’know,world peace and understanding”. But then, Rakesh Shreshtha, the photographer,is having a tough time getting them to stand in a straight line, because Aishwaryarefuses to stand next to Sushmita because Sushmita had said something abouther in a leading gossip magazine. Rachael and Anu want to stand togetherbecause they are “such good friends, y’know”. Manpreet on the other hand cannotget along well with Rachael, because there is some talk about Rachael schemingto get a contract already awarded to Manpreet. Anu believes her friendlyastrologer who has asked her to stand at the extreme right for all groupphotographs. Finally, Rakesh managed to pacify the girls and got a beautifulpicture of five beautiful girls smiling beautifully in a beautiful straight line,promoting world peace.

12.3 Marks

If Aishwarya is standing to the extreme left, which girl is standing in themiddle?

1) Manpreet

2) Sushmita

3) Rachael

4) Cannot say


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Solution:Anu stands to the extreme right and Rachael wants to stand next toAnu.

Thus, Rachael is second from right.

Now, Manpreet and Rachael cannot stand next to each other.

Thus, Manpreet has to be at the extreme left or at the second positionfrom the left.

If Manpreet is at the extreme left, Aishwarya and Sushmita have tooccupy the second and third position from the left.

However, Aishwarya and Sushmita cannot stand together.

Thus, Manpreet cannot be at the extreme left and so has to be secondfrom left.

Thus, one of Aishwarya and Sushmita is at the extreme left and theother is at the centre.

The final arrangement is as shown below:

Now, if Aishwarya stands to the extreme left, then Sushmita would haveto stand in the middle.

Hence, option 2.

13.3 Marks

If Aishwarya stands to the extreme left, who stands second from left?

1) Cannot say

2) Sushmita

3) Rachel

4) Manpreet

Solution:Refer to the arrangement obtained in the solution to the first question.


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Therefore, if Aishwarys stands to the extreme left, Manpreet standssecond from left.

Hence, option 4.

14.3 Marks

If Anu’s astrologer tells her to stand second from left and Aishwaryadecides to stand second from right, which girl stands on the extremeright?

1) Rachel

2) Sushmita

3) Cannot say

4) Manpreet

Solution:Anu is second from left and Aishwarya is second from right.

Since Aishwarya is second from right, Sushmita cannot be at the centreor at the extreme right.

Therefore, Sushmita is at the extreme left.

Since Rachael is next to Anu, Rachael has to be at the centre.

Thus, the only place available for Manpreet is at the extreme right.

Thus, Manpreet stands on the extreme right as shown below.

Hence, option 4.

15.3 Marks

In each of the following sentences the main statement is followed by foursentences each. Select a pair of sentences that relate logically with the givenstatement.

Either Sam is ill; or he is drunk.

Sam is ill.A.Sam is not ill.B.Sam is drunk.C.Sam is not drunk.D.


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1) AB

2) DA

3) AC

4) CD

Solution:This logical connective is of the following type

Either P or Q

The conclusions for the above type of logical connective are as follows

~P ⇒ Q 1.~Q ⇒ P 2.

Thus, if Sam is not ill, then he is drunk (BC) or if Sam is not drunk, then he isill (DA).

BC is not given in any of the answer options.

Thus, the pair DA relates logically with the given statement.

Hence, option 2.

16.3 Marks


Whenever Ram hears of a tragedy, he loses sleep.

Ram heard of a tragedy.A.Ram did not hear of a tragedy.B.Ram lost sleep.C.Ram did not lose sleep.D.

1) CA

2) BD

3) DB

4) AD



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Whenever P … Q which is the same as “If P then Q”


P ⇒ Q 1.~Q ⇒ ~P 2.

Thus, if Ram heard a tragedy, he lost sleep (AC) or, if Ram did not lose sleep,he had not heard of a tragedy (DB).

AC is not given in any of the answer options.

Therefore, DB relates logically with the given statement.

Hence, option 3.

17.3 Marks


Either the train is late; or it has derailed.

The train is late.A.The train is not late.B.The train is derailed.C.The train is not derailed.D.

1) AB

2) DB

3) CA

4) BC


Either P or Q


~P ⇒ Q 1.~Q ⇒ P 2.

Thus, if the train is not late, it has been derailed (BC) or, if the train is notderailed, it is late (DA).


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DA is not mentioned in any of the answer options.

Thus, the BC pair relates logically with the given statement.

Hence, option 4.

18.3 Marks


When I hear a horror story I have a nightmare.

I heard a story.A.I did not hear a horror story.B.I did not have a nightmare.C.I had a nightmare.D.

1) CB

2) AD

3) BC

4) AC


When P … Q which is the same as “If P then Q”


P ⇒ Q 1.~Q ⇒ ~P 2.

Thus, if I heard a horror story, I had a nightmare or if I did not have anightmare, I had not heard a horror story (CB).

Thus, the CB pair relates logically with the given statement.

Hence, option 1.

19.3 Marks


When I eat berries I get rashes.

I ate berries.A.


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I did not get rashes.B.I did not eat berries.C.I got rashes.D.

1) DA

2) BC

3) CB

4) AB


When P … Q which is the same as “If P then Q”.


P ⇒ Q 1.~Q ⇒ ~P 2.

Thus, if I ate berries, I got rashes (AD) or if I did not get rashes, I did not eatberries (BC).

AD is not mentioned in any of the answer options.

Thus, the BC pair relates logically with the given statement.

Hence, option 2.

Group Question


Amar, Akbar, Anthony are three friends. Only three colours are available for theirshirts, viz., red, green and blue. Amar did not wear a red shirt. Akbar did not weara green shirt. Anthony did not wear a blue shirt.

20.3 Marks

If Akbar and Anthony wear the same colour, then which of the followingis not true?

1) Amar wears blue and Akbar wears green.

2) Amar wears green and Akbar wears red.

3) Amar wears blue and Akbar does not wear blue.

4) Anthony wears red.


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Solution:Let the red, blue and green shirts be denoted by R, B and Grespectively.

Given conditions:

Amar does not wear R, hence only G or B.i.Akbar does not wear G, hence only R or B.ii.Anthony does not wear B, hence only R or G.iii.

Since Akbar and Anthony wear the same colour, both have to wear red.

As per option 1, Akbar wears green, which is not possible.

Hence, the statement in option 1 is not true.

All the other statements are possible.

Hence, option 1.

21.3 Marks

If two of them wear the same colour then how many of the followingstatements must be false?

Amar wears blue and Akbar does not wear green.I.Amar does not wear blue and Akbar wears blue.II.Amar does not wear blue and Akbar does not wear blue.III.Amar wears green. Akbar does not wear red. Anthony does not wear green.IV.

1) None

2) One

3) Two

4) Three

Solution:Given that any two wear the same colour, only the following 3 casessatisfy this condition:

Case 1: Amar = Akbar = B, Anthony = R or G

Case 2: Amar = Anthony = G, Akbar = R or B

Case 3: Akbar = Anthony = R, Amar = B or G

Consider the given statements:


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Statement 1: Amar = B, Akbar ≠ G

This combination is possible in cases 1 and 3. Hence, this statement isnot definitely false.

Statement 2: Amar ≠ B, Akbar = B

This combination is possible in case 2. Hence, this statement is notdefinitely false.

Statement 3: Amar ≠ B, Akbar ≠ B

This combination is possible in cases 2 and 3. Hence, this statement isnot definitely false.

Statement 4: Amar = G, Akbar ≠ R, Anthony ≠ G

This combination is not possible in any of the 3 cases listed above.Hence, this statement is definitely false.

Thus, there is only one statement that is definitely false.

Hence, option 2.

Group Question


Mr. Bankatlal acted as a judge for the beauty contest. There were four participants,viz., Ms. Andhra Pradesh, Ms. Uttar Pradesh, Ms. West Bengal and Ms.Maharashtra. Mrs. Bankatlal, who was very anxious about the results, asked himabout it as soon as he was back home. Mr. Bankatlal just said that the one who waswearing the yellow saree had won the contest. When Mrs. Bankatlal pressed forfurther details, he elaborated as follows:

All of them were sitting in a row.All of them wore sarees of different colours, viz., Green, Yellow, White and Red.There was only one runner-up and she was sitting beside Ms. Maharashtra.The runner-up was wearing the Green saree.Ms. West Bengal was not sitting at the ends and was not the runner-up.The winner and the runner-up were not sitting adjacent to each other.Ms. Maharashtra was wearing a white saree.Ms. Andhra Pradesh was not wearing the Green saree.The participants wearing the Yellow saree and the White saree were at the ends.

22. Who wore the Red saree?


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3 Marks

1) Ms. Andhra Pradesh

2) Ms. West Bengal

3) Ms. Uttar Pradesh

4) Ms. Maharashtra

Solution:Consider the following statements:

All of them were sitting in a row.1.All of them wore sarees of different colours, viz., Green, Yellow, White and Red.2.There was only one runner-up and she was sitting beside Ms. Maharashtra.3.The runner-up was wearing the Green saree.4.Ms. West Bengal was not sitting at the ends and was not the runner-up.5.The winner and the runner-up were not sitting adjacent to each other.6.Ms. Maharashtra was wearing a white saree.7.Ms. Andhra Pradesh was not wearing the Green saree.8.The participants wearing the Yellow saree and the White saree were at the ends.9.The winner was wearing Yellow saree (This is obtained from the facts that therunner-up was sitting next to Ms. Maharashtra and that the winner was not seatednext to the runner up. Thus, the winner would have to be at the other end. Theperson at the other end was wearing a yellow saree).

10.

Using (1), (2), (7), (9) and (10), we have

Using (3) and (4), we have

Using (5) and (8), we have the final arrangement as:

Thus, Ms. West Bengal wore the red saree.

Hence, option 2.


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23.3 Marks

Ms. West Bengal was sitting adjacent to …

1) Ms. Andhra Pradesh and Ms. Maharashtra

2) Ms. Uttar Pradesh and Ms. Maharashtra

3) Ms. Andhra Pradesh and Ms. Uttar Pradesh

4) Ms. Uttar Pradesh only

Solution:From the final table obtained in the solution to the first question, Ms. WestBengal was sitting adjacent to Ms. Uttar Pradesh and Ms. AndhraPradesh.

Hence, option 3.

24.3 Marks

Which saree was worn by Ms. Andhra Pradesh?

1) Yellow

2) Red

3) Green

4) White

Solution:From the final table obtained in the solution to the first question, Ms.Andhra Pradesh wore the Yellow saree.

Hence, option 1.

25.3 Marks

Who was the runner-up?

1) Ms. Andhra Pradesh

2) Ms. West Bengal

3) Ms. Uttar Pradesh

4) Ms. Maharashtra

Solution:From the final table obtained in the solution to the first question, Ms. UttarPradesh was the runner-up of the contest.

Hence, option 3.


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26.3 Marks

Abraham, Border, Charlie, Dennis and Elmer and their respective wives dinedtogether and were seated at a circular table. The seats were so arranged thatmen and women alternated and each woman was three places distant fromher husband. Mrs. Charlie sat to the left of Mr. Abraham. Mrs. Elmer sat twoplaces to the right of Mrs. Border. Who sat to the right of Mr. Abraham?

1) Mrs. Dennis

2) Mrs. Elmer

3) Mrs. Border

4) Mrs. Border or Mrs. Dennis

Solution:It is given that men and women alternated in their seating arrangement.Hence, each man is between two women.

Identify the women who cannot be seated to the right of Mr. Abraham.

Since each woman was three places away from her husband, Mrs. Abrahamcannot sit next to Mr. Abraham.

It is known that Mrs. Charlie is to the left of Mr. Abraham, so she cannot be atthe right side simultaneously.

Since Mrs. Elmer is two places to the right of Mrs. Border, Mrs. Elmer cannotbe sitting to the right of Mr. Abraham.

So, either Mrs. Border or Mrs. Dennis could sit to the right of Mr. Abraham.

Hence, option 4.

Group Question


Seven university cricket players are to be honoured at a special luncheon. Theplayers will be seated on the dais along one side of a single rectangular table.

A and G have to leave the luncheon early and must be seated at the extreme right end ofthe table, which is closest to the exit. B will receive the Man of the Match award and must be in the center chair.C and D who are bitter rivals for the position of wicket keeper, dislike one another andshould be seated as far apart as possible.E and F are best friends and want to sit together.

27.3 Marks

Which of the following may not be seated at either end of the table?


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1) C

2) D

3) G

4) F

Solution:Consider the blank seat from left to right as shown below.

(Left) __ __ __ __ __ __ __ (Right)

B will be at the centre. Simultaneously, A and G will occupy the twoseats at the extreme right.

Thus, the arrangement now is:

__ __ __ B __ A/G G/A

Since C and D have to be as far away as possible from each other, oneof them has to be to the immediate right of B while the other has to beat the extreme left seat.

Now, E and F have to be together. They anyways have only the secondand third seat from the left available.

Hence, they occupy those seats.

Thus, the final arrangement is as shown below.

D/C E/F F/E B C/D A/G G/A

Thus, F may not be seated at either end of the table.

Hence, option 4.

28.3 Marks

Which of the following pairs may not be seated together?

1) E and A

2) B and D

3) C and F

4) G and D


24 of 28 9/16/2011 10:18 AM

Solution:From the solution to the first question, it can be seen that B and D, Cand F, as well as G and D can be seated together.

Only E and A cannot never be seated together.

Hence, option 1.

29.3 Marks

Each question has a main statement followed by four statements labelled A,B, C and D. Choose the ordered pair of statements where the first statementimplies the second, and the two statements are logically consistent with themain statement.

Either the orangutan is not angry, or he frowns upon the world.

The orangutan frowns upon the world.A.The orangutan is not angry.B.The orangutan does not frown upon the world.C.The orangutan is angry.D.

1) CB only

2) DA only

3) AB only

4) CB and DA


Either P or Q


~P ⇒ Q 1.~Q ⇒ P 2.

Thus, if the orangutan is angry, he frowns upon the world (DA) or if theorangutan does not frown upon the world, the orangutan is not angry (CB).

Thus, both pairs (DA and CB) are logically consistent with the mainstatement.

Hence, option 4.

30.3 Marks

Each question has a main statement followed by four statements labelled A,


25 of 28 9/16/2011 10:18 AM

B, C and D. Choose the ordered pair of statements where the first statementimplies the second, and the two statements are logically consistent with themain statement.

Either Ravana is a demon, or he is a hero.

Ravana is a hero.A.Ravana is a demon.B.Ravana is not a demon.C.Ravana is not a hero.D.

1) CD only

2) BA only

3) CD and BA

4) DB and CA


Either P or Q


~P ⇒ Q 1.~Q ⇒ P 2.

Thus, if Ravana is not a demon, then he is a hero (CA) or if Ravana is not ahero, then he is a demon (DB).

Thus, both pairs (DB and CA) are logically consistent with the mainstatement.

Hence, option 4.

31.3 Marks


Whenever Rajeev uses the internet, he dreams about spiders.

Rajeev did not dream about spiders.A.Rajeev used the internet.B.Rajeev dreamt about spiders.C.Rajeev did not use the internet.D.


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1) AD

2) DC

3) CB

4) DA


Whenever P then Q which is the same as “If P then Q”


P ⇒ Q 1.~Q ⇒ ~P 2.

Thus, if Rajeev used the internet, he dreamt about spiders (BC) or if Rajeevdid not dream about spiders, he did not use the internet (AD).

The BC pair is not given in the options.

Therefore, the AD pair is logically consistent with the main statement.

Hence, option 1.

32.3 Marks


If I talk to my professors, then I do not need to take a pill for headache.

I talked to my professors.A.I did not need to take a pill for headache.B.I needed to take a pill for headache.C.I did not talk to my professors.D.

1) AB only

2) DC only

3) CD only

4) AB and CD



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If P then Q


P ⇒ Q 1.~Q ⇒ ~P 2.

Thus, if I talked to my professors, I did not need to take a pill for headache(AB) or if I needed to take a pill for my headache, I did not talk to myprofessors (CD).

Thus, both pairs (AB and CD) are logically consistent with the mainstatement.

Hence, option 4.


28 of 28 9/16/2011 10:18 AM

Group Question


Five women decided to go shopping to M.G. Road, Bangalore. They arrived at thedesignated meeting place in the following order: 1. Archana, 2. Chellamma, 3.Dhenuka, 4. Helen, and 5. Shahnaz. Each woman spent at least Rs. 1000. Beloware some additional facts about how much they spent during their shoppingspree.

The woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193.i.One woman spent Rs. 1340 and she was not Dhenuka.ii.One woman spent Rs. 1378 more than Chellamma.iii.One woman spent Rs. 2517 and she was not Archana.iv.Helen spent more than Dhenuka.v.Shahnaz spent the largest amount and Chellamma the smallest.vi.

[CAT 2003 Leaked Test]

1.3 Marks

What was the amount spent by Helen?

1) Rs. 1193

2) Rs. 1340

3) Rs. 2234

4) Rs. 2517

Solution:The amounts are Rs. 2,234, Rs. 1,193, Rs. 1,340 and Rs. 2,517. Thefifth amount is not given.

∵ One woman’s amount = Chellamma’s amount + Rs. 1,378

∵ All the women spent more than Rs. 1,000.

∴ Chellamma’s amount

= Rs. 2,517 – Rs. 1,378

= Rs. 1,139

∴ The biggest amount of Rs. 2,517 is spent by Shahnaz.

∵ It is given that Helen spent more than Dhenuka and Dhenuka did not

Section I


1 of 23 9/16/2011 10:28 AM

spend Rs. 1,340.

∴ Dhenuka spent Rs. 1,193.

We also know that the women who spent Rs. 2,234 arrived before thelady who spent 1193.

∴ Archana spent Rs. 2,234 and Helen spent Rs. 1,340.

The amount spent by Helen was Rs. 1,340.

Hence, option 2.

2.3 Marks

Which of the following amounts was spent by one of them?

1) Rs. 1139

2) Rs. 1378

3) Rs. 2571

4) Rs. 2718

Solution:Rs. 1,139 was one of the amounts which was spent by Chellamma.

Hence, option 1.

3.3 Marks

The woman who spent Rs. 1193 is

1) Archana

2) Chellamma

3) Dhenuka

4) Helen

Solution:


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The woman who spent Rs. 1,193 was Dhenuka.

Hence, option 3.

Group Question


Five friends meet every morning at Sree Sagar restaurant for an idli-vadabreakfast. Each consumes a different number of idlis and vadas. The number ofidlis consumed are 1, 4, 5, 6, and 8, while the number of vadas consumed are 0,1, 2, 4, and 6. Below are some more facts about who eats what and how much?

The number of vadas eaten by Ignesh is three times the number of vadas consumed bythe person who eats four idlis.

i.

Three persons, including the one who eats four vadas, eat without chutney.ii.Sandeep does not take any chutney.iii.The one who eats one idli a day does not eat any vadas or chutney. Further, he is notMukesh.

iv.

Daljit eats idli with chutney and also eats vada.v.Mukesh, who does not take chutney, eats half as many vadas as the person who eats twiceas many idlis as he does.

vi.

Bimal eats two more idlis than Ignesh, but Ignesh eats two more vadas than Bimal.vii.


4.3 Marks

Which one of the following statements is true?

1) Daljit eats 5 idlis.

2) Ignesh eats 8 idlis.

3) Bimal eats 1 idli.

4) Bimal eats 6 idlis.

Solution:From (i),

Number of vadas eaten by Ignesh is 6 and the person eating 4 idlis eats2 vadas.

From (vii),

Number of vadas eaten by Bimal = 4

Number of idlis eaten by Bimal = 8


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Number of idlis eaten by Ignesh = 6

Ignesh, Mukesh, Daljit and Bimal eat at least 1 vada and 1 idli.

∴ Sandeep doesn’t eat any vadas but eats 1 idli.

From (vi),

Number of vadas eaten by Mukesh = 2

Number of idlis eaten by Mukesh = 4

Daljit eats 5 idlis.

Hence, option 1.

5.3 Marks

Which of the following statements is true?

1) Sandeep eats 2 vadas.

2) Mukesh eats 4 vadas.

3) Ignesh eats 6 vadas.

4) Bimal eats 4 vadas.

Solution:Ignesh eats 6 vadas and Bimal eats 4 vadas.

There seems to be some problem with this question as there are twooptions which are correct.

Hence, option 3 or option 4.

6.3 Marks

Which of the following statements is true?

1) Mukesh eats 8 idlis and 4 vadas but no chutney.


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2) The person who eats 5 idlis and 1 vada does not takechutney.

3) The person who eats equal number of vadas and idlis alsotakes chutney.

4) The person who eats 4 idlis and 2 vadas also takes chutney.

Solution:Ignesh eats 6 vadas and 6 idlis with chutney.

Hence, option 3.

Group Question


Four families decided to attend the marriage ceremony of one of their colleagues.One family has no kids, while the others have at least one kid each. Each familywith kids has at least one kid attending the marriage. Given below is someinformation about the families, and who reached when to attend the marriage.

The family with 2 kids came just before the family with no kids.Shanthi who does not have any kids reached just before Sridevi’s family.Sunil and his wife reached last with their only kid.Anil is not the husband of Joya.Anil and Raj are fathers.Sridevi’s and Anita’s daughters go to the same school.Joya came before Shanthi and met Anita when she reached the venue.Raman stays the farthest from the venue.Raj said his son could not come because of his exams.

[CAT 2003 Re-Test]

7.3 Marks

Which woman arrived third?

1) Shanthi

2) Sridevi

3) Anita

4) Joya

Solution:Let’s organize the information given in a tabular form.


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Using first two statements, we have,

Anil, Raj and Sunil have kids.

∴ Raman is the husband of Shanthi.

∵ Joya came before Shanthi and met Anita on the Venue.

∴ Anita reached the venue first, Joya reached second, Shanthi reachedthird and Sridevi reached last.

As Sunil reached the last with his only kid, Sunil is the husband ofSridevi.

∵ Anil is not the husband of Joya.

∴ Raj is Joya’s husband and Anil is Anita’s husband.

From the table we can see that Shanthi arrived third.

Hence, option 1.

8.3 Marks

Name the correct pair of husband and wife.


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1) Raj and Shanthi

2) Sunil and Sridevi

3) Anil and Sridevi

4) Raj and Anita

Solution:Referring the solution given in the first question of the set we get that,

Out of the given choices, Sunil and Sridevi is the correct pair.

Hence, option 2.

9.3 Marks

Of the following pairs, whose daughters go to the same school?

1) Anil and Raman

2) Sunil and Raman

3) Sunil and Anil

4) Raj and Anil

Solution:The daughters of Anita and Sridevi go to the same school.

Referring the table given in the solution of the first question of the setwe get that,

Anita’s husband is Anil and Sridevi’s husband is Sunil.

∴ Sunil and Anil is the correct answer.

Hence, option 3.

10.3 Marks

Whose family is known to have more than one kid for certain?

1) Raman’s

2) Raj’s

3) Anil’s

4) Sunil’s

Solution:


7 of 23 9/16/2011 10:28 AM

Raj’s family consists of two kids for certain.

Anil has at least one kid, and hence, could be having exactly one kidalso.

Hence, option 2.

Group Question


The plan above shows an office block for six officers, A, B, C, D, E and F. Both Band C occupy offices to the right of corridor (as one enters the office block) and Aoccupies an office to the left of the corridor. E and F occupy offices on oppositesides of the corridor but their offices do not face each other. The offices of C andD face each other. E does not have a corner office. F’s office is further down thecorridor than A’s, but on the same side.

[CAT 2003 Re-Test]

11.3 Marks

If E sits in his office and faces the corridor, whose office is to his left?

1) A

2) B

3) C

4) D

Solution:


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From the data given we can figure out that A, F and D have offices onthe left side of the corridor and B, E and C have offices on the right sideof the corridor.

∵ E cannot occupy the corner office.

∴ E occupies an office in the middle of the right corridor.

∵ F cannot sit opposite E and A has to occupy an office before F.

∴ F occupies an office at far end of the left side of the corridor.

∴ D and C have to be at the beginning of the corridor.

∴ A has to be in the middle of the left corridor and B has to be at thefar end of the right corridor.

The arrangement of offices will be as shown in the figure above :

If E sits in his office and faces the corridor. C’s office is to his left.

Hence, option 3.

12.3 Marks

Whose office faces A’s office?

1) B

2) C

3) D

4) E

Solution:From the arrangement given in the solution of the first question of theset we get that,

E’s office faces A’s office.

Hence, option 4.


9 of 23 9/16/2011 10:28 AM

13.3 Marks

Who is/are F’s neighbour(s)?

1) A only

2) A and D

3) C only

4) B and C

Solution:Only A is F’s neighbour.

Hence, option 1.

14.3 Marks

D was heard telling someone to go further down the corridor to the lastoffice on the right. To whose room was he trying to direct that person?

1) A

2) B

3) C

4) F

Solution:D was trying to direct the person to B’s office as B’s office is last on theright side of the corridor.

Hence, option 2.

Group Question


Seven faculty members at a management institute frequent a lounge for strongcoffee and stimulating conversation. On being asked about their visit to thelounge last Friday we got the following responses.

JC : I came in first, and the next two persons to enter were SS and SM. WhenI left the lounge, JP and VR were present in the lounge. DG left with me.JP : When I entered the lounge with VR, JC was sitting there. There wassomeone else, but I cannot remember who it was.SM : I went to the lounge for a short while, and met JC, SS and DG in thelounge on that day.SS : I left immediately after SM left.DG : I met JC, SS, SM, JP and VR during my first visit to the lounge. I wentback to my office with JC. When I went to the lounge the second time, JP and VR


10 of 23 9/16/2011 10:28 AM

were there.PK : I had some urgent work, so I did not sit in the lounge that day, but justcollected my coffee and left. JP and DG were the only people in the lounge whileI was there.VR : No comments.

[CAT 2003 Re-Test]

15.3 Marks

Based on the responses, which of the two JP or DG, entered the loungefirst?

1) JP

2) DG

3) Both entered together

4) Cannot be deduced

Solution:

The information can be organised in a tabular form as shown above:

JC arrives first in the lounge, followed by SS and SM.

∴ DG must have followed them as SM met him before he left.

SM leaves after DG comes followed by SS.

JP and VR enter to find JC and DG sitting in the lounge.

JC leaves with DG, after meeting JP and VR.

DG comes back on his second visit to the lounge finding JP and VR stillsitting in the lounge.


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VR leaves the lounge, and only JP and DG are left behind in thelounge.

PK enters the lounge and finds only JP and DG sitting in the lounge.

PK leaves, which means that JP and DG must be the last two facultymembers to leave the lounge.

Between JP and DG, DG entered the lounge first.

Hence, option 2.

16.3 Marks

Who was sitting with JC when JP entered the lounge?

1) SS

2) SM

3) DG

4) PK

Solution:DG was sitting with JC when JP entered the lounge.

Hence, option 3.

17.3 Marks

How many of the seven members did VR meet on Friday in the lounge?

1) 2

2) 3

3) 4

4) 5

Solution:VR met JC, DG and JP in the lounge on Friday.

Hence, option 2.

18.3 Marks

Who were the last two faculty members to leave the lounge?

1) JC and DG

2) PK and DG


12 of 23 9/16/2011 10:28 AM

3) JP and PK

4) JP and DG

Solution:JP and DG were the last two faculty members to leave the lounge.

Hence, option 4.

Group Question


K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. Thereis a proposal to form a team from within the members of the department, subjectto the following conditions:

A team must include exactly one among P, R, and S.A team must include either M or Q, but not both. If a team includes K, then it must also include L, and vice versa.If a team includes one among S, U, and W, then it must also include the other two.L and N cannot be members of the same team.L and U cannot be members of the same team.The size of a team is defined as the number of members in the team.

[CAT 2006]

19.3 Marks

What could be the size of a team that includes K?

1) 2 or 3

2) 2 or 4

3) 3 or 4

4) Only 2

5) Only 4

Solution:As K is included, L is included. So, N and U cannot be included. As U isnot included, S and W are not included. One out of M and Q and oneout of P and R will be included.

Thus, the team will include: K, L, (M or Q) and (P or R).

Hence, option 5.


13 of 23 9/16/2011 10:28 AM

20.3 Marks

In how many ways a team can be constituted so that the team includesN?

1) 2

2) 3

3) 4

4) 5

5) 6

Solution:If the team includes N, it does not include L and K.

One out of M and Q can be included and one out of P, S and R can beincluded.

If S is a member, so are U and W.

Thus the possible teams are:

N, M, P1.N, M, R2.N, Q, P3.N, Q, R4.N, M, S, U, W5.N, Q, S, U, W6.

Hence, option 5.

21.3 Marks

What would be the size of the largest possible team?

1) 8

2) 7

3) 6

4) 5

5) Cannot be determined

Solution:If S is not included, the team can have P or R, M or Q, K and L.

If S is included, the team will have S, U, W, M or Q, N.

This is the largest possible team.


14 of 23 9/16/2011 10:28 AM

Hence, option 4.

22.3 Marks

Who can be a member of a team of size 5?

1) K

2) L

3) M

4) P

5) R

Solution:If K or L are included, N, U, S and W are excluded. One out of P and Rand one out of M and Q are included. Thus the team has only 4members.

If P or R are included, the team can have M or Q, K and L. This teamalso has 4 members.

A team having M can have S, U, W and N i.e., 5 members.

Hence, option 3.

23.3 Marks

Who cannot be a member of a team of size 3?

1) L

2) M

3) N

4) P

5) Q

Solution:A team sized 3 has to have M or Q and P or R. The only other memberthat can be selected all alone is N.

L cannot be selected as K has to be selected with him.

Hence, option 1.

Group Question


15 of 23 9/16/2011 10:28 AM


Answer the following questions based on the statements given below:

There are three houses on each side of the road.i.These six houses are labeled as P, Q, R, S, T and U.ii.The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White.iii.The houses are of different heights.iv.T, the tallest house, is exactly opposite to the Red coloured house.v.The shortest house is exactly opposite to the Green coloured house.vi.U, the Orange coloured house, is located between P and S.vii.R, the Yellow coloured house, is exactly opposite to P.viii.Q, the Green coloured house, is exactly opposite to U.ix.P, the White coloured house, is taller than R, but shorter than S and Q.x.

[CAT 2008]

24.3 Marks

What is the colour of the tallest house?

1) Red

2) Blue

3) Green

4) Yellow

5) None of these

Solution:We have to arrange six houses on opposite sides of a road.

From condition (vii), we can say that P, U and S lie on one side of theroad as follows:

From condition (viii) and (ix) we can further complete the arrangementas follows. We have also used the color of the house P from statement(x).


16 of 23 9/16/2011 10:28 AM

The only left house is definitely T. From conditions (v) and we cancomplete the arrangement as follows.

From condition (vi) it can be deduced that U is the shortest house. Alsofrom the last condition it can be deduced that P is the fourth tallest, R isthe fifth tallest and S and Q are second and third tallest not in thatorder.

Filling all this data we can see the arrangement as follows:

The color of the tallest house (T) is Blue.

Hence, option 2.

25.3 Marks

What is the colour of the house diagonally opposite to the Yellowcoloured house?

1) White

2) Blue

3) Green

4) Red

5) None of these


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Solution:The house diagonally opposite to the Yellow coloured house is S whichhas red colour.

Hence, option 4.

26.3 Marks

Which is the second tallest house?

1) P

2) S

3) Q

4) R


Solution:The second tallest house can be either S or Q. We cannot determine forsure which of them is the second tallest.

Hence, option 5.

Group Question


Answer the following questions based on the information given below:

In a sports event, six teams (A, B, C, D, E and F) are competing against eachother. Matches are scheduled in two stages. Each team plays three matches inStage-I and two matches in Stage-II. No team plays against the same team morethan once in the event. No ties are permitted in any of the matches. Theobservations after the completion of Stage-I and Stage-II are as given below.

Stage-I:

One team won all the three matches.Two teams lost all the matches.D lost to A but won against C and F.E lost to B but won against C and F.B lost at least one match.F did not play against the top team of Stage-I.

Stage-II:


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The leader of Stage-I lost the next two matches.Of the two teams at the bottom after Stage-I, one team won both matches, while theother lost both matches.One more team lost both matches in Stage-II.

[CAT 2008]

27.3 Marks

The team(s) with the most wins in the event is (are):

1) A

2) A & C

3) F

4) E

5) B & E

Solution:Let the bold letters denote the teams that have lost.

From condition 3 of stage I,

D lost to A.

D won against C.

D won against F.

These can be represented as:

D -- A

D -- C

D -- F

Similarly, condition 4 of stage I can be represented as:

E -- B

E -- C

E -- F

Since D and E have participated in three matches in stage I, they wouldnot be involved in any other match in stage I.

From the above representations it is clear that all other teams except A


19 of 23 9/16/2011 10:28 AM

have lost at least one match.

∴ From condition 1, of stage I, only A has won all the three matches instage I.

Also, A will participate in 2 more matches as every team participates in 3matches in stage I.

∴ A will win in 2 of the remaining 3 matches.

Also A is the top team as it wins all matches in stage I.

From condition 6 of stage I,

F did not play against A.

∴ A won against B and C which can be represented as:

B -- A

A -- C

The only 2 teams which have not won even a single match so far is Cand F.

From statement 6 of stage I, F loses in the remaining match against B,which can be

represented as:

F -- B

Stage I can be represented as:

D -- A B -- A

D -- C A -- C

D -- F F -- B

E -- B

E -- C

E -- F

From condition 1 of stage II,


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A lost both matches in stage II.

Also, since no team plays against the same team more than once in theevent, A plays matches against E and F.

A -- E

A -- F

Since one of the two teams at the bottom after stage I won bothmatches in stage II, F is the team which has won both the matches instage II.

Also C lost both matches in stage II.

F -- C

B -- C

The last condition states that one more team lost both matches in stageII.

∴ D lost both matches in stage II.

D -- B

D -- E

Stage II can be represented as:

A -- E

A -- F

F -- C

B -- C

D -- B

D -- E

Now, we can calculate the number of times each team has won.


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It can be observed from the above table that B and E have most wins inthe event.

Hence, option 5.

28.3 Marks

The two teams that defeated the leader of Stage-I are:

1) F & D

2) E & F

3) B & D

4) E & D

5) F & D

Solution:E and F defeated A.

Hence, option 2.

29.3 Marks

The only team(s) that won both the matches in Stage-II is (are):

1) B

2) E & F

3) A, E & F

4) B, E & F

5) B & F

Solution:B, E and F are the three teams that won both matches in stage II.


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Hence, option 4.

30.3 Marks

The teams that won exactly two matches in the event are:

1) A, D & F

2) D & E

3) E & F

4) D, E & F

5) D & F

Solution:From the table it is clear that the team that won excatly two matches inthe event are D and F.

Hence, option 5.


23 of 23 9/16/2011 10:28 AM

Group Question


The following graph shows the value of liquor supplied by 5 states in 1996 andthe excise duty rates in each state.

The amount of liquor supplied in 5 distilleries in Tamil Nadu i.e. A, B, C, D, E (frombottom to top) in lakh litres is shown in the graph below.

1.3 Marks

What is the lowest percentage difference in the excise duty rates for anytwo states?

Section I


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1) 13

2) 15

3) 20

4) Indeterminate

Solution:The approximate excise duty rate for each state is:

TN : 25%

AP : 60%

Maharashtra : 50%

MP : 40%

Delhi : 80%

The lowest percentage difference will be possible only when any twoconsecutive values are considered.

The excise duty rates, arranged in ascending order, are as follows:

25 - 40 - 50 - 60 - 80

The corresponding approximate percentage difference in each case is:

60%, 25%, 20%, 33.33%

Thus, the lowest percentage difference is 20%.

Hence, option 3.

2.3 Marks

Which of the five states manufactured liquor at the lowest cost?

1) Tamil Nadu

2) Delhi

3) The states which has the lowest value for (Wholesale price –Excise duty) per litre

4) Indeterminate


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Solution:The answer to this question cannot be found.

This is because the total quantity of liquor produced in each state is notknown.

Even if that quantity is known, one would have to assume that the totalcost of liquor comes only from excise duty.

Therefore, it is impossible to determine the state that produces liquor atthe lowest cost.

Hence, option 4.

3.3 Marks

If Excise duty is levied before the goods leave the factory (on the valueof the liquor), then which of the following choices shows the distilleriesin ascending order of the excise duty paid by them for the year 1996?(Assume the total liquor in TN is supplied by only these 5 distilleries).

1) ECABD

2) ADEBC

3) DCEBA

4) Indeterminate

Solution:This question can be answered by simple observation.

Only the 5 distilleries given supply liquor in TN.

Also, the excise duty is levied on the goods (based on the value of theliquor)

∴ Excise Duty ∝ Value of Liquor

From the bar chart for 1996, it is obvious that distillery D supplies theminimum amount (and hence value) of liquor and distillery A suppliesthe maximum.

Thus, the order starts from D and ends in A.

Hence, options 1,2 and 4 can be eliminated.

By observation, it is clear that the correct order is DCEBA.


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Hence, option 3.

4.3 Marks

If the Tamil Nadu distillery, with the least average simple annual growthin amount of liquor supplied in the given period had shown the samerate of growth as the one which grew fastest, what would that distillery’ssupply have been in 1998, in lakh litres?

1) 13

2) 15.4

3) 130

4) Indeterminate

Solution:Observe that distillery E remains relatively constant throughout theperiod while distillery C grows quite drastically in the given period.

Thus, E is the slowest growing distillery while C is the fastest growingone in the given period.

The value in 1996 for distillery E is approximately 2.5

The rate of growth between 1996 and 1998 for distillery C

= (11 − 1.5)/1.5 × 100

= 633.33% (approx)

If distillery E had grown at this rate, it supply in 1998 would have been

2.5 × 6.33 = 15.8 lakh litres (approx).

Hence, option 2.

Group Question


The graph below shows the market value of 4 shares at the end of each month ina period from January to June.


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5.3 Marks

Which share showed the greatest percentage increase in market valuein any month during the entire period?

1) A

2) B

3) C

4) D

Solution:Observe that C grows with a very grentle slope throughout the periodand so can be ruled out.

The three possible options are : D (between Feb and Mar), B (betweenMar and Apr) and A (between Jan and Feb).

A increased from 40 to 50 between Jan and Feb. This is a growth of25%.

B increased from 55 to 60 between Feb and Mar and from 60 to 65between Mar and Apr. The first is a growth of 9.09% while the second isa growth of 8.33%.

D increased from 95 to 115 between Feb and Mar. This is a growth ofapproximately 17%.

Thus, A showed the maximum percentage increase.

Hence, option 1.

6. In which month was the greatest absolute change in market value for


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3 Marks any share recorded?

1) March

2) April

3) May

4) June

Solution:The market value of D in the month of March increased to 115 from 95 inthe month of February.

There is no other absolute change greater than this during the givenperiod.

Hence, option 1.

7.3 Marks

In which month was the greatest percentage increase in market valuefor any share recorded?

1) February

2) March

3) April

4) May

Solution:The market value of A increased from 40 to 50 in February.

This is the highest percentage increase in the given period.

Hence, option 1.

8.3 Marks

An individual wishes to sell 1 share of C and 1 share of D to buy 1 shareof A at the end of a month. At the end of which month would theindividual’s profit/loss from this decision, due to share value changes,be the most?

1) February

2) March


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3) April

4) June

Solution:The profit/loss in the month of February = 90 + 72 – 50 = 112

The profit/loss in the month of March = 115 + 74 – 50 = 139

The profit/loss in the month of April = 105 + 75 – 40 = 140

The profit/loss in the month of June = 110 + 80 – 45 = 145

Thus, among the options given, the maximum profit was made in themonth of June.

Hence, option 4.

9.3 Marks

An individual decides to sell 1 share of A and 1 share of B to buy 1share of D at the end of the month. What can be the individual’sgreatest gain from this decision, due to share value changes?

1) 5

2) 10

3) 15

4) None

Solution:The person earns money on shares A and B and spends money onshare D.

The gain/loss in the month of Jan = 40 + 60 – 100 = 0

The gain/loss in the month of Feb = 50 + 55 – 95 = 10

The gain/loss in the month of Mar = 50 + 60 – 115 = –5

The gain/loss in the month of April = 40 + 65 – 105 = 0

The gain/loss in the month of May = 45 + 60 – 100 = 5

The gain/loss in the month of June = 45 + 55 – 110 = –10

Thus, the maximum possible gain can be 10.


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Hence, option 2.

Group Question


Study the following graph and answer questions that follow. The x-axis denotesthe years from 1983 to 1991.

10.3 Marks

The sum of food and fertilizer production has shown a constant valuefor how many years at a stretch?

1) None of the years

2) 3

3) 4

4) 5

Solution:


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The sum of food and fertilizer production has been constant at 8.5units from 1984 to 1988 i.e.5 consecutive years and then at 8 units from1990 to 1991 i.e. 2 consecutive years.

2 years is not given in any of the options.

Thus, the sum has shown a constant value for 5 years at a stretch.

Hence, option 4.

11.3 Marks

If in 1988, the sum of the food and fertilizer production was 170 milliontons, the value of food production must have been (approximately, inmillion tons) _____.

1) 90

2) 70

3) 100

4) Insufficient data

Solution:The sum of food and fertilizer production in 1988 as per the graph is 8.5units, and food production contributes 5 units to this.

The actual total production is 170 million tons.

Thus, the food production should be

Hence, option 3.

12.3 Marks

From its apparent behaviour, the food production in year 1992 can beexpected to …

1) go up.

2) go down.

3) remain the same as in the previous year.

4) Nothing can be said.

Solution:The food production follows the pattern shown below:


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Decrease - Constant - Increase - Constant - Decrease - Constant, postwhich it repeats.

From 89 to 91, the pattern has been Increase-Constant.

Hence, as per the pattern, the food production in 1992 should go down.

Hence, option 2.

13.3 Marks

Going by the previous trends, one can say that fertilizer production hasshown an anomalous behaviour in which year?

1) 1985

2) 1984

3) 1991

4) 1989

Solution:Observe that the fertilizer production was the same in 1984 and 1985.

Similarly, the fertiliser production in 1986 is the same as the productionin 1987. The same is observed even in 1990 and 1991.

Also, the value in each set of 2 years described above is different.

Going by this logic, the fertilizer production in 1989 and 1988 shouldhave been the same and it should have been different from the 1986-87period as well as the 1990-91 period.

Hence, as per the previous trends, the anomalous behaviour is in 1989.

Hence, option 4.

14.3 Marks

A scholar observed that if the production of fertilizers in 1989 had beenthe same as that in 1988, then the total fertilizer production for all thegiven years would have been 450 million tons. Using this information,and knowing that the food production has been plotted on the samescale, one may say that the food production in 1983 was _____(approximately, in million tons).

1) 80

2) 130

3) 105


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4) Indeterminate

Solution:Based on the condition given, the fertilizer production in 1989 shouldhave been 3.5 units

The total production of fertilizer = 2.5 + 3.5 + 3.5 + 2 + 2 + 3.5 + 3.5 + 1+ 1 = 22.5 units

The actual total production of fertilizers = 450 million tons.

The production of food in 1983 = 6.5 units.

Therefore, the actual food production = (6.5 × 450)/22.5

= 130 million tonnes

Hence, option 2.

Group Question


The following table shows the number of households in a country during theperiod from 1970 to 1990. The subsequent pie-charts show the distribution ofhouseholds for the years 1970 and 1990 based on the number of children.


11 of 23 9/16/2011 10:10 AM

15.3 Marks

Which of the following statements about the households is true?

1) There were more households with children in 1970 than in1990.

2) There were more households with 3 or more children in 1970than in 1990.

3) The number of households with two children decreasedslightly from 1970 to 1990.

4) None of the above


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Solution:Statement 1:

The number of households with children in 1970 = 65% of 120 = 78million

The number of households with children in 1990 = 60% of 160 = 96million

Thus, there were more households with children in 1990 than in 1970.

Thus, statement 1 is false.

Statement 2:

The number of households with 3 or more children in 1970 = 25% of120 = 30 million

The number of households with 3 or more children in 1990 = 20% of160 = 32 million

Thus, there were more households with 3 or more children in 1990 thanin 1970.


Statement 3:

The number of households with 2 children in 1970 = 20% of 120 = 24million

The number of households with 2 children in 1990 = 18% of 160 = 28.8million

Thus, the number of households with 2 children increased from 1970 to1990.


Thus, none of the statements are true.

Hence,option 4.

16.3 Marks

The average number of children per household in 1990 was _____.

1) 1.18


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2) 1.35

3) 2.0

4) Indeterminate

Solution:This question could have been answered using weighted averages, hadthe last category of the pie chart been “3 children”.

Since the category is “more than 3 children”, the maximum number ofchildren in a family can be anything.

Hence, the average number of children per household cannot be found.

Hence, option 4.

17.3 Marks

The simple annual growth rate of the number of households from 1970to 1990 was_____.

1) 1.52%

2) 1.65%

3) 2.10%

4) 3.00%

Solution:The number of households in 1970 and 1990 is 120 and 160 millionrespectively.

Hence, option 2.

18.3 Marks

Assuming that the average number of children per household in 1970was 3, how many households were without children in 1970?

1) 24 million

2) 42 million

3) 14 million

4) Indeterminate


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Solution:The number of households that were without children is independent ofthe average number of children.

In 1970, the number of households without children is 35% of 120, i.e.42 million.

Hence, option 2.

Group Question

Answer the questions based on the following graph.

19.3 Marks

In which year is the profit per rupee of equity the highest?

1) 1991

2) 1992

3) 1993

4) 1990

Solution:


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The values of the sales, expenditure, profit and equity can be plotted asshown in the first table above.

The profit per rupee is as calculated in the second table above.

From the table, it is clear that the profit per rupee of equity was thehighest in the year 1991.

Hence, option 1.

Alternatively,

Observe that the profit is less than the equity in each given year.

Thus, the profit per rupee of equity will be highest where the profit is asclose as possible to the equity figure.

The profit in 1991 is very close to the corresponding equity figure.

Hence, the profit per rupee is highest in 1991.

Hence, option 1.

20.3 Marks

In which year is the sales per rupee of equity the highest?

1) 1990

2) 1991

3) 1992

4) 1994

Solution:Refer to the first table in the solution to the first question.


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The sales per equity for each year is shown below:

1990: 80/10 = 8

1991: 92/10 = 9.2

1992: 106/25 = 4.24

1993: 128/25 = 5.12

Thus, the sales per rupee of equity is the highest in 1991.

Hence, option 2.

21.3 Marks

The simple annual growth rate in sales was the highest between theyears:

1) 1990-91

2) 1991-92

3) 1992-93

4) 1990-92

Solution:The growth rate for sales in 1991

The growth rate for sales in 1992

The growth rate for sales in 1993

Thus, the simple annual growth rate was the highest between 1992 and1993.

Hence, option 3.

Group Question


17 of 23 9/16/2011 10:10 AM


Note: The Y-axis denotes Solubility in kg/litre of water.

22.3 Marks

Which of the following salts has the greatest solubility?

1) Potassium Chlorate at 80°C

2) Potassium Chloride at 35°C

3) Potassium Nitrate at 39°C

4) Sodium Chloride at 85°C

Solution:The solubility of each salt under the given conditions is:

Potassium Chlorate at 80°C = 0.4 kg/litre (approx)

Potassium Chloride at 35°C = 0.4 kg/litre (approx)

Potassium Nitrate at 39°C = 0.45 kg/litre (approx)


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Sodium Chloride at 85°C = 0.4 kg/litre

Thus, Potassium Nitrate at 39°C has the highest solubility.

Hence, option 3.

23.3 Marks

Approximately how many kg of Potassium Nitrate can be dissolved in 10litres of water at 30°C?

1) 0.04

2) 0.4

3) 4

4) 0.35

Solution:At 30°C, the solubility of Potassium Nitrate is approximately 0.36 kg/litreof water.

Therefore, in 10 litres of water, the amount of soluble Potassium Nitrateis 0.36 × 10 = 3.6 kg

4 kg is the closest answer.

Hence, option 3.

24.3 Marks

By what percent is the solubility of Potassium Chlorate in waterincreased as the water is heated from 30°C to 80°C?

1) 100

2) 200

3) 250

4) 150

Solution:At 30°C, solubility of Potassium Chlorate = 0.15 kg/litre (approx)

At 80°C, the solubility of Potassium Chlorate = 0.4 kg/litre

∴ The percentage increase = (0.25/0.15) × 100 = 167% (approx).

Hence, option 4.


19 of 23 9/16/2011 10:10 AM

25.3 Marks

If 1 mole of Potassium Chloride weighs 0.07456 kg, approximately, howmany moles of Potassium Chloride can be dissolved in 100 litres ofwater at 36°C?

1) 700

2) 650

3) 480

4) 540

Solution:At 36°C, the solubility of Potassium Chloride is 0.4 kg/litre (approximate)

So, in 100 litres of water, the amount of soluble Potassium Chlorideis 0.4 × 100 = 40 kg

1 mole weighs 0.07456 kg.

Hence, the required number of moles is 40/0.07456 i.e. 536.5 ≈ 540moles.

Hence, option 4.

26.3 Marks

Which of the salts has the greatest change in solubility in kg/litre ofwater between 15°C and 25°C?

1) Potassium Chlorate

2) Potassium Nitrate

3) Sodium Chlorate

4) Sodium Nitrate

Solution:This can be directly solved by observation.

The salt that has the steepest curve between 15°C and 25°C betweenthose two temperatures will have the greatest change in solubility.

It is clear from the curve that, among the options given, SodiumChlorate has the steepest curve and hence, the greatest change insolubility.

Hence, option 3.


20 of 23 9/16/2011 10:10 AM

Group Question


Refer to the pie-charts given below and answer the questions that follow.

27.3 Marks

What fraction of Ghosh Babu’s weight consists of muscular and skinprotein?

1)

2)


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3)

4) Indeterminate

Solution:15% of Ghosh Babu's body consists of protein.

Out of this, (8 + 25 = 33%) comes from skin and muscular protein.

So, the required fraction is 33% of 15% of the body weight

i.e. 0.33 × 0.15 × Body Wieght

i.e. 0.05 × Body Wieght

Thus, 5% (or 1/20) of Ghosh Babu's weight consists of muscular andskin protein. Hence, option 3.

28.3 Marks

The ratio of distribution of protein in muscle to the distribution of proteinin skin is _____.

1) 3 : 1

2) 3 : 10

3) 1 : 3

4) 3.5 : 1

Solution:The ratio of the distribution of protein in muscle to the proteindistribution in skin = 25% of total protein : 8% of total protein

i.e. 25 : 8 or 3 : 1 (approx).

Hence, option 1.

29.3 Marks

What percent of Ghosh Babu’s body weight is made up of skin?

1) 0.15

2) 10

3) 1.2


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4) Indeterminate

Solution:The occurrence of protein in the skin is given.

But the weight of the skin is not known.

Hence, the skin percent in Ghosh Babu's weight cannot be found.

Hence, option 4.

30.3 Marks

In terms of total body weight, the proportion of material other than waterand protein is closest to _____.

1)

2)

3)

4)

Solution:The percentage of material other than water and protein in the totalbody weight is 15%.

So, the fraction of such material in the total body weight

Hence, option 1.


23 of 23 9/16/2011 10:10 AM

Group Question


The bar graph shows the breakup of engineering students in different categories ofengineering colleges in India. the number of students given in the graph is in thousands.

1.3 Marks

What was the total number of engineering students in 1989-90?

1) 28500

2) 4400

3) 4200

4) 420000

Solution:

The number of students in each category of college for each year can be asshown in the table above.

Section I


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As can be seen from the table, the total number of engineering students in1989-90 is 415000.

The closest answer option is 420000.

Hence, option 4.

2.3 Marks

The growth rate of students of Government Engineering Colleges is _____compared to that of Private Engineering Colleges between 1988-89 and1989-90.

1) more

2) less

3) equal

4)

Solution:The growth rate of Government Engineering College students between theyears 1988-89 and 1989-90 is

The growth rate of Private Engineering College students between the years1988-89 and 1989-90 is

Thus, the two growth rates are equal.

Hence, option 3.

3.3 Marks

The total number of Engineering Students in 1991-92, assuming a 10%reduction in the number over the previous year, is _____.

1) 5700

2) 57000

3) 44800

4) None of these

Solution:The total number of engineering students in 1990-91 is 560000.


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If there is a decrease of 10% in the next year, then the total number ofengineering students in the year 1991-92

= 0.9 × 560000

= 504000

Hence, option 4.

4.3 Marks

In 1990-91, what percent of Engineering Students were studying at the IITs?

1) 16

2) 15

3) 14

4) 12

Solution:The percentage of engineering students that were studying in the IITs in1990-91

Hence, option 3.

Group Question


Refer to the following pie chart and answer the questions that follow.


3 of 18 9/16/2011 10:12 AM

5.3 Marks

The operation profit in 1991-92 increased over that in 1990-91 by _____.


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1) 23%

2) 22%

3) 25%

4) 24%

Solution:The percentage increase in the operation profit in 1991-92 over 1990-91

Hence, option 1.

6.3 Marks

The interest burden in 1991-92 was higher than that in 1990-91 by _____.

1) 50%

2) Rs. 25 lakhs

3) 90%

4) More than one of the above

Solution:The interest in the year 1990-91 = 30% of 130 = Rs. 39 lakhs.

The interest in the year 1991-92 = 40% of 160 = Rs. 64 lakhs.

The difference in the interests = 64 – 39 = Rs. 25 lakhs.

Thus, the interest burden was higher by Rs. 25 lakhs.

This value when expressed as a percentage is (25/39) × 100 which is more than50%.

Hence, option 2.

7.3 Marks

If, on an average, a 20% rate of interest was charged on borrowed funds, thenthe total borrowed funds used by this company in the given two years amountedto _____.

1) Rs. 221 lakhs

2) Rs. 195 lakhs

3) Rs. 368 lakhs

4) Rs. 515 lakhs


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Solution:The interest in the year 1990-91 = 30% of 130 = Rs. 39 lakhs.

The interest in the year 1991-92 = 40% of 160 = Rs. 64 lakhs.

Thus, the total interest amount paid = 39 + 64 = Rs. 103 lakhs.

It is given that 103 lakhs is 20% of the total borrowed funds.

Hence, option 4.

8.3 Marks

The retained profit in 1991-92, as compared to that in 1990-91 was _____.

1) higher by 2.5%

2) higher by 1.5%

3) lower by 2.5%

4) lower by 1.5%

Solution:

Hence, option 4.

9.3 Marks

The equity base of these companies remained unchanged. Then the totaldividend earning (lakh rupees) by the share holders in 1991-92 was _____.

1) Rs. 104 lakhs

2) Rs. 9 lakhs

3) Rs. 12.8 lakhs

4) Rs. 15.6 lakhs

Solution:The total dividend earning by the share holders in 1991-92 is 8% of 160 lakhs,i.e. 12.8 lakhs.


6 of 18 9/16/2011 10:12 AM

Hence, option 3.

Group Question


The bar graph below shows the revenue obtained by a publishing house by selling books,magazines and journals (in Rs. lakhs).

10.3 Marks

Which year shows the highest change in revenue obtained from journals?

1) 1989

2) 1990

3) 1991

4) 1992

Solution:

The revenue obtained from each type of publication in each year is as shown inthe table above.

The change in revenue from journals for each year is +1, −2 and −1.

Thus, the highest change in revenue obtained from journals is in 1991.

Hence, option 3.


7 of 18 9/16/2011 10:12 AM

11.3 Marks

In 1992, what percent of the total revenue came from books?

1) 45

2) 55

3) 35

4) 25

Solution:The total revenue in 1992 is Rs. 173 lakhs and the revenue from books is Rs. 79lakhs.

Hence, the required percentage

Hence, option 1.

12.3 Marks

The number of years in which there was an increase in revenue from at leasttwo categories is _____.

1) 1

2) 2

3) 3

4) 4

Solution:For each year, the number of categories from which there was an increase inrevenue is:

1990: 3 (All categories)

1991: 2 (magazines and books)

1992: 1 (magazines)

Thus, in two different years, there was an increase in revenue from at least twocategories.

Hence, option 2.

13.3 Marks

If 1993 were to show the same percentage growth as 1992 over 1991, therevenue in 1993 must be _____.

1) Rs. 194 lakhs

2) Rs. 187 lakhs


8 of 18 9/16/2011 10:12 AM

3) Rs. 172 lakhs

4) Rs. 177 lakhs

Solution:The revenue in 1991 and 1992 is Rs. 169 lakhs and Rs. 173 lakhs respectivelyi.e. a growth of Rs. 4 lakhs.

The percentage increase in 1992 over 1991

1993 has to show the same percentage growth in revenue.

So, the total revenue in 1993 = 1.0231 × 173 = Rs. 177 lakhs

Hence, option 4.

14.3 Marks

The growth in total revenue from 1989 to 1992 is _____.

1) 21%

2) 28%

3) 15%

4) 11%

Solution:The total revenue in the years 1989 and 1992 is Rs. 150 lakhs and Rs. 173lakhs respectively.

So, the required percentage growth

Hence, option 3.

Group Question


A manufacturer can choose from any of the three types of tests available for checking thequality of his product. The graph that follows gives the relative costs for each of thesetests for a given percentage of defective pieces (p).


9 of 18 9/16/2011 10:12 AM

15.3 Marks

If p is equal to 0.2, then which test will be feasible?

1) Either 1 or 2

2) 2 only

3) 3 only

4) Either 2 or 3

Solution:From the graph, it can be seen that for p = 0.2, the relative cost is the same fortest 2 and 3 and is the least.

Hence, either one of test 2 or 3 is feasible.

Hence, option 4.

16.3 Marks

When will Test-3 be feasible?

1) p > 0.2

2) 0.1 < p < 0.2

3) 0.05 < p < 0.2

4) p < 0.05

Solution:From the graph, it is clear that test 3 will be feasible only when p > 0.2.

Hence, option 1.

17.3 Marks

Adopting Test-2 will be feasible if the percentage of defective pieces ‘p’ lies inthe range :


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1) 0.10 to 0.20

2) 0.20 to 0.30

3) 0.05 to 0.20

4) 0.00 to 0.05

Solution:From the graph, observe that test 2 is the cheapest in the range between p =0.05 and p = 0.2

Thus, test 2 is feasible when 0.05 < p < 0.2.

Hence, option 3.

18.3 Marks

When is Test-1 feasible?

1) p < 0.05

2) 0.0 < p < 0.2

3) 0.1 < p < 0.2

4) 0.05 to 0.2

Solution:From the graph, observe that test 1 is feasible only when p < 0.05.

Hence, option 1.

19.3 Marks

If p < 0.2, then the best alternative will be _____.

1) Conduct Test-2

2) Conduct Test-3

3) Conduct Test-1

4) Do not conduct Test-3

Solution:If p < 0.2, then either of test 1 or test 2 proves to be cheaper.

Hence, if p < 0.2, it is best not to conduct test 3.

Hence, option 4.

Group Question



11 of 18 9/16/2011 10:12 AM

All figures are in Rs. lakhs

20.3 Marks

The average revenue collected in the given period is approximately______.

1) Rs. 164 lakhs

2) Rs. 168 lakhs

3) Rs. 171 lakhs

4) Rs. 175 lakhs

Solution:

The revenue, expenditure and profit for each year can be plotted in a single tableas shown above.

The total revenue in the given period = 120 + 135 + 145 + 165 + 185 + 200 + 220= Rs. 1170 lakhs

Hence, option 2.

21.3 Marks

The total expenditure for the given period forms what percent of the revenuesduring the same period?

1) 75%

2) 67%

3) 62%


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4) 83%

Solution:From the solution to the first question, the total revenue for the given period = Rs.1170 lakhs.

The total expenditure for the given period = 100 + 110 + 115 + 125 + 135 + 140 +150 = Rs. 875 lakhs

Hence, option 1.

22.3 Marks

Which year showed the greatest percentage increase in profit as compared to theprevious year?

1) 1993

2) 1994

3) 1990

4) 1992

Solution:The percentage increase in profit in the years 1990, 1992, 1993 and 1994 is

1990: (5/20) × 100 = 25%

1992: (10/30) × 100 = 33.33%

1993: (10/40) × 100 = 25%

1994: (10/50) × 100 = 20%

Thus, 1992 showed the greatest percentage increase.

Hence, option 4.

23.3 Marks

In which year was the growth in expenditure as compared to the previous year themaximum?

1) 1993

2) 1995

3) 1990

4) 1992


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Solution:Consider the years mentioned in the answer options.

The absolute growth in expenditure in each of these years is Rs. 10 lakhs. In such a case, the growth in expenditure is maximum for the fraction that has thelowest denominator i.e. the inital year which has the least expenditure.

The least initial value of expenditure is in 1989 (Rs. 100 lakhs) and sothe greatest percentage growth in expenditure is 10%.

Hence, option 3.

24.3 Marks

If the profit in 1996 shows the annual rate of growth that it had shown in 1995 overthe previous year, then what approximately what will be the profit in 1996?

1) Rs. 72 lakhs

2) Rs. 82 lakhs

3) Rs. 93 lakhs

4) Rs. 78 lakhs

Solution:

If the profit in 1996 shows the same growth rate, the profit in 1996 = 1.167 × 70 = Rs.81.69 lakhs

Hence, option 2.

Group Question



14 of 18 9/16/2011 10:12 AM

25.3 Marks

In which year was the increase in raw material the maximum?

1) 1992

2) 1993

3) 1994

4) 1995

Solution:

The actual values under each head are shown in the table above.

The amount of raw-material in the years 1991, 1992, 1993, 1994 and 1995 isrespectively 60, 50, 65, 75 and 80 units.

Thus, the maximum increase in the amount of raw material is in 1993. Hence, option 2.

26.3 Marks

For which period was the change in profit the maximum?

1) 1991-92

2) 1992-93

3) 1993-94

4) 1994-95


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Solution:The change in profit is the maximum in the period 1993 to 1994, because theprofit in 1993 was 20 units which reduced to –30 units in 1994.

Thus, the profit changed by 20 − (−30) = 50 units.

Hence, option 3.

27.3 Marks

Which component of the cost of production has remained more or less constantover the period?

1) Interest

2) Overheads

3) Wages

4) Raw material

Solution:This question can be solved directly by observation.

From the graph, observe that only the interest component remains more or lessconstant throughout the given period.

Hence, option 1.

28.3 Marks

In which year were the overheads, as a percentage of the raw material, themaximum?

1) 1995

2) 1994

3) 1992

4) 1993

Solution:The overheads, as a percentage of the raw material, for the years given in theoptions is :

1992 : (20/50) × 100 = 40%

1993 : (15/65) × 100 = 23.07%

1994 : (25/75) × 100 = 33.33%

1995 : (20/80) × 100 = 25%

Thus, the overheads as a percentage of the raw material were the highest in1992.


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Hence, option 3.

29.3 Marks

Over the period, the profits formed what approximate percent of the total cost?

1) 3%

2) 5%

3) 8%

4) 11%

Solution:From 1991 to 1995, the total amount spent on raw-materials, wages, overheads,interest is respectively 330, 290, 90 and 260 units.

Thus, the total cost in the given period is 330 + 290 + 90 + 260 = 970 units. In the same period, the total profit is 45 units.

Thus, the required percentage is (45/970) × 100 = 4.64% ≈ 5%.

Hence, option 2.

30.3 Marks

If the interest component is not included in the total cost calculation, which yearwould show the maximum profit per unit cost?

1) 1991

2) 1992

3) 1993

4) 1995

Solution:Excluding the interest component, the total cost in 1991, 1992, 1993, 1994 and1995 is respectively 115, 125, 140, 165 and 165 units.

The profit in 1991, 1992, 1993, 1994 and 1995 is respectively 15, 25, 20, –30and 15 units.

Start with the simplest calculation:

The profit in 1992 is (25/125) × 100 i.e. 20% or 1/5th.

For all the other years, the same ratio is less than 1/5.

Hence, the maximum profit is seen in 1992.

Hence, option 2.


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18 of 18 9/16/2011 10:12 AM

Group Question


1.3 Marks

What is the average value of the contract secured during the years shown in thediagram?

1) Rs. 103.48 crores

2) Rs. 105 crores

3) Rs. 100 crores

4) Rs.125.2 crores

Solution:

Hence, option 1.

2.3 Marks

Compared to the performance in 1985 (i.e. taking it as the base), what can yousay about the performances in the years ’84, ’85, ’86, ’87, ’88 respectively, inpercentage terms?

1) 150, 100, 211, 216, 97

2) 100, 67, 141,144, 65

3) 150, 100, 200, 215, 100

4) 120, 100, 220, 230, 68

Section I


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Solution:If you consider the performance in the year 1985 as the base, the performancefor the years 1984, 85, 86, 87 and 88 is respectively

Thus, the performance for the years 1984, 85, 86, 87 and 88 in percentageterms is respectively 150, 100, 211, 216 and 97.

Hence, option 1.

Alternatively,

This question can also be solved by considering the answer options.

Consider option 2:

The values given for each year in option 2 indicate the actual performance forthese 5 years. The actual values are unrelated in the sense that they are notcalculated using the 1985 value as a base. When the performance in the year1985 is taken as a base, it implies that given the current performance in anyyear, what would have been the performance in that year had the performancein the year 1985 been 100. Therefore, the values given in option 2 cannot bethe performance figures considering 1985 as the base year.


Consider option 4.

Since 1985 is the base year, the performance in 1985 is taken to be 100.

Observe that the actual performance in 1988 is marginally less than the actualperformance in 1985 (approximately 3% less).

However, as per the values given in option 4, the performance in 1988 is 2/3 ofthe performance in 1985 (i.e. approximately 32% less).

Therefore, the values given in option 4 cannot be the required performancefigures.


Consider option 3.

As per the values in option 3, the performance in 1986 is exactly double theperformance in 1985.


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However, the actual performance is 141 in 1986 and 67 in 1985 i.e. morethan double.

Therefore, the values given in option 3 cannot be the required performancefigures.


Hence, option 1.

3.3 Marks

In which year is the highest percentage decline seen in the value of thecontracts secured compared to the preceding year?

1) 1985

2) 1988

3) 1984

4) 1986

Solution:Since the question mentions percentage decline and not percentage change,all the years mentioned need not be considered.

Observe that, with respect to the previous year, the value of the contractssecured decreases only in 1985 and in 1988.

Therefore, they can be the only possible options.


The percentage decline in 1985 = [(100.5 − 67)/100.5] × 100

= 33.33%

The percentage decline in 1988 = [(143.9 − 65)/143.9] × 100

= 55% (approximately)

Thus, the highest percentage decline is in 1988.

Hence, option 2.

4.3 Marks

Each question is followed by two statements, A and B. Select the correct optionbased on the following instructions:

Mark (1) if the question can be answered by one of the statements, but not by theother.Mark (2) if the question can be answered by using either statement, independentlyof the other.


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Mark (3) if the question can be answered by using both statements together, butnot by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

What is the distance x between two cities A and B (in km)? x is an integer.

B. x ≤ 10 km

1) 1

2) 2

3) 3

4) 4

Solution:Using Statement A alone:

Thus, a unique value of x cannot be found.

Thus, the question cannot be answered using statement A alone.

Using Statement B alone:

Assuming that A and B are two different cities, x can take any value from 1 to 9.


Thus, the question cannot be answered using statement B alone.

Using both the statements together:

When both the statements are combined, the only valid value of x is x = 4.

Thus, the distance between the two cities is 4 km.

Thus, the question can be answered using both the statements together but not byusing either statement alone.

Hence, option 3.

Group Question



4 of 23 9/16/2011 9:55 AM

Prakash has to decide whether or not to test a batch of 1000 widgets before sendingthem to the buyer. In case he decides to test, he has two options: (1) Use test I; (2) Usetest II. Test I costs Rs. 2 per widget. However, the test is not perfect. It sends 20% ofthe bad widgets to the buyer as good. Test II costs Rs. 3 per widget. It identifies all thebad widgets. A defective widget identified before sending can be corrected at a cost ofRs. 25 per widget. All defective widgets are identified at the buyer’s end and a penaltyof Rs. 50 per defective widget has to be paid by Prakash.

5.3 Marks

Prakash should not test if the number of bad widgets in the lot …

1) is less than 100.

2) is more than 200.

3) is between 120 and 190.

4) Indeterminate

Solution:The total number of widgets = 1000

Let the total number of bad widgets be x.

The charges incurred under test I:

Testing charges = 1000 × 2 = Rs. 2,000

Penalty = 0.2x × 50 = Rs. 10x

Repair charges = 0.8x × 25 = Rs. 20x

∴ Total cost incurred under test I = 2000 + 30x

The charges incurred under test II

Testing charges = 1000 × 3 = Rs. 3,000

Repair charges = Rs. 25x

∴ Total cost incurred under test II = 3000 + 25x

When there is no test conducted:

If there is no test, then the only cost incurred is the penalty at the buyer'send.

The penalty charged at buyer’s end = x × 50 = Rs. 50x

It is beneficial not to conduct a test when the cost without the test is less thanthe cost with the test.

Consider Test I:


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i.e. 50x < 2000 + 30x

∴ 20x < 2000

∴ x < 100

Thus, when the number of bad widgets is less than 100, it is better to notconduct a test than to conduct test I.

Consider Test II:

i.e. 50x < 3000 + 25x

∴ 25x < 3000

∴ x < 120

Thus, when the number of bad widgets is less than 120, it is better to notconduct a test than to conduct test II. Thus, in any case, when the number of bad widgets is less than 100, it isbetter not to conduct a test.

Hence, option 1.

6.3 Marks

If there are 120 defective widgets in the lot, Prakash …

1) should either use Test I or not test at all.

2) should either use Test II or not test at all.

3) should use either Test I or Test II.

4) should use Test I only.

Solution:The total number of bad widgets i.e. x = 120

Referring to the solution in the first question,

Total cost incurred under test I = 2000 + 30x = 2000 + (30 × 120) = Rs. 5,600

Total cost incurred under test II = 3000 + 25x = 3000 + (25 × 120) = Rs. 6,000

If there is no test, then the penalty charged at buyer’s end = 50 × 120 = Rs.6,000

Since test I is the cheapest, Prakash should use test I only.

Hence, option 4.


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7.3 Marks

If the number of defective widgets in the lot is between 200 and 400, Prakash…

1) may use Test I or Test II.

2) should use Test I only.

3) should use Test II only.

4) cannot decide.

Solution:Let the total number of bad widgets be x.

Find the number of defective widgets for which one test is cheaper than theother.

Total cost of Test I: 2000 + 30x

Total cost of Test II: 3000 + 25x

First find the value of x for which test II is cheaper than test I.

∴ 2000 + 30x > 3000 + 25x

∴ 5x > 1000

∴ x > 200

Thus, for any number of defective widgets greater than 200, it would becheaper to go for test II than test I.

Now find the value of x for which test I is cheaper than test II.

∴ 2000 + 30x < 3000 + 25x

∴ 5x < 1000

∴ x < 200

Thus, for any number of defective widgets less than 200, it would be cheaperto go for test I than test II.

Hence, option 3.

8.3 Marks

If Prakash is told that the lot has 160 defective widgets, he should …

1) use Test I only.

2) use Test II only.


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3) do no testing.

4) either use Test I or do no test.





Thus, test I is the least expensive and so Prakash should go for test I.

Hence, option 1.

9.3 Marks

If there are 200 defective widgets in the lot, Prakash …

1) may use either Test I or Test II.

2) should use Test I or not use any test.

3) should use Test II or not use any test.

4) cannot decide.





Since the amount spent for test I or test II is the same, Prakash canuse either test I or test II.

Hence, option 1.

10.3 Marks

In a six-node network, two nodes are connected to all the other nodes. Of theremaining four, each is connected to four nodes. What is the total number of linksin the network?

1) 13


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2) 15

3) 17

4) 26

Solution:Let the 6 nodes be A, B, C, D, E and F.

2 nodes are connected to all the other nodes.

Let these 2 nodes be A and B.

Thus A is connected to C, D, E and F, forming 4 links i.e. AC, AD, AE and AF.

Similarly, B also forms four links through the nodes C, D, E and F i.e. BC, BD, BEand BF.

Finally, A and B are connected to each other thereby forming a link AB (which isthe same as BA).

Thus, 4 + 4 + 1 i.e. 9 links are formed.

Now, each of the four nodes i.e. C, D, E and F is connected to four nodes.

For each of these nodes, two connections are with A and B each.

Thus, each node is connected to two other nodes.

Assume that C is connected to D and E, thus forming two links CD and CE.

Now, D is already connected to A, B and C (AD, BD and CD).

Thus, D can only be connected to one more node, say F, forming the link DF.

Similarly, E can now only be connected only to F, forming EF.

Finally, all the four links for F have already been formed i.e. AF, BF, EF and DF.

Thus, no new link for F can be formed.

Thus, the number of new links is 4 (CD, CE, DF and EF)

∴ The total number of links = 9 + 4 = 13 links

Hence, option 1.

Group Question



9 of 23 9/16/2011 9:55 AM

A company produces five types of shirts - A, B, C, D, E - using cloth of three qualities -High, Medium and Low as well as using dyes of three qualities - High, Medium andLow. One shirt requires exactly 1.5 m of cloth. The following table gives respectively:

The number of shirts (of each category) produced, in thousands.1.The percentage distribution of cloth quality in each type of shirt.2.The percentage distribution of dye quality in each type of shirt.3.

11.3 Marks

What is the total requirement of cloth?

1) 150000 m

2) 200000 m

3) 225000 m

4) 250000 m

Solution:Total requirement of cloth = Total number of shirts × Cloth required per shirt

The total number of shirts produced (in thousands) = 20 + 30 + 30 + 10 + 10= 100

Amount of cloth required per shirt = 1.5 m

∴ Total requirement of cloth = 100000 × 1.5 = 150000 m.

Hence, option 1.

12.3 Marks

How many metres of low-quality cloth are consumed?

1) 22500 m

2) 46500 m

3) 60000 m

4) 40000 m

Solution:No Type A shirt uses low quality cloth.


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The total cloth required for Type B shirts is 30000 × 1.5 = 45000 m.

30% of this cloth is of low quality.

Hence, first find the total cloth required for each type of shirt.

The total cloth required for Type C, D and E shirts is 45000 m, 15000 m and15000 m respectively.

Type C, D and E shirts use 30%, 40% and 90% low quality cloth respectively.

∴ Total amount of low quality cloth required = (0.3 × 45000) + (0.3 ×45000) + (0.4 × 15000) + (0.9 × 15000)

= 13500 + 13500 + 6000 + 13500

= 46500 m.

Thus, 46500 metres of low quality cloth are consumed.

Hence, option 2.

13.3 Marks

How many metres of high quality cloth are consumed by Type A shirts?

1) 8000 m

2) 112000 m

3) 24000 m

4) 30000 m

Solution:The number of Type A shirts made = 20000

∴ The total amount of cloth required for Type A shirts = 20000 × 1.5 = 30000

Each type A shirt uses 80% high quality cloth.

∴ The total amount of high quality cloth required for Type A shirts = 0.8 ×30000 = 24000 m.

Thus, 24000 metres of high quality cloth are consumed by Type A shirts.

Hence, option 3.

14.3 Marks

What is the ratio of the three qualities of dyes in high-quality cloth?

1) 2 : 3 : 5


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2) 1 : 2 : 5

3) 7 : 9 : 10

4) Indeterminate

Solution:The relationship between the proportion of dyes and the proportion of acertain quality of cloth is not known.

One cannot assume that the proportion of dyes applicable to a certain shirttype is also applicable to the cloth of different quality levels within the sameshirt type.

Hence, even though the total amount of cloth required and the proportion ofdyes used in each type of shirt can be found, the proportion of dyes in thecloth of a certain quality within a specific shirt type cannot be calculated.

Hence, the required ratio cannot be found.

Hence, option 4.

15.3 Marks

What is the ratio of low-quality dye used for Type C shirts to low-qualitydye used for Type D shirts?

1) 3 : 2

2) 2 : 1

3) 1 : 2

4) 2 : 3

Solution:Number of Type C shirts made = 30000

Each Type C shirt uses 40% low quality dye.

∴ Amount of low-quality dye required for Type C shirts = 0.4 × 30000 =12000 units

Number of Type D shirts made = 10000

Each Type D shirt uses 60% low quality dye.

∴ Amount of low-quality dye required for Type D shirts = 0.6 × 10000 = 6000units

Thus, the required ratio = 12000 : 6000 = 2 : 1


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Hence, option 2.

16.3 Marks


Mark (1) if the question can be answered by one of the statements, but not by theother.Mark (2) if the question can be answered by using either statement, independentlyof the other.Mark (3) if the question can be answered by using both statements together, butnot by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

What is the ratio of the volume of the given right circular cone to the one obtainedfrom it?

The smaller cone is obtained by passing a plane parallel to the base and dividing theoriginal height in the ratio 1 : 2.

A.

The height and the base of the new cone are one-third those of the original cone.B.

1) 1

2) 2

3) 3

4) 4

Solution:Using statement A alone:

Since the smaller cone is obtained by cutting the original cone in a plane parallelto the base , the height, circumference as well as radius of the new cone areproportional to the old cone.

∴ Height of new cone : Height of old cone = Radius of new cone : Radius of oldcone = 1 : 3

∴ Volume of new cone : Volume of old cone = (rnew : rold)3 = (1 : 3)3 = 1 : 27

Thus, the question can be answered using statement A alone.

Using statement B alone:

Since the base of the new cone is one-third of the original cone, the radius of thenew cone is also one-third of the original cone.

∴ Volume of new cone : Volume of old cone = (rnew : rold)3 = (1 : 3)3 = 1 : 27

Thus, the question can be answered using statement B alone.


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Thus, the question can be answered using any one statement independently. Hence, option 2.

Group Question


The questions that follow are based on the price fluctuations of four commodities -Arhar, Pepper, Sugar and Gold - during the period February 1999 - July 1999 as shownin the figures below. In the graphs, A2 implies the second week of April, JN2 implies thesecond week of June and so on.


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17.3 Marks

“Price change” of a commodity is defined as the absolute difference inthe final and initial price of that commodity expressed as a percentage of thefirst price of that commodity. Which commodity shows the highest pricechange?

1) Arhar

2) Pepper

3) Sugar

4) Gold

Solution:For Arhar: Initial price = Rs 1,700, Final Price = Rs 2,200.

∴ Price Change = [(2200 − 1700)/1700] × 100 = 500/17 ≈ 30%

For Pepper: Initial price = Rs 18,500, Final Price = Rs 19,400.

∴ Price Change = [(19400 − 18500)/18500] × 100 = 900/185 ≈ 5%


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For Sugar: Initial price = Rs 1,435, Final Price = Rs 1,410.

∴ Absolute difference in the final and initial price of sugar = Rs. 25

∴ Price Change = [25/1435] × 100 = 500/287 i.e. < 2%

For Gold: Initial price = Rs 4,250, Final Price = Rs 3,725.

∴ Absolute difference in the final and initial price of sugar = Rs. 525

∴ Price Change = [525/4250] × 100 = 210/17 ≈ 12.3%

Thus, Arhar shows the highest price change.

Hence, option 1.

18.3 Marks

Price volatility (PV) of a commodity is defined as follows:

What is the commodity with the lowest price volatility?

1) Arhar

2) Pepper

3) Sugar

4) Gold

Solution:

Thus, it can be seen that Sugar has the lowest PV.

Hence, option 3.

19.3 Marks

Mr. X, a funds manager with an investment company invested 25% of hisfunds in each of the four commodities at the beginning of the period. He sold


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the commodities at the end of the period. His investments in the commoditiesresulted in:

1) 17% profit

2) 5.5% loss

3) No profit, no loss

4) 4.3% profit

Solution:Let the profit/loss percentage on Arhar, Pepper, Sugar and Gold be P1, P2,P3 and P4 respectively.

If the person has invested W1, W2, W3 and W4 proportion of his investmentin Arhar, Pepper, Sugar and Gold respectively, the total profit/loss is nothingbut the weighted average of the individual profit/loss.

∴ Total Profit/Loss = (P1W1 + P2W2 + P3W3 + P4W4)/(W1 + W2 + W3 + W4)

Since Mr. X invested 25% of hits total investments in each of the fourcommodities, W1 = W2 = W3 = W4 = 0.25

∴ Total Profit/Loss = 0.25 × (P1 + P2 + P3 + P4) = (P1 + P2 + P3 + P4)/4

For Arhar: P1 = [(2200 − 1700)/1700] × 100 = 29.4 % profit

For Pepper: P2 = [(19400 − 18500)/18500] × 100 = 4.9 % profit

For Sugar: P3 = [(1410 − 1435)/1435] × 100 = 1.7 % loss = −1.7 % profit

For Gold: P4 = [(3720 − 4250)/4250] × 100 = 12.5 % loss = −12.5 % profit ∴ Total Profit/Loss = (29.4 + 4.9 − 1.7 − 12.5)/4 = 20.1%/4 = 5%(approximately)

Since the closest answer is given in option 4, that is marked as the correctanswer.

Hence, option 4.

20.3 Marks

The price volatility of the commodity with the highest PV during theFebruary-July period is approximately equal to:

1) 3%

2) 40%

3) 20%


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4) 12%

Solution:Arhar had the highest PV during the Februrary-July period and the value ofthis PV was approximately 40%.

Hence, option 2.

Group Question


The primitive tribes on the island of Lexicophobos have recently developed a languagefor themselves which has a very limited vocabulary. In fact, the words can be classifiedinto only three types: the “Bingoes”, the “Cingoes” and the “Dingoes”.

The Bingoes type of words are: Grumbs, Harrumphs, IhavitooThe Cingoes type of words are: Ihavitoo, Jingongo, KoolodoThe Dingoes type of words are: Lovitoo, Metoo, Nana

They have also devised some rules of grammar:

Every sentence must have only five words.I.Every sentence must have two Bingoes, one Cingo and two Dingoes.II.If Grumbs is used in a sentence, Ihavitoo must also be used and vice versa.III.Koolodo can be used in a sentence only if Lovitoo is used.IV.

21.3 Marks

Which choice of words in a sentence is not possible, if no rules of grammarare to be violated?

1) Grumbs and Harrumphs as the Bingoes and Ihavitoo as the Cingo.

2) Harrumphs and Ihavitoo as the Bingoes.

3) Grumbs and Ihavitoo as the Bingoes and Lovitoo and Nana as theDingoes.

4) Metoo and Nana as the Dingoes.

Solution:Consider Option 1:

According to condition III. Grumbs and Ihavitoo have to be part of the samesentence.

Ihavitoo is a Bingo as well as a Cingo.

The condition does not specify whether Ihavitoo is to be used as a Bingo oras a Cingo.


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Thus, if Grumbs and Harrumphs are used as Bingoes and Ihavitoo is used asa Cingo, no condition is violated.

Thus, the choice of words in option 1 is possible.


Consider Option 3:

Using Grumbs and Ihavitoo as the Bingoes and Lovitoo and Nana as theDingoes ensures that the relevant conditions (II and III) are satisfied.



Consider Option 4:

The only relevant condition here is that there have to be 2 Dingoes.

Since Metoo and Nana are not connected to any other word, they can beused together.


Hence, option 4 can be eliminated. Consider Option 2:

Ihavitoo and Grumps have to be together in a sentence.

However, if Harrumphs and Ihavitoo as the Bingoes are part of the samesentence, the number of slots available for Bingoes is exhausted. Thus,Grumps cannot be used in the same sentence.

This violates condition III.

The only way Ihavitoo, Grumps and Harrumphs can be used in the samesentence is if Ihavitoo is used as a Cingo while the other two are used asBingoes.

Thus, the choice of words in option 2 is not possible.

Hence, option 2.

22.3 Marks

If Grumbs and Harrumphs are the Bingoes in a sentence, and no rule ofgrammar is violated, which of the following is/are necessarily true?

Ihavitoo is the Cingo.I.Lovitoo is the Dingo.II.


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Either Lovitoo or Metoo must be one of - or both - the Dingoes.III.

1) I only

2) II only

3) III only

4) I and III only

Solution:Consider Statement I:

Grumbs and Ihavitoo have to be part of the same sentence.

Since Grumbs and Harrumphs are already used as Bingoes, Ihavitoo cannotbe used as a Bingo.

Therefore, Ihavitoo has to be used as a Cingo.

Since, only one Cingo is required, Ihavitoo is the only Cingo.

Thus, Statement I is definitely true.


Consider Statement II:

With the given combination, it is possible that the Dingoes are Metoo andNana. This does not violate any condition.

On the other hand, having Lovitoo as a Dingo also does not violate anycondition.

Thus, Statement II may or may not be true.

Consider Statement III:

Any two of the the three possible Dingoes can be chosen without violatingany given condition.

Hence, statement III is true.

Thus, statements I and III are true.

Hence, option 4.

23.3 Marks

Which of the following is a valid sentence if no grammar rule is to beviolated?


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1) Grumbs Harrumphs Ihavitoo Lovitoo Metoo.

2) Grumbs Harrumphs Ihavitoo Jingongo Lovitoo.

3) Harrumphs Ihavitoo Jingongo Lovitoo Metoo.

4) Grumbs Ihavitoo Koolodo Metoo Nana.

Solution:According to condition II, there should be exactly one Cingo in eachsentence.

Consider option 2:

Since Grumbs and Harrumphs are Bingoes, Ihavitoo has been used as aCingo.

At the same time, Jingongo is also a Cingo.

Since there cannot be two Cingoes in a single sentence, this combination isinvalid.


Consider option 3:

According to condition III, Ihavitoo and Grumbs have to be part of the samesentence.

Since Ihavitoo is part of option 3 and Grumbs is not, this is not a validcombination.


Consider option 4:

According to condition IV, Koolodo can be used in a sentence only if Lovitoois used.

Since Koolodo is used in option 4 but Lovitoo is not, this is not a validcombination.


Consider option 1:

The sentence satisfies all the given conditions.

Hence, it is a valid combination.


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Hence, option 1.

24.3 Marks

If in a sentence Grumps is the Bingo and no rule of grammar is violated,which of the following cannot be true?

1) Harrumphs must be a Bingo.

2) Ihavitoo must be a Bingo.

3) Lovitoo may be used.

4) All three Bingoes are used.

Solution:If Grumps is the Bingo, any one of Harrumphs or Ihavitoo can be the otherBingo.

If Ihavitoo is the other Bingo, one from Jingongo or Koolodo can be theCingo.

If Harrumphs is the other Bingo, Ihavitoo has to be the Cingo.

In either case, a valid combination can be formed.

Hence, Ihavitoo need not necessarily be a Bingo.

Hence, the statement in option 2 is not true.

Hence, option 2.

25.3 Marks


Mark (1) if the question can be answered by one of the statements, but not by theother.Mark (2) if the question can be answered by using either statement, independentlyof the other.Mark (3) if the question can be answered by using both statements together, butnot by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

What is the average weight of the 3 new members who have recently beenincluded into the team?

The average weight of the team increases by 20 kg.A.The 3 new members substitute three other members whose weights are 64 kg, 75 kg and 66kg.

B.

1) 1

2) 2


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3) 3

4) 4


It has not been mentioned whether these new members have been added to theteam or have replaced a few members. Depending on the case, the calculations foraverage changes.

Thus, the average weight cannot be found.



The 3 new members replace 3 other members whose total weight is 205 kg.

However, the number of members in the team as well as the impact of thereplacement on the average weight is not known.

Thus, the average weight cannot be found.



Since these new members replace three old members, the total number ofmembers remains the same.

Since the number of members in the team is not known, the average weight cannotbe found.

Thus, the question cannot be answered on the basis of the two statements.

Hence, option 4.


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1.3 Marks

Each question is followed by two statements, A and B. Select the correctoption based on the following instructions:

Mark (1) if the question can be answered by one of the statements, but not bythe other.Mark (2) if the question can be answered by usingeither statement, independently of the other.Mark (3) if the question can be answered by using both statements together,but not by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

A and B work at digging a ditch alternately for a day each. If A can dig a ditchin ‘a ’ days and B can dig it in ‘b ’ days, will the work get done faster if Abegins the work?

A.

b > aB.

1) 1

2) 2

3) 3

4) 4


A can dig ‘1/a’ part of the ditch in one day while B can dig ‘1/b’ part of theditch in one day.

Irrespective of who starts first, the total work done at the end of 2 days isalways [(1/a) + (1/b)]

Similarly, if the total number of days taken to complete the work is an evennumber, the total amount of work done is 2n × [(1/a) + (1/b)]

Thus, if the total amount of work done is of the form given above, the totaltime taken to complete the work is the same irrespective of who starts.

Had the work been completed in say, 3 days, the total amount of work donewould have been [(2/a) + (1/b)] or [(1/a) + (2/b)]

Thus, in general, had the work taken an odd number of days for completion,

Section I


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the total amount of work would have been [(2n/a) + ((2n − 1)/b)] or [((2n −1)/a) + (2n/b)]

Since the total amount of work done, as per the given equation, falls in thefirst category, the work gets completed in an even number of days.

Since the work gets completed in an even number of days, it takes the sametime irrespective of who starts.



Since b > a, B does less work per day compared to A.

Assume that A can do 5 units of work per day while B can do 2 units of workper day.

Also, assume that the total work consists of 18 units.

If A starts first, the work gets completed in 5 days.

If B starts first, the work gets completed in 6 days.

Thus, the work gets completed faster if A starts.

Now, assume that the total work consists of 20 units.

If A starts first, the work gets completed in 6 days.

If B starts first, the work gets completed in 6 days.

Now, the work does not get completed faster if A starts.

Thus, the work may or may not get completed faster if A starts, depending onthe amount of work.


Thus, the question can be answered by one of the statements but not by theother.

Hence, option 1.

Group Question


A, B, C and D are to be seated in a row. However, C and D cannot be seated


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together. Also, B cannot be at the third place.

2.3 Marks

Which of the following must be definitely false?

1) A is at the first place.

2) A is at the second place.

3) A is at the third place.

4) A is at the fourth place.

Solution:The given data does not mention whether the third place is from theright or from the left.

As such, assign the first place to the seat at the extreme right orextreme left and proceed from there. Assume that the seat at theextreme left is the first place.

Given conditions:

(i) B cannot be at the third place (ii) C and D cannot sit together.

Since B cannot be at the third place, B can possibly take any of theother three places. Assume B to be at each place and see thecombinations possible.

All the possible cases are listed below:

Case 1: When B is at seat 1





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From the 4 cases listed above, it can be seen that A can never be at thefirst place.

Hence, option 1.

3.3 Marks

If A is not at the third place, then C can occupy which of the followingplaces?

1) The first place only.

2) The third place only.

3) Any one of the the first and third place.

4) Any of the four places.

Solution:If A is not at the third place, there are two possible candidates for thethird place i.e. C and D.

If any of them is at the third place, the other cannot occupy the twoplaces adjacent to it (i.e. second and fourth place). The other place hasto mandatorily occupy the first place. If C is at the third place, D has to be at the first place while if D is at thethird place, C has to be at the first place.

Thus, C can occupy any one of the first and third place.

Hence, option 3.

4.3 Marks

If A and B are together then which of the following must necessarily betrue?

1) C is not at the first place.

2) A is at the third place.

3) D is at the first place.

4) C is at the first place.

Solution:From the solution to the first question, observe that A and B can be


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together only if B is at the second place and A is at the third place.

Thus, A has to necessarily be at the third place.

Hence, option 2.

Group Question


The table below shows the amount of money invested (in Rs. crore) in the coreinfrastructural areas of two districts, Chittoor and Khammam, in Andhra Pradesh.

5.3 Marks

By what percent was the total investment in the two districts more in1996 as compared to that in 1995?

1) 14%

2) 21%

3) 24%

4) 18%

Solution:The total investment in the year 1995 = 2923.1 + 7081.6 = 10004.7crores

The total investment in the year 1996 = 3489.5 + 8352 = 11841.5 crores

∴ The required percentage = [(11841.5 − 10004.7)/10004.7] × 100

≈ 1836.8/100

≈ 18.4%

Hence, option 4.


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6.3 Marks

The investment in Electricity and Thermal Energy in 1995 in these twodistricts formed what percent of the total investment made in that year?

1) 41%

2) 47%

3) 52%

4) 55%

Solution:The total investment in Electricity and Thermal Energy in the year 1995= 815.2 + 632.4 + 2065.8 + 1232.7 = 4746.10 crores

The total investment made in the year 1995 = 2923.10 + 7081.6 =10004.70 crores

Hence, option 2.

7.3 Marks

In Khammam district, the investment in which area in 1996 showed theleast percentage increase over the investment in that area in 1995?

1) Electricity

2) Chemical

3) Solar

4) Nuclear

Solution:The percentage increase for each area mentioned in the options is:

Electricity : [(2365.1 − 2065.8)/2065.8] × 100 ≈ 14.5%

Chemical : [(986.4 − 745.3)/745.3] × 100 ≈ 32.5%

Solar : [(1792.1 − 1363.5)/1363.5] × 100 ≈ 31.4%

Nuclear : [(2182.1 − 1674.3)/1674.3] × 100 ≈ 30.3%

Thus, Electricity shows the least percentage improvement over theprevious year.

Hence, option 1.


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Alternatively,

Such problems can often be solved faster using approximations andcalculating the value in terms of a range rather than a precise value. Ifall the calculations fall within the same range, one can go into furtherdetail.

Consider each option here:

Electricity : There is an approximate increase of 300 over an initial valueof approximately 2000. This implies a percentage increase of roughly15%.

Chemical : There is an approximate increase of 240 over an initial valueof approximately 740. Since 240 is 33.33% of 720, the percentage herehas to be marginally less than 33.33% but definitely greater than 30%.

Solar : There is an approximate increase of 430 over an initial value ofapproximately 1350. 405 is 30% of 1350. Hence, the percentage herehas to be close to 30%.

Nuclear : There is an approximate increase of 500 over an initial value ofapproximately 1700. This implies a percentage increase of roughly 30%.

Thus, it is evident that the lowest percentage increase is for Electricity.

However, note that the percentage increase for the other three areas arevery cloe to each other. Hence, if the maximum percentage increasehad been asked, Electricity could have been eliminated but the otherthree values would have to be calculated in a little more detail.

Hence, option 1.

8.3 Marks

The total investment in Khammam was approximately how many timesthe total investment in Chittoor in the two given years?

1) 2.8

2) 2.0

3) 2.4

4) 1.7

Solution:The total investment in Chittoor in the years 1995 and 1996 is = 2923.10


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+ 3489.50 = 6412.60 crores

The total investment in Khammam in the years 1995 and 1996 is =7081.6 + 8352 = 15433.60 crores

Hence, option 3.

9.3 Marks

If the total investment in Khammam shows the same rate of increase in1997, as it had shown from 1995 to 1996, what would be the totalinvestment in Khammam (approximately) in 1997 (in Rs. crore)?

1) 9,850

2) 10,020

3) 9,170

4) 8,540

Solution:The percentage increase in the investment in Khammam from the year1995 to 1996 is

So, the investment in 1997 in Khammam = 1.1794 × 8352 = Rs. 9,850crores (approximately).

Hence, option 1.

10.3 Marks



What is the price of tea?

Price of coffee is Rs. 5 more than that of tea.A.Price of coffee was Rs. 5 less than the price of a cold drink which costs three timesB.


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the price of tea.

1) 1

2) 2

3) 3

4) 4

Solution:Let the price of coffee and tea be Rs. x and Rs. y respectively.

Using statement A alone:

x = y + 5

Since this is a single equation in two variables, a unique solution cannot befound.



Let the price of a cold drink be Rs. z

∴ x = z − 5 and z = 3y

∴ x = 3y − 5

Since this is a single equation in two variables, a unique solution cannot befound.



x = y + 5 and x = 3y − 5

∴ y + 5 = 3y − 5

∴ y = 5

Thus, the price of tea is Rs. 10.

Thus, the question can be answered using both the statements together butnot by using either statement alone.


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Hence, option 3.

Group Question


In a game played by two people there are initially N match sticks kept on thetable. A move in the game consists of a player removing either one or twomatchsticks from the table. The one who takes the last matchstick loses. Playersmake moves alternately. The player who makes the first move is A. The otherplayer is B.

11.3 Marks

The smallest value of N (greater than 5) that ensures a win for B is_____.

1) 7

2) 6

3) 10

4) 8

Solution:Let N = 1. Since there is only one matchstick, A picks it up and losesthe game.

Let N = 2. Here A picks 1 match stick and B loses the game.

Let N = 3. Here A picks 2 match sticks and B loses the game.

Let N = 4. If A picks 1 match stick, B picks 2 match sticks and A losesthe game. If A picks 2 match sticks, B picks 1 match sticks and A stillloses the game.

Thus, when there are exactly 1, 4, 7.. matchsticks left just before A hasto pick them up, A definitely loses the game.

Consider the given options:

Let N = 6. Here A picks 2 match sticks. If B picks 1 matchstick, A nowpicks 2 and B loses the game. If B picks 2 match sticks, A picks 1 and Bstill loses the game.

Let N = 7.

Assume that A picks 2 match sticks.

The sequence of picking up is as follows:


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A: 2B : 1A: 1/2B : 2/1

Thus, 1 matchstick is left for A and so A loses the game.

Now, assume that A picks 1 match stick.

The sequence of picking up is as follows:

A: 1B : 2A: 1/2B : 2/1

Thus, 1 matchstick is again left for A and so A loses the game. Thus, there have to be 7 matchsticks left for B to definitely win thegame.

Hence, option 1.

12.3 Marks

The largest of N (less than 50) that ensures a win for B is _____.

1) 46

2) 47

3) 48

4) 49

Solution:As seen in the solution to the previous question, if the number of matchsticks left just before A's turn are 1, 4, 7 and so on, A loses the game.

If one continues with this series, A loses the game if there are either 46or 49.

Since, 49 is the largest number just less than 50, the largest numberless than 50 that ensures a win for B is 49.

Hence, option 4.

Group Question


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Ghosh Babu stays at Ghosh Housing Society, Aghosh Colony, Dighospur ,Kolkata. In Ghosh Housing Society, 6 people daily read Ganashakti and 4 peopleread Anand Bazar Patrika. In Ghosh Housing Society there is no person whoreads both the newspapers. The total number of people who read either of thesetwo newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Thenumber of people who read Ganashakti in Aghosh Colony and Dighospur is 33and 121 respectively, while the number of people who read Anand Bazar Patrikain Aghosh Colony and Dighospur is 32 and 117 respectively.

13.3 Marks

The number of people in Dighospur who read only Ganashakti is _____.

1) 121

2) 83

3) 79

4) 127

Solution:In Dighospur, the number of people who read Ganashakti is 121 whilethe number of people who read Anand Bazaar Patrika is 117.Also, the number of people who read either of these two newspapers is200.

Thus, the number of people who read both the newspapersin Dighospur = 121 + 117 – 200 = 38

Thus, the number of people who read only Ganashakti in Dighospur =121 – 38 = 83

Hence, option 2.

14.3 Marks

The number of people in Aghosh Colony who read both thesenewspapers is _____.

1) 13

2) 20

3) 19

4) 14

Solution:In Agosh Colony, the number of people who read Ganashakti is 33 andthe number of people who read Anand Bazaar Patrika is 32.


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The total number of people who read either of these two newspapers is52.

Thus, the number of people who read both the newspapers in AgoshColony = 33 + 32 – 52 = 13

Hence, option 1.

15.3 Marks

The number of people in Aghosh Colony who read only one paper is_____.

1) 29

2) 19

3) 39

4) 20

Solution:The number of people in Aghosh colony who read at least one of thetwo newspapers = 52

From the solution to the previous question, the number of people inAghosh colony who read both the newspapers = 13

∴ Number of people in Aghosh colony who read exactly onenewspaper = 52 − 13 = 39

Hence, option 3.

Group Question



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16.3 Marks

When was the per capita production of milk the least?

1) 1990

2) 1992

3) 1994

4) 1996

Solution:

Per capita production of milk = (Total production of milk)/(Femalepopulation + Male population)

For 1990: Per capita production = 5/(34 + 36) = 5/70 = 1/14

For 1992: Per capita production = 7/(35 + 37) = 7/72

For 1994: Per capita production = 8/(37 + 39) = 8/76 = 2/19

For 1996: Per capita production = 6/(40 + 43) = 6/83

Now,


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1990: 5/70 = 1/14

1992: 7/72 = 1/(72/7) = 1/10.28

1994: 2/19 = 1/(19/2) = 1/9.5

1996: 6/83 = 1/(83/6) = 1/13.82

Since each fraction has the same numerator, the fraction with thelargest denominator has the smallest value.

Thus, 1/14 is the smallest value.

Thus, the per capita production was the least in 1990.

Hence, option 1.

17.3 Marks

When was the per capita production of food-grains the most?

1) 1992

2) 1993

3) 1994

4) 1995

Solution:The per capita production of food-grains for years 1992, 1993, 1994 and1995 is

1992: 20/72 = 1/(72/20) = 1/3.6

1993: 21/74 = 1/(74/21) = 1/3.52

1994: 25/76 = 1/(76/25) = 1/3.04

1995: 31/79 = 1/(79/31) = 1/2.55

Since each fraction has the same numerator, the fraction with thesmallest denominator has the largest value.

Thus, 31/79 has the largest value.


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Thus, the per capita production of food grains was highest in 1995.

Hence, option 4.

18.3 Marks

In which year was the difference between the increase in the productionof food-grains and milk the maximum?

1) 1993

2) 1994

3) 1995

4) 1996

Solution:This question can be solved by direct observation.

It is evident that the difference between the increase in the production offood grains and milk was maximum in 1995.

Hence, option 3.

19.3 Marks

If milk contains 320 calories and food-grains contain 160 calories, inwhich year was the per capita consumption of calories the highest?

1) 1993

2) 1994

3) 1995

4) 1996

Solution:The per capita consumption of calories in the years 1993, 1994, 1995and 1996 is respectively,

1993: 5920/74 = 80


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1994: 6560/76 = 86.32

1995: 7200/79 = 91.14

1996: 6240/83 = 75.18

Thus, the per capita consumption of calories is the most in 1995.

Hence, option 3.

20.3 Marks

If one gallon of milk contains 120 gm of a particular nutrient and one tonof food-grains contains 80 gm of the same nutrient, in which year wasthe availability of this nutrient the maximum?

1) 1993

2) 1994

3) 1995

4) 1996

Solution:The availability of the concerned nutrient for each given year is:

1993: (120 × 8) + (80 × 21) = 960 + 1680 = 2640 million gms

1994: (120 × 8) + (80 × 25) = 960 + 2000 = 2960 million gms

1995: (120 × 7) + (80 × 31) = 840 + 2480 = 3320 million gms

1996: (120 × 6) + (80 × 27) = 720 + 2160 = 2880 million gms

Thus, the availability of the nutrient was maximum in 1995.

Hence, option 3.

21.3 Marks

Referring to the above question, in which year was the per capitaconsumption of this nutrient the highest?

1) 1993

2) 1994

3) 1995

4) 1996


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Solution:The per capita consumption of the nutrient for each of the given years is:

1993: 2640/(36 + 38) = 2640/74 = 35.67

1994: 2960/(37 + 39) = 2960/76 = 38.95

1995: 3320/(39 + 40) = 3320/79 = 42.03

1996: 2880/(40 + 43) = 2880/83 = 34.7

Thus, the per capita consumption was the highest in 1995.

Hence, option 3.

22.3 Marks



What is the value of p + q?

A.

B.

1) 1

2) 2

3) 3

4) 4


Since this is a single linear equation in three variables, a unique solution


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cannot be found for this equation.



Since this is a single linear equation in three variables, a unique solutioncannot be found for this equation.



Even when the two statements are combined, we have two equations andthree unknowns. Therefore, a unique solution cannot be found.

The only conclusion obtained on solving these two equations is p + 7q = 0.

Thus, the value of p + q cannot be found.

Thus, the question cannot be answered by either of the statements.

Hence, option 4.

Group Question


A, B, C, D, E and F are a group of friends from a club. There are two doctors, onelecturer, one architect, one accountant and one lawyer in the group. There aretwo married couples in the group. The lawyer is married to D who is a doctor. Nolady in the group is either an architect or an accountant. C, the accountant, ismarried to F who is a lecturer. A is married to D and E is not a doctor.

23.3 Marks

What is E's profession?

1) Lawyer

2) Architect

3) Lecturer

4) Accountant

Solution:There are 6 people (A, B, C, D, E and F) who have the followingoccupations (D1, D2, Ac, Ar, Lc and Lw) in no particular order.

The lawyer is married to D, who is a doctor. At the same time, A is


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married to D.

Thus, A (Lw) is married to D(D1).

C (Ac) is married to F(Lc).

Since E is not a doctor, E can only be the architect while B is the otherdoctor.

Thus, E is the architect.

Hence, option 2.

24.3 Marks

How many members of the group are male?

1) 2

2) 3

3) 4


Solution:From the solution to the previous question, it is clear that C being theaccountant, cannot be a lady. Hence, F is a lady.

Also, one out of A and D is a lady.

Since E is the architect, E cannot be a lady.

However, B (the other doctor) can be male or female.

Thus, the total number of females cannot be found.

Hence, the total number of men cannot be found.

Hence, option 4.

25.3 Marks


Mark (1) if the question can be answered by one of the statements, but not bythe other.Mark (2) if the question can be answered by usingeither statement, independently of the other.Mark (3) if the question can be answered by using both statements together,but not by either statement alone.


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Mark (4) if the question cannot be answered by either of the statements.

If a, b, c are integers, is (a − b + c) > (a + b − c)?

b is negative.A.c is positive.B.

1) 1

2) 2

3) 3

4) 4

Solution:Is (a – b + c) > (a + b – c)?

Subtracting a from both sides, the question gets converted to a comparisonbetween (–b + c) and (b – c)

The same question can now be written as : Is c > b?


b is negative, but there is no mention of c.



c is positive, but there is no mention of b.



Since c is positive and b is negative, c > b.

Thus, the question can be answered by using both statements together butnot by using either statement alone.

Hence, option 3.


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1.3 Marks



What is the area bounded by the two lines and the co-ordinate axes in thefirst quadrant?

The lines intersect at a point which also lies on the lines 3x − 4y = 1 and 7x − 8y = 5.A.The lines are perpendicular, and one of them intersects the y-axis at an intercept of4.

B.

1) 1

2) 2

3) 3

4) 4


The lines intersect at the point of intersection of 3x − 4y = 1 and 7x − 8y = 5.

On solving these equations you get, x = 3 and y = 2.

Thus, the given lines intersect at the point (3, 2).

However, the point of intersection of these two lines with the x-axis and they-axis is not known.

Therefore, the required area cannot be found.



One of the lines passes through the point (0, 4).

Section I


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If the co-ordinates of any other point through which this line passes areknown, one can find the equation of this line.

If this equation is known, the equation of the other line and its x-intercept canbe found.

In such a case, the area can be calculated.

Since no other co-ordinate is known, the above calculations are not possible.

Therefore, the required area cannot be found.



Line L1 passes through (0, 4) as well as (3, 2).

Hence, the slope of this line can be found. This slope is −2/3.

Since the other line i.e. L2 is perpendicular to this line, the slope of L2 is 3/2.

Using this slope and the co-ordinates (3, 2), the equation of line L2 can befound.

Once this equation is known, the x-intercept of L2 can be found bysubstituting y = 0 in L2.

Thus, all four co-ordinates of the bounded area are now known.

Therefore, the area of the bounded region can be calculated.

Thus, the question can be answered using both the statements together, butnot by using either statement alone.

Hence, option 3.

2.3 Marks

A cube is made into a number of smaller cubes by dividing each edge intofour equal parts. What is the minimum number of similar additional smallcubes that would be required to create a bigger cube which would completelyenclose the original cube?

1) 152

2) 261

3) 61

4) 148


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Solution:When a cube is cut into four equal parts on each edge, the total number ofsmaller cubes created is 4 × 4 × 4 = 64 (Length × Breadth × Height)

When a bigger cube encloses the original cube using small cubes similar tothe ones just created, it implies that one small cube gets added to the lengthon each side.

Thus, the length of the bigger cube consists of 6 small cubes.

Similarly, the breadth as well as height of the bigger cube will consist of 6small cubes each.

Thus, the bigger cube consists of 6 × 6 × 6 = 216 cubes

So, the number of additional smaller cubes = 216 – 64 = 152

Hence, option 1.

Group Question


The bar chart below shows the total sales, total expenditure and share capital offour companies, A, B, C and D. ‘Profits’ is defined as the difference between totalsales and total expenditure.

3.3 Marks

Which company has the lowest profit per rupee of sales?

1) A

2) B


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3) C

4) D

Solution:

Profit = Sales − Expenditure

Profit per rupee of sales = Profit/Sales

These figures can be calculated as shown in the table above.

It can be seen from the table that the profit per rupee of sales is theleast for the company C (0.0833).

Hence, option 3.

4.3 Marks

Which company has the lowest profit per rupee of the share capital?

1) A

2) B

3) C

4) D

Solution:Profit per rupee of share capital = Profit/Share Capital

The profit per rupee of share capital for each company is given below:

A : 5/10 = 0.5

B : 1/0.5 = 2

C : 1/8 = 0.125

D : 3/5 = 0.6

Thus, company C has the lowest profit per rupee of the share capital.


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Hence, option 3.

5.3 Marks

Which company has the highest sales per rupee of the share capital?

1) A

2) B

3) C

4) D

Solution:Sales per rupee of share capital = Sales/Share Capital

This ratio for each company can be calculated from the table in thesolution to the first question and is given below.

A : 20/10 = 2

B : 4/0.5 = 8

C : 12/8 = 1.5

D : 15/5 = 3

Thus, company B has the highest sales per rupee of the share capital.

Hence, option 2.

6.3 Marks

Which company has the lowest profit per rupee of the total expenditure?

1) A

2) B

3) C

4) D

Solution:Profit per rupee of the expenditure = Profit/Expenditure

This ratio can be calculated for each company from the table in thesolution to the first question and is given below.

A : 5/15 = 0.33


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B : 1/3 = 0.33

C : 1/11 = 0.09

D : 3/12 = 0.25

Thus, company C has the lowest profit per rupee of the totalexpenditure.

Hence, option 3.

7.3 Marks



A train started from Station A, developed engine trouble and reached StationB, 40 minutes late. What is the distance between Stations A and B?

The engine trouble developed after travelling 40 km from Station A and the speedreduced to 1/4 of the original speed.

A.

The engine trouble developed after travelling 40 km from station A in two hours andthe speed reduced to 1/4 of the original speed.

B.

1) 1

2) 2

3) 3

4) 4


Since the time in which the train travelled the 40 kms is not known, thedistance cannot be found.




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The train travelled 40 km in 2 hours, and then the engine trouble started.

Since the speed reduces to 1/4 of the original speed, the time taken if 4 timesthe original time.

If the time taken to travel the balance distance at 40 km is t minutes, then thetime taken to travel the same distance at the revised speed is 4t minutes.

Thus, the additionl time taken is 4t − t = 3t minutes.

The train reached 40 minutes late.

∴ 3t = 40

∴ t = 40/3

Once this time, the balance distance travelled and the total distance can becalculated.



Hence, option 1.

Group Question


Recently, Ghosh Babu spent his winter vacation on Kyakya Island. During thevacation, he visited the local casino where he came across a new card game. Twoplayers, using a normal deck of 52 playing cards, play this game. One player iscalled the “Dealer” and the other is called the “Player”. First, the Player picks acard at random from the deck. This is called the “base card”. The amount inrupees equal to the face value of the base card is called the “base amount”. Theface values of Ace, King, Queen and Jack are ten. For other cards, the face valueis the number on the card. Once the Player picks a card from the deck, the Dealerpays him the base amount. Then the Dealer picks a card from the deck and thiscard is called the “top card”. If the top card is of the same suit as the base card,the player pays twice the base amount to the Dealer. If the top card is of the samecolour as the base card (but not the same suit) then the Player pays the base


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amount to the Dealer. If the top card happens to be of a different colour than thebase card, the Dealer pays the base amount to the Player.

Ghosh Babu played the game 4 times. In the first game, he picked the eight ofclubs and the Dealer picked the queen of clubs. In the second, he picked the tenof hearts and the Dealer picked the two of spades. Next time, Ghosh Babu pickedthe six of diamonds and the Dealer picked the ace of hearts. In the finallygame, he picked the eight of spades and the Dealer picked jack ofspades. Answer the following questions based on the information givenabout these four games.

8.3 Marks

If Ghosh Babu stopped playing the game when his gain was themaximum, the gain in Rs. would have been:

1) 12

2) 20

3) 16

4) 4

Solution:Assume that the Player gets an amount n from the Dealer at thebeginning of each game.

The amount with the Player at the end of the game is as shown below:

Case I : If the Dealer picks a card from the same suit, the Player pays2n to the Dealer and is left with −n

Case II : If the Dealer picks a card of the same colour but not from thesame suit, the Player pays n to the Dealer and is left with 0

Case III : If the Dealer picks a card from a different colour, thePlayer gets n from the Dealer and is left with 2n

Game I :

Ghosh Babu picked the eight of clubs and so the Dealer gave him Rs.8. The Dealer picked the queen of clubs (same suit card) and GhoshBabu gave him Rs. 16.

Thus, Ghosh Babu had a loss of Rs. 8 at the end of the first game.

In the second game, Ghosh Babu picked the ten of hearts and so theDealer gave him Rs. 10. The Dealer picked the two of spades (differentcolour card) and gave Ghosh Babu Rs. 10.


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Thus, the amount with Ghosh Babu at the end of the second game(Ghosh Babu's gain) was −8 + 10 + 10 = Rs. 12.

In the third game, Ghosh Babu picked the six of diamonds and so theDealer gave him Rs. 6. The Dealer picked the ace of hearts (samecolour card) and so Ghosh Babu gave him the base amount i.e. Rs. 6.Thus, there was no profit and no loss.

Thus, Ghosh Babu's gain at the end of the third game was again Rs.12.

In the final game, Ghosh Babu picked the eight of spades and got Rs. 8from the Dealer. The Dealer then picked the jack of spades (same suitcard) and so Ghosh Babu gave him Rs. 16.

Thus, at the end of the fourth game, the amount with Ghosh Babu (hisgain) was 12 + 8 − 16 = Rs. 4

Thus, the maximum gain was at the end of either Game II or Game III.

Therefore, Ghosh Babu would have stopped here.

The gain at this stage was Rs. 12.

Hence, option 1.

9.3 Marks

The initial amount that Ghosh Babu had (before the beginning of thegame sessions) was Rs. X. At no point did he have to borrow anymoney. What is the minimum possible value of X?

1) 16

2) 8

3) 100

4) 24

Solution:As seen from the solution to the previous question, Ghosh Babuincurred a loss of Rs. 8 at the end of the first game.

Thus, if he already had at least Rs. 8 before the beginning of the gamesessions, he would have got Rs. 8 from the Dealer at the neginning ofthe first game and would have paid Rs. 16 to the Dealer at the end ofthe first game. He would therefore have a zero balance, but would notneed to borrow money.


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Thus, the minimum possible value of X is 8.

Hence, option 2.

10.3 Marks

If the final amount of money that Ghosh Babu had with him was Rs.100, what was initial amount that he had?

1) 120

2) 8

3) 4

4) 96

Solution:From the solution to the first question, Ghosh Babu had a gain of Rs. 4at the end of four games.

Thus, if he had Rs. 100 at the end of the fourth game, he should havehad Rs. (100 – 4) = Rs. 96 with him at the start of the session.

Hence, option 4.

11.3 Marks



What is the first term of an arithmetic progression of positive integers?

The sum of the squares of the first and second term is 116.A.The fifth term is divisible by 7.B.

1) 1

2) 2

3) 3

4) 4


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The sum of the squares of the first and second term is 116.

The arithmetic progression is of positive integers.

The only positive integers that add up to 116 and are both perfect squares are100 and 16.

Thus, the squares of the first and second term are 16 and 100.

Thus, the first term is one from 4 and 10.

If the first term is 10, 4 becomes the second term and the third term becomes−2.

This is not possible as the arithmetic progression is of positive integers.

Therefore, the first term is 4.


Using statement B alone.

The fifth term is divisible by 7.

∴ a + 4d = 7n

Since this is a linear equation in 3 variables, the value of a cannot be found.

Therefore, the first term cannot be found.



Hence, option 1.

12.3 Marks


Mark (1) if the question can be answered by one of the statements, but not bythe other.Mark (2) if the question can be answered by usingeither statement, independently of the other.


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Mark (3) if the question can be answered by using both statements together,but not by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

What are the values of the 3 integers a,b and c?

ab = 8A.bc = 9B.

1) 1

2) 2

3) 3

4) 4


ab = 8 ... (i)

The combinations possible are (1, 8), (2, 4), (4, 2), (8, 1), (−1, −8), (−2, −4),(−4, −2) and (−8, −1)

Thus, a unique value of a and b cannot be found.



bc = 9 ... (ii)

The combinations possible are (1, 9), (3, 3), (9, 1), (−1, −9), (−3, −3) and (−8,−1)

Thus, a unique value of b and c cannot be found.



This is possible if a = 8 and b = 9 or if a = −8 and b = −9.

In the first case, c = 1, while in the second case, c = −1.


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Thus, a = 8, b = 9 and c = 1 or a = −8, b = −9 and c = −1.

Again, a unique value of a, b and c cannot be found.


Hence, option 4.

13.3 Marks


Either Sita is sick or she is careless.

Sita is not sick.A.Sita is not careless.B.Sita is sick.C.Sita is careless.D.

1) AB

2) AD

3) BA

4) DA


Either P or Q

This implies that if P does not occur then Q occurs or if Q does not occurthen P occurs.

The conclusions for this type of logical connective are as follows

~P ⇒ Q 1.~Q ⇒ P 2.

Thus, if Sita is not sick, then she is careless (i.e. AD), or , if Sita is notcareless then she is sick. (i.e. BC).

However, BC is not part of any option.

Thus, AD relates logically with the given statement.

Hence, option 2.


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14.3 Marks


Ram gets a swollen nose whenever he eats hamburgers.

Ram gets a swollen nose.A.Ram does not eat hamburgers.B.Ram does not get a swollen nose.C.Ram eats hamburgers.D.

1) AB

2) DC

3) AC

4) CB


Q whenever P

This connective is of the same type as : If P then Q.


P ⇒ Q 1.~Q ⇒ ~P 2.

Thus, if Ram eats hamburgers, he gets a swollen nose (i.e. DA) or if Ramdoes not get a swollen nose, he does not eat hamburgers (i.e. CB).

DA is not part of the options.

Therefore, CB relates logically with the given statement.

Hence, option 4.

15.3 Marks


Either the employees have no confidence in the management or they arehostile by nature.

They are hostile by nature.A.They are not hostile by nature.B.They have confidence in the management.C.They have no confidence in the management.D.


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1.3 Marks



If R is an integer between 1 and 9, P − R = 2370, what is the value of R?

P is divisible by 4.A.P is divisible by 9.B.

1) 1

2) 2

3) 3

4) 4


P is divisible by 4 and R is an integer between 1 and 9.

P can be divisble by 4 if P = 2372 or P = 2376

For these values of P, R = 2 or R = 6.

Thus, a unique value of R cannot be found.



P is divisible by 9 and R is an integer between 1 and 9.

P can be divisible by 9 if P = 2376.

For this value of P, R = 6.

Thus, the only possible value of (P, R) is (2376, 6).

Section I


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Thus, the question can be answered using statement B alone but not byusing statement A alone.

Thus, the question can be answered using one of the statements, but not byusing the other statement.

Hence, option 1.

2.3 Marks



A man distributed 43 chocolates to his children. How many of his children aremore than five years old?

A child older than five years gets 5 chocolates.A.A child less than or equal to 5 years gets 6 chocolates.B.

1) 1

2) 2

3) 3

4) 4


A child older than five years gets 5 chocolates.

Since there are 43 chocolates, there can be a maximum of 8 children who areolder than 5 years.

However, the actual number of children who are older than five years cannotbe found.



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A child less than or equal to 5 years gets 6 chocolates.

The actual number of children who are older than five years cannot be found.

Thus, the actual number of children who are older than five years cannot befound.



Let the number of children who are less than or equal to 5 years be x and thenumber of children who are older than five years be y. ∴ 5x + 6y = 43

Since x and y stand for number of people, they should have integral values.

Therefore, the only possible value of (x, y) is (5, 3)

Thus, 3 children are more than 5 years old.

Thus, the question can be answered using both statements together, but notby using either statement alone.

Hence, option 3.

3.3 Marks



Ramu went by car from Kolkata to Trichy via Chennai, without any stoppages.The average speed for the entire journey was 40 kmph. What was theaverage speed from Chennai to Trichy?

The distance from Chennai to Trichy is 0.3 times the distance from Kolkata toChennai.

A.

The average speed from Chennai to Trichy was twice the average speedfrom Kolkata to Chennai.

B.


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1) 1

2) 2

3) 3

4) 4


The average speed for the entire journey was 40 kmph.

Let the distance between Kolkata and Chennai be 10 km. Therefore, thedistance between Chennai and Trichy is 3 km.

The average speed from Chennai to Trichy cannot be found from this data.



Let the average speed from Chennai to Trichy be 2x kmph, then the averagespeed from Kolkata to Chennai is x kmph. The average speed for the whole journey is given as:

40 = Total Distance Travelled/Total Time Taken

∴ 40 = [10 + 3]/[(10/x) + (3/2x)]

∴ 40 = (13 × 2x)/23

∴ x = (40 × 23)/26

∴ 2x = (40 × 23)/13 kmph

This is the average speed from Chennai to Trichy.


Hence, option 3.

4.3 Marks


Mark (1) if the question can be answered by one of the statements, but not by


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the other.Mark (2) if the question can be answered by usingeither statement, independently of the other.Mark (3) if the question can be answered by using both statements together,but not by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

x, y and z are three positive odd integers. Is x + z divisible by 4?

y − x = 2A.z − y = 2 B.

1) 1

2) 2

3) 3

4) 4


y − x = 2

Since the relationship between x and z is not known, and the value of x is notknown, the value of x + z cannot be found.



z − y = 2

Since the relationship between x and z is not known, and the value of z is notknown, the value of x + z cannot be found.



Adding the two equations, we get z – x = 4

∴ z = x + 4

Now, z + x = x + 4 + x = 2x + 4

Since x is an odd integer, z + x = 2(2k + 1) + 4


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= 4k + 6

Thus, x + z is not divisible by 4. Thus, the question can be answered using both the statements together butnot by using either statement alone.

Hence, option 3.

5.3 Marks



The unit price of product P1 is non-increasing and that of product P2 isdecreasing. Which product will be costlier 5 years hence?

Current unit price of P1 is twice that of P2.A.5 years ago, the unit price of P2 was twice that of P1.B.

1) 1

2) 2

3) 3

4) 4

Solution:The unit price of P1 either decreases or remains constant. The unit price ofP2 keeps on decreasing.

Using Statement A alone:

The current price of P1 is twice that of P2.

P1 and P2 can both follow a decreasing trend.

However, the rate of decrease is not known.

Thus, if the rate of decrease for P1 is much higher than P2, P2 can becostlier 5 years hence.


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P1 can also remain constant.

If P1 remains constant, P1 will be costlier 5 years hence.



5 years ago, the unit price of P2 was twice that of P1.

Depending on the rate of decrease of P1 and P2, one of them will becostlier 5 years from now.



When both the statements are combined, it seems that the rate of decreaseof P2 is much more than the rate of decrease of P1.

However, the question does not say that the rate of decrease for a particularproduct is constant throughout.

Hence, the costlier product cannot be determined.

Thus, the question cannot be answered using either of the statements. Hence, option 4.

6.3 Marks



X is older than Y, Z is younger than W and V is older than Y. Is Z youngerthan X?

W may not be older than V.A.W is not older than V.B.

1) 1

2) 2


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3) 3

4) 4

Solution:X > Y, Z < W, V > Y.

To find the relationship between X and Z, Z needs to be compared to either Xor Y.


W may not be older than V.

From this data, no relationship can be identified between X and Z.



W is not older than V.

Again, from this data, no relationship can be identified between X and Z.



Even when both the statements are combined, no relationship can beestablished.


Hence, option 4.

7.3 Marks



How long did Mr. X take to cover 5000 km. journey with 10 stopovers?


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The ith stopover lasted i2 minutes.A.The average speed between any two stopovers was 66 kmph.B.

1) 1

2) 2

3) 3

4) 4


The 1st stopover lasted 12 minutes, the 2nd stopover lasted 22 minutes and soon. The 10th stopover lasted 102 minutes.

Therefore,

However, the actual travelling time is not known.

Hence, the total time cannot be calculated.



However, the stopover time is not known.

Hence, the total time cannot be calculated.



The stopover time is obtained from statement A while the travelling time isobtained from statement B.

From this data, the total time can be calculated.



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Hence, option 3.

8.3 Marks



x + y > 0A.x and y are positive integers and each is greater than 2.B.

1) 1

2) 2

3) 3

4) 4


x + y > 0.

Consider x = y = 2

The value of the expression becomes 2 i.e. > 1

Consider x = y = 1

The value of the expression becomes 1.



When the expression of the left hand side is simplified, you get [x2y + xy2]/(x2

+ y2)


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Since x and y are positive integers, this expression will be positive.

Since the numerator consists of x2 and y2, each multiplied by a positivenumber greater than 2, the numerator will be definitely larger than thedenominator.

Hence, the value of the expression is greater than 1.


Thus, the question can be answered by one of the statement but not by theother.

Hence, option 1.

9.3 Marks



Is it more profitable for Company M to produce Q?

Product R sells at a price four times that of Q.A.One unit of Q requires 2 units of labour, while one unit of R requires 5 units oflabour. There is no other constraint on production.

B.

1) 1

2) 2

3) 3

4) 4


Though the selling price of Q and R can be compared, the cost and effortinvolved in producing Q and R is not known.

Hence, it cannot be said whether it is profitable for Company M to produce Q.


11 of 39 9/16/2011 10:20 AM



Though the effort involved in producing Q and R is known, the selling price ofQ and R cannot be compared. Hence, it cannot be said whether it is profitable for Company M to produce Q.



Since there is no other constraint, except labour, the selling price can beassumed to be directly proportional to the amount of labour involved.

Since R sells at a price four times that of Q, R should ideally require 8 unitsof labour for every 2 units of labour needed by Q.

However, R actually requires only 5 units of labour.

Thus, R uses less labour than required and gets a higher selling price.

Hence, it is more profitable for the company to produce R and not Q.


Hence, option 3.

10.3 Marks



What is the value of the prime number x?

x2 + x is a two-digit number greater than 50.A.

x3 is a three-digit number.B.

1) 1


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2) 2

3) 3

4) 4


x2 + x > 50

∴ x(x + 1) > 50

For x = 5; x(x + 1) = 5 × 6 = 30

For x = 7; x(x + 1) = 7 × 8 = 56

For x = 11; x(x + 1) = 11 × 12 = 132

Thus, the only prime number that satisfies the twin conditions of x2 + x beinga two-digit number that is greater than 50 is 7.



100 ≤ x3 ≤ 999

For x = 5; x3 = 125

For x = 7; x3 = 343

For x = 11; x3 = 1331

Thus, both x = 5 and x = 7 are valid values.



Thus, the question can be answered using statement A alone but not byusing statement B alone.



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Hence, option 1.

11.3 Marks



The average of three unequal quotations for a particular share is Rs. 110. Ifall the amounts are quoted in integral rupee values, does the highestquotation exceed Rs. 129?

The lowest quotation is Rs. 100.A.One of the quotations is Rs. 115.B.

1) 1

2) 2

3) 3

4) 4


The sum of the value of the three quotations is 3 × 110 = Rs. 330

The lowest quotation is Rs. 101 and no two quotations are equal.

The maximum possible value of any quotation can be obtained when thesecond highest quotation is Rs. 101

In such a case, the maximum possible value of a quotation = 330 − (100 +101) = Rs. 129.

Thus, the highest quotation does not exceed Rs. 129.



One of the quotations is Rs. 115.


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Therefore, the sum of the other two quotations is Rs. 215

Since the lowest quotation value is not known, the highest quotation valuecan be anything.




Hence, option 1.

12.3 Marks



How many people (from a group surveyed) read both Indian Express andTimes of India?

Out of a total of 200 readers, 100 read Indian Express, 120 read Times of India and 50read Hindu.

A.

Out of a total of 200 readers, 100 read Indian Express, 120 read Times of India and 50read neither.

B.

1) 1

2) 2

3) 3

4) 4


100 people read Indian Express, 120 read Times of India and 50 read Hindu.

Since this involves three newspapers, the number of people who read bothindian Express and Times of India cannot be found.


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If the survey comprises only two newspapers (Indian Express and Times ofIndia), the number of people who read at least one newspaper is 150.

Therefore, the number of people who read both newspapers is 100 + 120− 150 = 70

If the survey comprises three newspapers (including Hindu), the 50 who readneither Times of India nor Indian Express consists of those who read onlyHindu and those who do not read all three newspapers.

Since this breakup is not known, the number of people who read bothnewspapers cannot be found.



Even when the data is combined, the number of people who read bothnewspapers cannot be found.

Thus, the question cannot be answered by either statement.

Hence, option 4.

13.3 Marks



X says to Y, “I am 3 times as old as you were 3 years ago”. How old is X?

Y’s age 17 years from now would be the same as X’s present age.A.X’s age nine years from now is 3 times Y’s present age.B.

1) 1

2) 2


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3) 3

4) 4

Solution:Let the current ages of X and Y be x and y years respectively.

∴ x = 3(y − 3)

∴ 3y – x = 9 …(i)


y + 17 = x

∴ x – y = 17 …(ii)

Solving (i) and (ii), you get x = 30 and y = 13

Thus, X is 30 years old.



x + 9 = 3y

∴ 3y − x = 9 …(iii)

Since equations (iii) and (i) are the same, the value of x and y cannot befound.



Thus, the question can be answered by one of the statements, but not by theother.

Hence, option 1.

14.3 Marks


Mark (1) if the question can be answered by one of the statements, but not bythe other.


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Mark (2) if the question can be answered by usingeither statement, independently of the other.Mark (3) if the question can be answered by using both statements together,but not by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

What is the area under the lines GHI and JKL in the given quadrilateralOPQR, if it is known that all the small spaces are squares of the same area?

Length ABCDEQ is greater than or equal to 60.A.Area OPQR is less than or equal to 1512.B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the side of each small square be a units.

Thus, the area under the lines GHI and JKL is (3a × 2a) + (a × 2a) = 8a2


Length ABCDEQ is greater than or equal to 60

∴ 10a ≥ 60

∴ a ≥ 6

Since the exact value of a is not known, the required area cannot be found.



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Area OPQR is less than or equal to 1512.

∴ 42a2 ≤ 1512

∴ a2 ≤ 36

∴ a ≤ 6

Since the exact value of a is not known, the required area cannot be found.



When both the statements are combined, the only possible value of a is 6.

Hence, the required area is 8 × 62 = 288


Hence, option 3.

15.3 Marks



What is the radius of the circle?

The ratio of its area to its circumference is greater than 7.A.Diameter of the circle ≤ 32B.

1) 1

2) 2

3) 3


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4) 4


(πr2)/(2πr) > 7

∴ r/2 > 7

∴ r > 14

Thus, the radius can be any value greater than 14, but the exact value cannotbe found.



d ≤ 32

∴ r ≤ 16

Thus, the radius can be any value up to 16, but the exact value cannot befound.



When both statements are combined, the possible integral values of r are 14and 15.

A unique value of r can still not be found.


Hence, option 4.

16.3 Marks




20 of 39 9/16/2011 10:20 AM


What is the time difference between New York and London, if according toGMT sun rises in London before New York?

The departure time of the flight at New York is exactly 9.00 a.m. local time and thearrival time at London is 10.00 a.m. local time.

A.

The flight time is 5 hours.B.

1) 1

2) 2

3) 3

4) 4


As the duration of the journey is not known, the time difference cannot becalculated.



As the time of departure and arrival is not known, the time difference cannotbe calculated.



The flight departs at 9.00 a.m. New York time and arrives at 2 p.m. Londontime.

The local time of arrival in London is 10.00 a.m.

Thus, if London is ahead of New York, the time difference is 4 hours whileLondon is behind New York, the time difference is 20 hours.

Since London is ahead of New York, the time difference is 4 hours.


Hence, option 3.


21 of 39 9/16/2011 10:20 AM

17.3 Marks



Mr. Murthy takes the morning train to his office from station A to station B, andhis colleague Mr. Rahman joins him on the way. There are three stations C, Dand E on the way, not necessarily in that sequence. What is the sequence ofstations?

Mr. Rahman boards the train at D.A.Mr. Thomas, who travels between C and D has two segments of his journey incommon with Mr. Murthy but none with Mr. Rahman.

B.

1) 1

2) 2

3) 3

4) 4


Mr. Rahman boards the train at D.

This does not give any indication about the sequence of stations.



Since the station at which Mr. Rahman boards the train is not known, thesequence cannot be determined.



Mr. Thomas boards the train at C and gets down at D.

Mr. Rahman boards the train at D.


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Since Mr. Thomas has 2 segments of his journey common with Mr. Murthyand none with Mr. Rahman, the two common segments have to be CE andED.

Hence, the order of stations has to be A-C-E-D-B.


Hence, option 3.

18.3 Marks



What is the length of the line SQ which is the diagonal of a square as well asthe diameter of a circle?

All four vertices of the square lie on the circumference of the circle.A.The numerical value of the area of the circle is twice the length of SQ.B.

1) 1

2) 2

3) 3

4) 4


The data given in this statement is the same as the data given in thequestion.

Hence, the length of SQ cannot be found.



The numerical value of the area of the circle is twice the length of SQ, where


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SQ is the diameter of the circle.

∴ π × SQ2/4 = 2SQ

∴ SQ = 8/π

Thus, the value of SQ can be found.




Hence, option 1.

19.3 Marks



P, Q, R and S are four consecutive even integers. What is the value of thelargest integer among these?

The average of the four numbers is the first prime number greater than 10.A.The relation between the largest and smallest number is less than 10.B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the numbers P, Q, R and S be x − 3, x − 1, x + 1 and x + 3 respectively.

Hence, the average of these 4 numbers is x. The largest integer among theseis x + 3.


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The average of the four numbers is the first prime number greater than 10 i.e.11.

∴ x = 11

Therefore, the largest integer among these is 11 + 3 = 14.



The relation between the largest and smallest number is less than 10.

This does not provide any information.




Hence, option 1.

20.3 Marks



What is the price of an apple?

The average of the price of an apple and the price of an orange is Rs. 5.A.24 apples and 24 oranges cost Rs. 240.B.

1) 1

2) 2

3) 3


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4) 4

Solution:Let the cost of an apple and an orange be a and r respectively.


(a + r)/2 = 5

∴ a + r = 10

Since this is a single linear equation in two variables, a unique value of a andr cannot be found.



24a + 24r = 240

∴ a + r = 10

Since this is a single linear equation in two variables, a unique value of a andr cannot be found.



Since both the statements give the same equation, there is still only oneequation in terms of two variables.

Hence, the value of a and r cannot be found.

Thus, the question cannot be answered using either of the statements.

Hence, option 4.

21.3 Marks




26 of 39 9/16/2011 10:20 AM


How much money does Prem have?

Prem has at least 100 rupees more than Jagdish.A.The total money that both Prem and Jagdish have is not more than 500 rupees.B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the money with Prem and Jagdish be p and j respectively.


p – j ≥ 100

However, the amount with Prem cannot be determined from this inequation.



p + j ≤ 500

However, the amount with Prem cannot be determined from this inequation.



Even if both the inequations are combined, the exact amount with Premcannot be determined.


Hence, option 4.

22.3 Marks


Mark (1) if the question can be answered by one of the statements, but not bythe other.Mark (2) if the question can be answered by using


27 of 39 9/16/2011 10:20 AM

either statement, independently of the other.Mark (3) if the question can be answered by using both statements together,but not by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

Given that x and y are non-negative. What is the value of x?

2x + 2y ≤ 40A.x − 2y ≥ 20B.

1) 1

2) 2

3) 3

4) 4

Solution:x ≥ 0, y ≥ 0


2x + 2y ≤ 40 ...(i)

The exact value of x cannot be obtained from this inequation.



x − 2y ≥ 20 ...(ii)

The exact value of x cannot be obtained from this inequation.



From (i) we get x + y ≤ 20

Subtracting 3y from both the sides of the inequality we get x − 2y ≤ 20 – 3y,which will be an integer less than 20 as y is a non negative integer.

From (ii) we get x − 2y ≥ 20

∴ from the above argument we get 20 ≤ x − 2y ≤ 20 – 3y, this will bepossible only when y = 0 and the equality holds.


28 of 39 9/16/2011 10:20 AM

Thus, x = 20

Thus, the question can be answered by using both the statements.

Hence, option 3.

23.3 Marks



Is the average of the largest and the smallest of four given numbers greaterthan the average of four numbers?

The difference between the largest and the second largest numbers is greater thanthe difference between the second smallest and the smallest numbers.

A.

The difference between the largest and the second largest numbers is less than thedifference between the second smallest and the smallest numbers.

B.

1) 1

2) 2

3) 3

4) 4

Solution:If the numbers are a, b, c and d in the descending order,


If (a − b) > (c − d), then a + d > b + c

∴ a + d + a + d > a + d + b + c

Dividing both the sides by 4,


29 of 39 9/16/2011 10:20 AM

Thus, the average of the largest and smallest number is greater than theaverage of all four numbers.



If (a − b) < (c − d), then a + d < b + c

∴ a + d + a + d < a + d + b + c

Dividing both the sides by 4,

Thus, the average of the largest and smallest number is less than theaverage of all four numbers.


Thus, the question can be answered using either statement, independently ofthe other.

Hence, option 2.

24.3 Marks



What are the ages of three brothers?

The product of their ages is 21.A.The sum of their ages is not divisible by 3.B.

1) 1


30 of 39 9/16/2011 10:20 AM

2) 2

3) 3

4) 4


The product of the brothers' ages is 21.

There are two combinations that give this value i.e. (1, 3, 7) and (1, 1, 21).

Since a unique combination cannot be identified, the ages cannot be found.



The sum of their ages is not divisible by 3.

The ages cannot be calculated from this data. Thus, the question cannot be answered using statement B alone.


For the two combinations, the sum of the ages is 11 and 23 respectively.

Both these numbers are not divisible by 3.

Thus, both combinations are still valid.

Hence, the ages cannot be found.


Hence, option 4.

25.3 Marks




31 of 39 9/16/2011 10:20 AM


Two types of widgets, namely type A and B, are produced on a machine. Thenumber of machine hours available per week is 80. How many widgets of typeA must be produced?

One unit of the type A widget requires 2 machine hours and one unit of the type Bwidget requires 4 machine hours.

A.

The widget dealer wants to supply at least 10 units of type A widget per week and hewould not accept less than 15 units of type B widget.

B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the number of type A and type B widgets be a and b respectively.

The number of machine hours available is 80.


One type A widget requires 2 machine hours while one type B widget requires4 machine hours.

∴ 2a + 4b = 80

Since this is a linear equation in two variables, the value of a and b cannot befound.



a ≥ 10 and b ≥ 15

However, this does not give the exact value of A.



If the dealer makes the minimum number of widgets of each type, the timethat will be taken is:

10 units of type A require 20 hours.


32 of 39 9/16/2011 10:20 AM

15 units of type B require 60 hours.

This consumes all 80 hours available.

Thus 10 widgets of type A must be produced.

Hence, option 3.

26.3 Marks



What is the area of a regular hexagon?

The length of the boundary of the hexagon is 36 cm.A.The area of the hexagon is 6 times the area of an equilateral triangle formed on oneof the sides.

B.

1) 1

2) 2

3) 3

4) 4


The perimeter of the hexagon is 36 cm.

Therefore, the side of the hexagon is 6 cm.

One the side of a regular hexagon is known, the area can be easily found.



For any regular hexagon, the area is always 6 times the area of an equilateraltriangle formed on one of the sides of the hexagon.


33 of 39 9/16/2011 10:20 AM

Thus, this information does not provide the area of the hexagon.




Hence, option 1.

27.3 Marks



What is the price of one kg mangoes?

10 kgs of mangoes and two dozen oranges cost Rs. 252.A.2 kgs of mangoes can be bought in exchange for one dozen oranges.B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the cost of one kg mangoes be x and the cost of one dozen oranges be y.


10x + 2y = 252

Since this is a single linear equation in two variables, the value of x and ycannot be found.



34 of 39 9/16/2011 10:20 AM


2x = y

This is a single linear equation in two variables and so the value of x and ycannot be calculated.



Substitute the second equation in the first.

∴ 10x + 2(2x) = 252

∴ 14x = 252

∴ x = 18

Thus, the cost of one kg mangoes is Rs. 18


Hence, option 3.

28.3 Marks



Is the distance from the office to home less than the distance from the cinemahall to home?

The time taken to travel from home to the office is as much as the time taken fromhome to the cinema hall, both distances being covered without stopping.

A.

The road from the cinema hall to home is bad and the speed reduces as compared tothat on the road from home to the office.

B.

1) 1

2) 2


35 of 39 9/16/2011 10:20 AM

3) 3

4) 4


The time from home to office = time from home to cinema hall.

Thus, Distance ∝ Speed.

Since the relationship between the two speeds is not given, the two distancescannot be compared.



Speed from cinema hall to home < speed from home to office.

Since the relationship betwen the time taken on these two stretches is notknown, the two distances cannot be compared.


Using both the statements together.

Since time is constant, and the speed from home to the cinema hall is lessthan the speed from home to the office, the distance from home to thecinema hall is less than the distance from home to office.

Thus, the question can be answered by using both the statements togetherbut not by using either statement alone.

Hence, option 3.

29.3 Marks



If twenty sweets are distributed among some boys and girls such that each


36 of 39 9/16/2011 10:20 AM

girl gets two sweets and each boy gets three sweets, what is the number ofboys and girls?

The number of girls is not more than five.A.If each girl gets three sweets and each boy gets two sweets, the total number ofsweets required for the children will still be the same.

B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the number of boys and girls be B and G respectively.

2G + 3B = 20


G ≤ 5

If G = 1, B = 6

If G = 4, B = 4

Thus, two combinations of G and B are possible.

Hence, the number of boys and girls cannot be found.



3G + 2B = 20

∴ 2G + 3B = 3G + 2B

∴ G = B

Substituting this in any one of the two equations, you get, G = B = 4.

Thus, there are 4 boys and 4 girls.


Thus, the question can be answered using statement B alone but not by


37 of 39 9/16/2011 10:20 AM

using statement A alone.

Thus, the question can be answered by one the statements but not by theother.

Hence, option 1.

30.3 Marks



If the selling price were to be increased by 10%, the sales would reduce by10%. In what ratio would the profits change?

The cost price remains constant. A.The cost price increases by 10%.B.

1) 1

2) 2

3) 3

4) 4

Solution:If the original selling price is S and the sales is V, the total revenue is SV.

When the selling price becomes 1.1s and the sales reduce to 0.9V, the totalrevenue is 0.99SV.

Thus, the revenue decreases by 1%.

Using Statement A alone.

Let the cost price be C.

Hence, the old profit is SV − CV and the new profit is 0.99SV − 0.9CV.

However, this does not indicate the necessary profit ratio.



38 of 39 9/16/2011 10:20 AM


In the first case, the profit = (S − C) × V

In the second case, the profit = 1.1(S − C) × 0.9V = 0.99(S − C)V

Now, the required ratio can be found.




Hence, option 1.


39 of 39 9/16/2011 10:20 AM

1.3 Marks



Is segment PQ greater than segment RS?

PB > RE, BQ = ES A.B is a point on PQ and E is a point on RS.B.

1) 1

2) 2

3) 3

4) 4


If B is a point on PQ and E is a point on RS, then

PB + BQ > RE + ES

∴ PQ > RS

Since it is not known if B and E are on those segments, the above conclusionmay or may not be true.



B is a point on PQ and E is a point on RS.

However, this does not provide any other useful information.


Section I


1 of 31 9/16/2011 10:21 AM


Since it is known that B is a point on PQ and E is a point on RS, PQ > RS asseen from statament A.

Thus, the question can be answered using both the statements together, butnot by using either statement alone.

Hence, option 3.

2.3 Marks



Three boys had a few Coffee Bite toffees with them. The number of toffeeswith the second boy was four more than those with the first and the numberof toffees with the third boy was four more than those with the second. Howmany toffees were there in all?

The number of toffees with each of them is a multiple of 2.A.The first boy ate up four toffees from what he had and the second boy ate up sixtoffees from what had and the third boy gave them two toffees each from what hehad and the number of toffees remaining with each of them formed a geometricprogression.

B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the number of toffees with the 1st, 2nd and the 3rd boy be (n − 4), n and (n+ 4) respectively.


This statement does not provide any useful information.



2 of 31 9/16/2011 10:21 AM


The first, second and third boy now have (n − 8), (n − 6) and n toffeesrespectively.

(n − 8), (n − 6) and n are in G.P.

∴ (n − 6)2 = n(n − 8)

∴ n = 9




Hence, option 1.

3.3 Marks



Little Beau Peep lost her sheep. She couldn’t remember how many werethere. She knew that in the next year she would have 400 more sheep thanthe number she had last year. How many sheep were there?

The number of sheep last year was 20% more than the year before that and thissimple rate of increase continued to be the same for the next 10 years.

A.

The increase is compounded annually.B.

1) 1

2) 2

3) 3

4) 4


3 of 31 9/16/2011 10:21 AM

Solution:Let the number of sheep last year be x.


Since the number of sheep grows by 20% every year, the number of sheepthis year is 1.2x and the number of sheep next year is 1.44x.

∴ 1.44x = x + 400

∴ x = 909

Thus, she had 1091 sheep this year.



The rate of increase is not known.


Thus, the question can be answered using statement A alone but not byusing statament B alone.


Hence, option 1.

4.3 Marks



What will the total cost of creating a one foot border of tiles along the insideedges of a room be?

The room is 48 feet in length and 50 feet in breadth.A.Every tile costs Rs. 10.B.


4 of 31 9/16/2011 10:21 AM

1) 1

2) 2

3) 3

4) 4


Since no cost is known, the total tiling cost cannot be found.



Since the dimensions of the room and that of each tile are not known, thetotal tiling cost cannot be found.



Since the dimensions of an individual tile are not known, the total tiling costcannot be found.


Hence, option 4.

5.3 Marks



Ten boys go to a neighbouring orchard. Each boy steals a few mangoes.What is the total number of mangoes that they steal?

The first boy steals 4 mangoes, the fourth boy steals 16 mangoes, the eighth boysteals 32 mangoes and the tenth boy steals 40 mangoes.

A.

The first boy stole the minimum number of mangoes and the tenth boy stole themaximum number of mangoes.

B.


5 of 31 9/16/2011 10:21 AM

1) 1

2) 2

3) 3

4) 4


From the statement, it is possible that the number of mangoes stolen by thenth peron is 4n.

However, it is not given that the number of mangoes stolen forms a series.

Thus, the remaining 6 boys could have stolen any number of mangoes.



This does not provide any useful information regarding number of mangoesstolen.



The only additional information obtained by combining the two statements isthat the other six boys could have stolen anywhere between 5 and 39mangoes.

However, the actual number of mangoes stolen cnanot be obtained.


Hence, option 4.

6.3 Marks




6 of 31 9/16/2011 10:21 AM


If x, y and z are real numbers, is z - x even or odd?

xyz is odd.A.xy + yz + zx is even.B.

1) 1

2) 2

3) 3

4) 4


Given xyz is odd, it implies that each of x, y and z is odd.

If x and z are odd, then z – x is even.



Given xy + yz + xz is even, consider the following possibility.

If x is even and y is even, then even if z is odd or even, the given sum is even.

Hence, nothing can be concluded about z – x being odd or even.




Hence, option 1.

7.3 Marks


Mark (1) if the question can be answered by one of the statements, but not bythe other.Mark (2) if the question can be answered by usingeither statement, independently of the other.


7 of 31 9/16/2011 10:21 AM

Mark (3) if the question can be answered by using both statements together,but not by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

What is the value of x, if x and y are consecutive positive even integers?

(x − y)2 = 4A.

(x + y)2 < 100B.

1) 1

2) 2

3) 3

4) 4

Solution:Since x and y are consecutive positive even integers, x − y = ± 2


Considering the equation obtained from the data given in the question, thisstatement will always be true for any x and y that satisfy the above equation.



(x + y)2 < 100

Consider different sets of consecutive positive integers.

(2 + 4)2 = 36 < 100

(4 + 6)2 = 100

Thus, x has to be one out of 2 and 4.

However, it has been mentioned whether x is the greater or the lesser of thetwo integers.

Hence, a unique value of x cannot be found. Thus, the question cannot be answered using statement B alone.



8 of 31 9/16/2011 10:21 AM

Since statement A does not provide any additional data, this is the same asusing statement B alone.

Hence, the value of x still cannot be found.


Hence, option 4.

8.3 Marks



What is the profit percent?

The cost price is 80% of the selling price.A.The profit is Rs. 50.B.

1) 1

2) 2

3) 3

4) 4


Let the selling price be Rs. 100.

Hence, the cost price is Rs. 80 and the profit is Rs. 20

Therefore, the profit percent = (20/80) × 100 = 25%.



Though the profit is known, the cost price or selling price is not known.

Hence, the profit percent cannot be found.


9 of 31 9/16/2011 10:21 AM




Hence, option 1.

9.3 Marks



What is the area of the triangle?

Two sides are 41 cm each.A.The altitude to the third side is 9 cm long.B.

1) 1

2) 2

3) 3

4) 4


Though two sides are known, the third side or the angle between these twosides is not known.

Hence, the area cannot be found.


Using Statament B alone:

The area of a triangle cannot be found just using the altitude to a side, unlessthe triangle is equilateral in nature.


10 of 31 9/16/2011 10:21 AM

Nothing of that sort is known here.



Once both the statements are combined, the triangle can be drawn as shownbelow.

In the given triangle, ∠ADB = ∠ADC = 90°.

Thus, base BC = 2 × 40 = 80 cms.

Hence,

= 360 sq. cms.


Hence, option 3.

10.3 Marks




11 of 31 9/16/2011 10:21 AM

What is the price of a banana?

With Rs. 84, I can buy 14 bananas and 35 oranges.A.If the price of bananas is reduced by 50% then I can buy 48 bananas in Rs. 12.B.

1) 1

2) 2

3) 3

4) 4


Let the price of one banana be Rs. x and the price of an orange be Rs. y.

∴ 14x + 35y = 84

∴ 2x + 5y = 12

It is not given that the price of the banana or orange needs to be an integer.

Hence, there can be multiple solution sets possible.

Therefore, the price of a banana cannot be found.



I can buy 48 bananas in Rs. 12.

Hence, one banana costs Rs. 0.25 as per the new price.

This price is half of the old price.

Thus, the price of a banana is Rs. 0.5



Thus, the question can be answered by one statement but not by the other.

Hence, option 1.


12 of 31 9/16/2011 10:21 AM

11.3 Marks



What is the perimeter of the rectangle ABCD?

Area of the rectangle is 48 square units.A.Length of the diagonal is 10 units.B.

1) 1

2) 2

3) 3

4) 4


Area = Length × Breadth = 48

Multiple combinations such as (1, 48), (2, 24), (3, 16), (4, 12), (6, 8) arepossible.

Hence, the perimeter cannot be found.


Using Statement B alone.

Since the diagonal measures 10 units, (Length)2 + (Breadth)2 = 100

There can be multiple solutions to this equation.

Hence, the perimeter cannot be found.



Let l and b denote length and breadth of the given rectangle respectively.


13 of 31 9/16/2011 10:21 AM

lb = 48 and l2 + b2 = 100

(l2) +(b2) − 2lb =(l − b)2 = 100 − (2 × 48) = 4

∴ (l − b) = 2

l2 + b2 + 2lb = (l + b)2 = 100 + (2 × 48) = 196

∴ (l + b) = 14

∴ l = 8, b = 6

Thus, the perimeter is 28 units.


Hence, option 3.

12.3 Marks



What is the number x?

The L.C.M. of x and 18 is 36.A.The H.C.F. of x and 18 is 2.B.

1) 1

2) 2

3) 3

4) 4


LCM of x and 18 is 36.


14 of 31 9/16/2011 10:21 AM

The possible combinations are:

(i) LCM of 4 and 18 is 36.

(ii) LCM of 12 and 18 is 36.

(iii) LCM of 36 and 18 is 36.

Thus, there is no unique value for x.



HCF of x and 18 is 2.

The possible combinations are:

(i) HCF of 2 and 18 is 2.

(ii) HCF of 4 and 18 is 2.

(iii) HCF of 8 and 18 is 2.

and so on.

Thus, there is no unique value for x.



x × 18 = 36 × 2

∴ x = 72/18 = 4


Hence, option 3.

13.3 Marks




15 of 31 9/16/2011 10:21 AM


Is x + y – z + t even?

x + y + t is even.A.tz is odd.B.

1) 1

2) 2

3) 3

4) 4


x + y + t is even.

Hence, x + y − z + t becomes Even − z

If z is even, this difference will be even and vice versa.

Since z is not known, nothing can be said about the difference.



tz is odd.

This is possible when both t and z are odd.

However, nothing is known about x and y.

Hence, nothing can be said about the difference.



Since z is odd, x + y − z + t will become Even − Odd i.e. Odd.



16 of 31 9/16/2011 10:21 AM

Hence, option 3.

14.3 Marks



A tractor travelled a distance of 5 m. What is the radius of the rear wheel?

The front wheel rotates ‘N’ times more than the rear wheel over this distance.A.The circumference of the rear wheel is ‘t’ times that of the front wheel.B.

1) 1

2) 2

3) 3

4) 4


This simply means that the front wheel is smaller than the rear wheel.

Since the value of N and the radius of the front wheel is not known, theradius of the rear wheel cannot be found.



Since the value of t is not known, the two wheels cannot be compared.



Even when the two statements are combined, no numerical value is known.

Hence, the radius of the rear wheel cannot be found.


17 of 31 9/16/2011 10:21 AM


Hence, option 4.

15.3 Marks



What is the ratio of the two liquids A and B in the mixture finally, if these twoliquids kept in three vessels are mixed together? (The containers are of equalvolume).

The ratios of liquid A to liquid B in the first and second vessels is 3 : 5 and 2 : 3respectively.

A.

The ratio of liquid A to liquid B in vessel 3 is 4 : 3.B.

1) 1

2) 2

3) 3

4) 4


There is no data regarding the third vessel.

Hence, the ratio cannot be found.



There is no data regarding the first and second vessel.

Hence, the ratio cannot be found.




18 of 31 9/16/2011 10:21 AM

The ratio in which the liquids from the three vessels are taken is not known.

Hence, the required ratio cannot be found.


Hence, option 4.

16.3 Marks



If α, β are the roots of the equation ax2 + bx + c = 0, then what is the value of(α2 + β2)?

α + β = (−b/a)A.αβ = c/aB.

1) 1

2) 2

3) 3

4) 4


The sum of the roots is always (−b/a)

Hence, the required value cannot be found.



The sum of the roots is always (c/a)



19 of 31 9/16/2011 10:21 AM




Hence, option 3.

17.3 Marks



What is the cost price of the article?

After selling the article, a loss of 25% is incurred on the cost price.A.The selling price is three-fourths of the cost price.B.

1) 1

2) 2

3) 3

4) 4


S.P. = 0.75 × C.P.

Since neither the selling price nor the loss is known, the cost price cannot befound.


20 of 31 9/16/2011 10:21 AM



S.P. = 0.75 × C.P.

Since neither the selling price nor the loss is known, the cost price cannot befound.



Since both the statements provide the same information, the cost pricecannot be found.


Hence, option 4.

18.3 Marks



What is the Selling Price of the article?

The profit on Sales is 20%.A.The profit on each unit is 25% and the cost price is Rs. 250.B.

1) 1

2) 2

3) 3

4) 4


The profit on sales is 20%, but the actual profit is not known.


21 of 31 9/16/2011 10:21 AM



Cost Price = Rs. 250

Profit = 250/4 = Rs. 62.5

∴ Selling Price = 250 + 62.5 = Rs. 312.5




Hence, option 1.

19.3 Marks



How many different triangles can be formed?

There are 16 coplanar, straight lines.A.No two lines are parallel.B.

1) 1

2) 2

3) 3

4) 4


The number of parallel lines among the 16 given and the number of


22 of 31 9/16/2011 10:21 AM

intersection points is not known.

Hence, the number of triangles cannot be found.



Since the number of lines is not known, the number of triangles cannot befound.



There are 16 coplanar lines that are non-parallel.

There are two cases:

(i) If all lines intersect at the same point, then no triangle can be formed.

(ii) If all the lines intersect at different points, then several triangles can beformed, the number of which depends on the number of intersection points.

Thus, the number of triangles still cannot be found.


Hence, option 4.

20.3 Marks



What is the total worth of Lakhiram’s assets?

A compound interest at 10% on his assets, followed by a tax of 4% on the interest,fetched him Rs. 1,500 this year.

A.

The interest is compounded once every four months.B.

1) 1


23 of 31 9/16/2011 10:21 AM

2) 2

3) 3

4) 4


It is not known whether the 10% interest is on a annual or non-annual basis.

Also, it is not known if this year is the first year of the interest or not. Sincethis is a case of compound interest, the interest will change every year.

Hence, the worth cannot be calculated.



Nothing is known about the rate, principal, tenure etc.




Whether the interest of 10% is on a per annum or half yearly or quarter yearlybasis is still not known.

Also, it is not known whether the given year is this year or not.



Hence, option 4.

21.3 Marks




24 of 31 9/16/2011 10:21 AM


How old is Sachin in 1997?

Sachin is 11 years younger than Anil whose age will be a prime number in 1998.A.Anil’s age was a prime number in 1996.B.

1) 1

2) 2

3) 3

4) 4


Anil’s age could be any prime number greater than 11 (13, 17, 19, 23, 29 ...)in 1998.

Hence, a unique value of Sachin's age cannot be found.



Since there is no mention of Sachin, Sachin's age cannot be found.



Anil’s age is a prime number in 1996 and 1998, thus his age in those twoyears could be 11 and 13, 17 and 19, 29 and 31 and so on.

Thus, Sachin’s age in 1997 can have multiple possible values and so cannotbe uniquely determined.


Hence, option 4.

22.3 Marks




25 of 31 9/16/2011 10:21 AM


What is the number of type-2 widgets produced, if the total number ofwidgets produced is 20,000?

If the production of type-1 widgets increases by 10% and that of type-2 decreases by6%, the total production remains the same.

A.

The ratio in which type-1 and type-2 widgets are produced is 2 : 1.B.

1) 1

2) 2

3) 3

4) 4


Since the original production of any one type of widget is not known, thenumber of type-2 widgets cannot be found.

Also, it is not known if there are any types of widgets also beingmanufactured.



It is not known if there are other types of widgets also being manufactured.




Even when the statements are combined, it is not known whether there areother types of widgets produced.


Hence, option 4.

23.3 Marks

Each question is followed by two statements, A and B. Select the correct


26 of 31 9/16/2011 10:21 AM

option based on the following instructions:


What is the value of a3 + b3?

a2 + b2 = 22A.ab = 3B.

1) 1

2) 2

3) 3

4) 4

Solution:a3 + b3 = (a + b)(a2 − ab + b2)


Since the value of a + b and ab is not known, the required value cannot befound.



Since the value of a + b and a2 + b2 is not known, the required value cannotbe found.



Now every term apart from a + b is known.

(a + b)2 = a2 + b2 + 2ab

Thus, (a + b)2 can be found.


27 of 31 9/16/2011 10:21 AM

But, (a + b) will have two values, positive and negative.

Hence, a3 + b3 will also have two values.

Thus, a unique value cannot be found.


Hence, option 4.

From either statement I alone or statement II alone, we cannot find the valuesof a and b for there is only one equation in each statement and there are twounknowns.

Combining statements I and II, we have,

a2 + b2 = 22 …(i)

ab = 3 …(ii)

Substituting the value of a from equation (ii) in (i), we get

Solving equation (iii) will give us more than one value for a.

Hence, the combination of statements I and II also will not give us a uniquesolution.

Hence, option 4.

24.3 Marks



Is the three digit number completely divisible by 99?

The number is divisible by 9 and 11 simultaneously.A.If the digits of the number are reversed, the number is divisible by 9 and 11.B.


28 of 31 9/16/2011 10:21 AM

1) 1

2) 2

3) 3

4) 4


The prime factors of 99 are 9 and 11.

Since the number is simultaneously divisible by 9 and 11, the number isdivisible by 99.



If the number obtained by reversing the digits is divisible by 99, then theoriginal number is also divisible by 99.

Let us consider the original number to be xyz

If zyx has to be divisible by 9, then z + y + x = 9n.

z + y + x is the same as x + y + z.

∴ x + y + z = 9n.

Thus, xyz is divisible by 9. If zyx has to be divisible by 11, then (z + x − y) should either be 0 or amultiple of 11.

(z + x − y) is the same as (x + z − y).

Thus, (x + z − y) is either 0 or a multiple of 11.

Thus, xyz is divisible by 11.

Thus, xyz is divisible by 9 and 11 i.e. 99.


Thus, the question can be answered using either statement alone.


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Hence, option 2.

25.3 Marks



A person is walking from Mali to Pali, which lies to its North-East. What is thedistance between Mali and Pali?

When the person has covered 1/3rd of the distance, he is 3 km East and 1 km Northof Mali.

A.

When the person has covered 2/3rd of the distance, he is 6 km East and 2 km Northof Mali.

B.

1) 1

2) 2

3) 3

4) 4


Since the person is 3 km East and 1 km North of Mali, the distance betweenthis point and the starting point can be found using Pythagoras Theorem.

This distance is 1/3rd of the total distance.

Hence, the total distance can be found.



Since the person is 6 km East and 2 km North of Mali, the distance betweenthis point and the starting point can be found using Pythagoras Theorem.

This distance is 2/3rd of the total distance.

Hence, the total distance can be found.


30 of 31 9/16/2011 10:21 AM



Hence, option 2.


31 of 31 9/16/2011 10:21 AM

1.3 Marks



What is the value of x and y?

3x + 2y = 45A.10.5x + 7y = 157.5B.

1) 1

2) 2

3) 3

4) 4


3x + 2y = 45.

Since this is a single equation in two variables, the value of x and y cannot befound.



10.5x + 7y = 157.5.

Since this is a single equation in two variables, the value of x and y cannot befound.



The second equation, if divided by 3.5 gives the same co-efficients as the first

Section I


1 of 20 9/16/2011 10:21 AM

equation.

Thus, the two equations cannot be solved to get a value for x and y.


Hence, option 4.

2.3 Marks



Three friends, P, Q and R are wearing hats, either black or white. Eachperson can see the hats of the other two persons. What is the colour of P’shat?

P says that he can see one black hat and one white hat.A.Q says that he can see one white hat and one black hat.B.

1) 1

2) 2

3) 3

4) 4


Since the number of black and white hats in all is not specified, the colour ofP's hat cannot be determined.



Since the number of black and white hats in all is not specified, the colour ofP's hat cannot be determined.



2 of 20 9/16/2011 10:21 AM


There are two cases possible:

Case 1: Q is wearing a white hat.

Here, both P and Q see R wearing the black hat.

Hence, the other white hat is worn by P.

Thus, P's hat is white.

Case 2: Q is wearing a black hat.

Here, both P and Q see R wearing the white hat.

Hence, the other black hat is worn by P.

Thus, P's hat is black.

Thus, the colour of P's hat can still not be determined.


Hence, option 4.

3.3 Marks



What is the speed of the car?

The speed of the car is 10 kmph more than that of the motor-cycle.A.The motor-cycle takes 2 hours more than the car to cover 100 km.B.

1) 1

2) 2

3) 3

4) 4


3 of 20 9/16/2011 10:21 AM

Solution:Let the speed of the car and the motor-cycle be c and m kmph respectively.


c = m + 10

Since the speed of the motor-cycle or the time required to cover a constantdistance is not known, the speed of the car cannot be calculated.



(100/m) − (100/c) = 2

Since the speed of the motor-cycle is not known, the speed of the car cannotbe calculated.



c = m + 10 …(i)

(100/m) − (100/c) = 2 ...(ii)

Substituting the value of m in terms of c in equation (ii),

c2 − 10c – 500 = 0

Solving the above quadratic question, you get a unique answer for c.


Hence, option 3.

4.3 Marks




4 of 20 9/16/2011 10:21 AM


What is the cost price of the chair?

The chair and the table are sold, respectively, at profits of 15% and 20%.A.If the cost price of the chair is increased by 10% and that of the table is increased by20%, the profit reduces by Rs.20.

B.

1) 1

2) 2

3) 3

4) 4


Though the profit percentages are known, neither the actual profit nor theactual selling price is known.

Hence, the cost price cannot be calculated.



The change (if any) in the selling price is not known.

Also, the original profit is not known.

Hence, the cost price cannot be calculated.



There is no information on the impact on selling price. The original profit isalso not known.

Hence, the cost price cannot be found.


Hence, option 4.


5 of 20 9/16/2011 10:21 AM

5.3 Marks



After what time will the two persons, Tez and Gati, meet while moving aroundthe circular track? Both of them start at the same point and at the same time.

Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s andincreases his speed by 0.5 m/s at the end of every second thereafter.

A.

Gati can complete one entire round in exactly 10 seconds.B.

1) 1

2) 2

3) 3

4) 4


Since the circumference of the track is not known, the time cannot becalculated.



Since the circumference of the track is not known, the time cannot becalculated.



The circumference can be found since Gati completes one round in 10seconds and her speed increases by 0.5 m/s.

However, the direction in which both of them are moving is not known.

Thus, the time cannot be found.


6 of 20 9/16/2011 10:21 AM


Hence, option 4.

6.3 Marks



In the figure below, if ∠YBC = ∠CAX = ∠YOX = 90°, then find the length ofAB.

Radius of the arc is givenA.OA = 5B.

1) 1

2) 2

3) 3

4) 4

Solution:OC is the radius of the quarter circle.


If the figure OACB is a square then, AB = OC.

Knowing OC we can calculate AB.


7 of 20 9/16/2011 10:21 AM

If OACB is rectangle then, AB = OC.

Knowing OC we can calculate AB.



It is not known whether OACB is a square or a rectangle.

Since nothing is known about OACB, AB cannot be calculated.


Thus, the question can be answered by using one of the statement, but notby other.

Hence, option 1.

7.3 Marks



Is n odd?

n is divisible by 5, 7 and 9.A.0 < n < 400B.

1) 1

2) 2

3) 3

4) 4



8 of 20 9/16/2011 10:21 AM

Since n is divisible by 5, 7 and 9, n is also divisible by their L.C.M i.e. 315.

Hence, n can be 315, 630, 945 and so on.

Thus, n can be even or odd.



0 < n < 400.

Thus, n can be even or odd.



When both the statements are combined, there can be only one possiblevalue of n.

∴ n = 315.

Thus, n is odd.


Hence, option 3.

8.3 Marks



A.

B.


9 of 20 9/16/2011 10:21 AM

1) 1

2) 2

3) 3

4) 4


This result can be obtained for both a + b and b2 − a.

Thus, the relationship between a and b cannot be established.



The required value = (2 + 3)/2 = 2.5




Hence, option 1.

9.3 Marks



Radha and Rani appeared for an examination. What was the total number ofquestions?

Radha and Rani together solved 20% of the paper.A.

Radha alone solved 3/5th of the paper solved by RaniB.


10 of 20 9/16/2011 10:21 AM

1) 1

2) 2

3) 3

4) 4


Radha and Rani together solved 20% of the paper.

Since no other information is given, the total number of questions cannot befound.



The number of questions solved by Radha and Rani is in the ratio 3 : 5

However, the total number of questions cannot be found.



Radha and Rani together solved 8x questions and so the total number ofquestions is 40x.

Since x is not known, the total number of questions cannot be found.

Thus, the questions cannot be answered by either of the statements.

Hence, option 4.

10.3 Marks



What is the value of a?


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Ratio of a and b is 3 : 5 where b is positive.A.Ratio of 2a and b is 12 : 10 where a is positive.B.

1) 1

2) 2

3) 3

4) 4


Since the value of b is not known, the value of a cannot be found.



Since the value of b is not known, the value of a cannot be found.



Both statements lead to the same ratio.

Now, since b is still unknown, the value of a cannot be found.


Hence, option 4.

11.3 Marks


Mark (1) if the question can be answered by one of the statements, but not bythe other.Mark (2) if the question can be answered by usingeither statement, independently of the other.Mark (3) if the question can be answered by using both statements together,


12 of 20 9/16/2011 10:21 AM

but not by either statement alone.Mark (4) if the question cannot be answered by either of the statements.

In a group of 150 students, find the number of girls.

Each girl was given 50 paisa, while each boy was given 25 paisa to purchase goodstotalling Rs. 49.

A.

Girls and boys were given 30 paisa each to buy goods totalling Rs. 45.B.

1) 1

2) 2

3) 3

4) 4

Solution:Let the number of boys and girls be respectively b and g.

b + g = 150 ... (i)


0.25b + 0.5g = 49 ... (ii)

On solving (i) and (ii), g = 46.

Thus, there are 46 girls.



0.3b + 0.3g = 45

If this equation is divided by 0.3, you get (i).

Thus, now there is only one equation and two unknowns.

Hence, the number of girls cannot be found.





13 of 20 9/16/2011 10:21 AM

Hence, option 1.

12.3 Marks



There are four envelope E1, E2, E3, E4 in which one was supposed to putletters L1, L2, L3, L4 meant for persons C1, C2, C3, C4 respectively but bymistake the letters got jumbled up and went in wrong envelopes. Now if C2 isallowed to open an envelope at random, then how will he identify theenvelope containing the letter for him?

L2 has been put in E1.A.The letter belonging to C3 has gone in the correct envelope.B.

1) 1

2) 2

3) 3

4) 4


If L2 is put in E1, then C2 will know that his letter is in the envelop E1.



If the letter L3 is put in E3, the other three letters can go into any of the threeremaining envelopes.

Hence, C2 cannot identify the envelope.




14 of 20 9/16/2011 10:21 AM


Hence, option 1.

13.3 Marks



There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4.If an even numbered rack has to contain an odd numbered book and an oddnumbered rack contains an even numbered book then what is the position ofbook 4?

The second book has been put in the third rack.A.The third book has been put in the second rack.B.

1) 1

2) 2

3) 3

4) 4

Solution:An odd numbered rack has to contain an even numbered book and viceversa.


Since the second book is in the third rack, the fourth book can only be in thefirst rack.



The third book is in the second rack.

The fourth book cab in either the first or third rack. It's exact position cannot


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be found.




Hence, option 1.

14.3 Marks



What is the value of X in terms of a?

Arithmetic mean of X and Y is a while the geometric mean is also a.A.

B.

1) 1

2) 2

3) 3

4) 4


Solving the equations (i) and (ii), X = a



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a is not mentioned in all.




Hence, option 1.

15.3 Marks



Two concentric circles C1 and C2 have radii r1 and r2. If C1 fully encloses C2,what is the radius of C1?

The difference of their circumference is k cm.A.The difference of their areas is m sq. cm.B.

1) 1

2) 2

3) 3

4) 4

Solution:r1 > r2


2π(r1 − r2) = k ... (i)

The value of r1 cannot be found from this.


17 of 20 9/16/2011 10:21 AM



π(r12 − r22) = m ... (ii)

The value of r1 cannot be found from this.



If you divide (ii) by (i), you get an equation in terms of r1 + r2.

Taking this equation and (i), the value of r1 can be found.


Hence, option 3.

16.3 Marks



A circle circumscribes a square. What is the area of the square?

Radius of the circle is given.A.Length of the tangent from a point 5 cm away from the centre of the circle is given.B.

1) 1

2) 2

3) 3

4) 4


The diameter of the circle is the same as the diagonal of the square.


18 of 20 9/16/2011 10:21 AM

Since the radius of the circle is given, the diameter of the circle andconsequently, the diagonal of the square can be found.

Using this, the side of the square and the area of the square can be found.



The distance between the tangent and the centre of the circle is nothing butthe radius of the circle.

Once the radius of the circle is known, one can find the side of the squareand the area of the square.



Hence, option 2.

17.3 Marks



The average weight of students in a class is 50 kg. What is the number ofstudents in the class?

The heaviest and the lightest members of the class weigh 60 kg and 40 kgrespectively.

A.

Exclusion of the heaviest and the lightest members from the class does not changethe average weight of the student.

B.

1) 1

2) 2

3) 3

4) 4


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Solution:Let the number of students in the class be n. Thus, the total weight of thestudents is 50n.


Two members weigh 100 kg together.

The weight of the remaining n − 2 students is 50n − 100. Thus, the average isstill 50.

This does not give the total number of students.

Thus the question cannot be answered using statement A alone.


This is the same as the information given in statement A.



Both the statements give the same information.

Hence, the total number of students cannot be found.


Hence, option 4.

18.3 Marks



A small storage tank is spherical in shape. What is the storage volume of thetank?

The wall thickness of the tank is 1 cm.A.When the empty spherical tank is immersed in a large tank filled with water, 20litres of water overflow from the large tank.

B.


20 of 20 9/16/2011 10:21 AM

1.3 Marks

Choose 1; if the question can be answered by using one of the statementsalone, but cannot be answered using the other statement alone.

Choose 2; if the question can be answered by using either statement alone.

Choose 3; if the question can be answered by using both statements together,but cannot be answered using either statement alone.

Choose 4; if the question cannot be answered even by using both statementstogether.

Consider three real numbers, X, Y and Z. Is Z the smallest of thesenumbers?

X is greater than at least one of Y and Z.A.Y is greater than at least one of X and Z.B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4

Solution:From statement A, there are four possibilities.

X > Y > Z

X > Z > Y

Z > X > Y

Y > X > Z

∴ This statement alone is not sufficient.

From statement B, there are four possibilities.

Y > X > Z

Y > Z > X

Section I


1 of 35 9/16/2011 10:29 AM

X > Y > Z

Z > Y > X


Using both statements together we get,

Either X > Y > Z or Y > X > Z.

In both the cases Z is smallest.

Hence, option 3.

2.3 Marks





Let X be a real number. Is the modulus of X necessarily less than 3?

X(X + 3) < 0A.X(X – 3) > 0B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4

Solution:From statement A

X (X + 3) < 0

∴ –3 < X < 0

∴ |X| < 3

∴ Statement A alone is sufficient.


2 of 35 9/16/2011 10:29 AM

From statement B

X(X – 3) > 0

X < 0 or X > 3

This statement does not give a unique answer.

Hence, option 1.

3.3 Marks





How many people are watching TV programme P?

Number of people watching TV programme Q is 1000 and number of people watchingboth the programmes, P and Q, is 100.

A.

Number of people watching either P or Q or both is 1500.B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4

Solution:From Statement A

Q = 1000

P ∩ Q = 100

This doesn’t gives any information regarding how many people are watchingTV programme P

From Statement B


3 of 35 9/16/2011 10:29 AM

P ∪ Q = 1500

This statement alone is not sufficient.

Let’s combine the information in both the statements.

∴ P ∪ Q = P + Q − P ∩ Q

∴ 1500 = P + 1000 – 100

∴ P = 600

Hence, option 3.

Alternatively

By combining both the statements together we can arrive at the above Venndiagram which gives the number of people watching programme P.

Hence, option 3.

4.3 Marks





Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR +


4 of 35 9/16/2011 10:29 AM

RQ?

Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.A.Diameter of the circumscribed circle of the triangle PQR is equal to 26 cm.B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4


PF = PR – FR = PR – OD = PR – 5

QD = QR – DR = QR – OF = QR – 5

∵ PE = PF and QE = QD

∴ PE = PR – 5 and QE = QR – 5

∴ PQ = PE + QE = PR – 5 + QR – 5

∴ PR + QR = PQ + 10

This statement alone is not sufficient to find PR + RQ.

From Statement B


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Diameter of the circumscribing circle = hypotenuse of the triangle

∴ PQ = 26

∵ PR2 + RQ2 = PQ2

But this does not give the value of PR + RQ.


Let’s combine both the statements.

∴ PR + QR = PQ + 10 = 26 + 10 = 36

Hence, option 3.

5.3 Marks





Harshad bought shares of a company on a certain day, and sold them thenext day. While buying and selling he had to pay to the broker one percent ofthe transaction value of the shares as brokerage. What was the profit earnedby him per rupee spent on buying the shares?

The sales price per share was 1.05 times that of its purchase price.A.The number of shares purchased was 100.B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4

Solution:From Statement A

The cost of buying the shares for Harshad is


6 of 35 9/16/2011 10:29 AM

CP + 0.01 CP = 1.01 CP

The cost of selling the shares for Harshad is

SP – 0.01 SP = 0.99 SP

∴ Profit = Cost of selling – Cost of buying

= 0.99 SP – 1.01 CP

∵ SP = 1.05 CP

Profit = (0.99 × 1.05 CP) – 1.01 CP

= 0.0295 CP

∴ Profit earned per rupee spent on buying the shares is Rs 0.0295.

From the number of shares given in the statement B, we cannot concludeanything.

Hence, option 1.

6.3 Marks





For any two real numbersa ⊕ b = 1 if both a and b are positive or both a and b are negative. = –1 if one of the two numbers a and b is positive and the othernegative.What is (2 ⊕ 0) ⊕ (–5 ⊕ –6)?

a ⊕ b is zero if a is zero.A.a ⊕ b = b ⊕ aB.

[CAT 2000]

1) 1

2) 2


7 of 35 9/16/2011 10:29 AM

3) 3

4) 4

Solution:(2 ⊕ 0) ⊕ (–5 ⊕ –6)

= (2 ⊕ 0) ⊕ 1

From statement A

(0 ⊕ 2) = 0 but we don’t know the value of (2 ⊕ 0).

∴ Statement A alone is not sufficient to answer the question.

From statement B

(2 ⊕ 0) = (0 ⊕ 2)

∴ Statement B alone is not sufficient to answer the question.

After combining both the statements, we get,

(2 ⊕ 0) = (0 ⊕ 2) = 0

∴ (2 ⊕ 0) ⊕ (–5 ⊕ –6)

= (2 ⊕ 0) ⊕ 1

= 0 ⊕ 1

= 0

∴ Both the statements are required to answer the question.

Hence, option 3.

7.3 Marks






8 of 35 9/16/2011 10:29 AM

There are two straight lines in the x-y plane with equations ax + by = c , dx +ey = f. Do the two straight lines intersect?

a, b, c, d, e and f are distinct real numbers.A.c and f are non-zero.B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4

Solution:Statement A implies that a, b, c, d, e, f are distinct real numbers.

∴ Statement A alone is not sufficient.

Statement B implies that the equations are not homogenous equations.

∴ Statement B is also not sufficient.

Even after combining both the statements the above condition is not clear.

∴ We cannot be sure whether the lines are intersecting or parallel.

Hence, option 4.

8.3 Marks





O is the centre of two concentric circles. ae is a chord of the outer circle and itintersects the inner circle at point; b and d. c is a point on the chord in


9 of 35 9/16/2011 10:29 AM

between b and d. What is the value of ac/ce?

bc/cd = 1A.A third circle intersects the inner circle at b and d and the point c is on the linejoining the centres of the third circle and the inner circle.

B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4


bc = cd

If c is the midpoint of bd it would also be midpoint of ae because circles areconcentric.

∴ ac = ce

∴ The question can be answered using statement A alone.

From Statement B


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If c is the point on the line joining the two centres, it has to bisect the chordbd.

∴ c will also bisect the chord ae as the circles are concentric.

∴ ac = ce

∴ The question can be answered using statement B alone also.

Hence, option 2.

9.3 Marks





Ghosh Babu has decided to take a non-stop flight from Mumbai toNo-man’s-land in South America. He is scheduled to leave Mumbai at 5 am,Indian Standard Time on December 10, 2000. What is the local time atNo-man’s-land when he reaches there?

The average speed of the plane is 700 kilometres per hour.A.The flight distance is 10,500 kilometres.B.

[CAT 2000]

1) 1

2) 2

3) 3


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4) 4

Solution:By combining both the statements we can get the duration of the flight. Butfor the arrival time we should have the information regarding the time zonedifference of Mumbai and No man’s land.

Hence, option 4.

10.3 Marks





What are the ages of two individuals, X and Y?

The age difference between them is 6 years.A.The product of their ages is divisible by 6.B.

[CAT 2000]

1) 1

2) 2

3) 3

4) 4


X – Y = 6

From statement B

XY is divisible by 6.

∵ There are many possible values for example (12, 6), (18, 12), (24, 18) ...

∴ The question cannot be answered even by combining both the statements.

Hence, option 4.


12 of 35 9/16/2011 10:29 AM

11.3 Marks





What are the values of m and n?

n is an even integer, m is an odd integer, and m is greater than n.A.Product of m and n is 30.B.

[CAT 2001]

1) 1

2) 2

3) 3

4) 4

Solution:Statement A doesn’t provide any specific values of m and n.



m × n = 30 = 1 × 30 = 2 × 15 = 3 × 10 = 5 × 6

We cannot say what the values of m and n are.

∴ Statement B alone is also not sufficient to answer the question.

If we combine both the statements A and B together, then we have only onepossibility m = 15 and n = 2

∴ We have answered the question using both the statements A and Btogether.

Hence, option 3.

Note: Negative integers are not considered as Even or Odd.


13 of 35 9/16/2011 10:29 AM

12.3 Marks





Is Country X's GDP higher than country Y's GDP?

GDPs of the countries X and Y have grown over the past five years at compoundedannual rate of 5% and 6% respectively.

A.

Five years ago, GDP of country X was higher than that of country Y.B.

[CAT 2001]

1) 1

2) 2

3) 3

4) 4

Solution:Statement A does not give us the actual values of their GDPs 5 years ago.


We know that GDP of country X is greater than that of Y but we do not knowby how much it is greater.

Even after combining both the statements the question cannot be answered.

Hence, option 4.

13.3 Marks






14 of 35 9/16/2011 10:29 AM

What is the value of X?

X and Y are unequal even integers, less than 10, and X/Y is an odd integer.A.X and Y are even integers, each less than 10, and product of X and Y is 12.B.

[CAT 2001]

1) 1

2) 2

3) 3

4) 4


∵ Both have to be even numbers, the only possibility is X = 6 and Y = 2

∴ Statement A alone is sufficient to answer the question.


12 = 1 × 12 = 2 × 6 = 3 × 4

∵ Both are even integers and less than 10, the possible set of values of Xand Y are (2, 6) and (6, 2).

∴ X is either 2 or 6.

∴ No unique solution can be found using statement B alone.

Hence, option 1.

Note: Negative integers are not considered as Even or Odd.

14.3 Marks





On a given day a boat ferried 1500 passengers across the river in twelve


15 of 35 9/16/2011 10:29 AM

hours. How many round trips did it make?

The boat can carry two hundred passengers at any time.A.It takes 40 minutes each way and 20 minutes of waiting time at each terminal.B.

[CAT 2001]

1) 1

2) 2

3) 3

4) 4

Solution:Statement A only gives the maximum capacity of the boat.

∴ The number of trips cannot be calculated.



Time required to make one round trip = 40 + 40 + 40 = 120 minutes = 2 hours

∴ The total number of trips made = 12/2 = 6

∴ Statement B alone is sufficient to answer the question.

Hence, option 1.

15.3 Marks





What will be the time for downloading software?

Transfer rate is 6 Kilobytes per second.A.The size of the software is 4.5 megabytes.B.


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[CAT 2001]

1) 1

2) 2

3) 3

4) 4

Solution:Statement A alone is not sufficient because it gives only the rate at whichdata is transferred but it does not give the size of the software.

Statement B alone is not sufficient because it gives only the size of thesoftware but it does not give the rate of data transfer.

Combining both the statements A and B together, we can get the time todownload.

∵ Time required for data transfer = (Size of the software)/(Rate of datatransfer)

Hence, option 3.

16.3 Marks





A square is inscribed in a circle. What is the difference between the area ofthe circle and that of the square?

The diameter of the circle is 25 cm.A.

The side of the square is 25 cm.B.

[CAT 2001]

1) 1

2) 2

3) 3


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4) 4


∵ Diameter of the circle = Diagonal of the square

∴ Area of the square can be computed and thus the required difference.

∴ Statement A alone is sufficient to answer the question.


∵ Diagonal of the square = × side = Diameter of the circle

∴ Area of the circle can be computed and thus the required difference.

∴ Statement B alone is also sufficient to answer the question.

∴ We can answer the question using either statement alone.

Hence, option 2.

17.3 Marks





Two friends, Ram and Gopal, bought apples from a wholesale dealer. Howmany apples did they buy?

Ram bought one-half the number of apples that Gopal bought.A.The wholesale dealer had a stock of 500 apples.B.

[CAT 2001]

1) 1

2) 2

3) 3

4) 4


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Solution:Statement A simply gives the ratio of apples between Ram and Gopal.

∴ Statement A is not alone sufficient to answer the question.

Statement B doesn’t provide any information related to number of applesbought by Ram and Gopal.

Even after combining both the statements A and B together, the questioncannot be answered.

Hence, option 4.

18.3 Marks

Each question is followed by two statements A and B. Answer each questionusing the following instructions:

Answer (1) if the question can be solved by any one of the statements, but notthe other one.Answer (2) if the question can be solved by using either of the two statements.Answer (3) if the question can be solved by using both the statementstogether and not by any one of them.Answer (4) if the question cannot be solved with the help of the given dataand more data is required.

In a hockey match, the Indian team was behind by 2 goals with 5 minutesremaining. Did they win the match?

Deepak Thakur, the Indian striker scored 3 goals in the last 5 minutes of the match.A.Korea scored a total of 3 goals in the match.B.

[CAT 2002]

1) 1

2) 2

3) 3

4) 4

Solution:From statement A alone, it is not clear whether Korea too scored in the last 5minutes or not.

From statement B alone, it is not clear whether India scored in the last 5minutes or not.

Using both the statements, there are two cases possible:


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Case 1:

In this case, the match ended in a draw.

Case 2:

In this case, India wins the match.

∴ Even after combining both the statements, we cannot say whether Indiawon the match or not.

Hence, option 4.

19.3 Marks



Four students were added to a dance class. Would the teacher be able todivide her students evenly into a dance team (or teams) of 8?

If 12 students were added, then the teacher could put everyone in teams of 8without any left overs.

A.

The number of students in the class is currently not divisible by 8.B.

[CAT 2002]

1) 1

2) 2

3) 3

4) 4


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Solution:Consider statement A:

Let x be the total number of students present in the class.

∵ (x + 12) − (x + 4) = 8

∴ If (x + 12) is divisible by 8, then (x + 4) too is divisible by 8.

Statement A alone is sufficient to answer the question.

From statement B alone, we cannot conclude anything.

Hence, option 1.

20.3 Marks



Is x = y?

B. (x − 50)2 = (y − 50)2

[CAT 2002]

1) 1

2) 2

3) 3

4) 4



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∴ (x + y)2 = 4xy

∴ x2 + y2 + 2xy − 4xy = 0

∴ (x − y)2 = 0

∴ x = y


Consider statement B:

(x – 50)2 = (y – 50)2

∴ Either (x − 50) = (y − 50) or (x − 50) = −(y − 50)

∴ Either x = y or x + y = 100, which gives infinite values for x and y.

∴ Statement B alone is not sufficient.

Hence, option 1.

21.3 Marks

Each question is followed by two statements A and B. Answer each questionusing the following instructions.Mark (1) if the question can be answered by using statement A alone but notby using statement B alone.Mark (2) if the question can be answered by using statement B alone but notby using statement A alone.Mark (3) if the question can be answered by using both the statementstogether but not by using either of the statements alone.Mark (4) if the question cannot be answered on the basis of the twostatements.

A dress was initially listed at a price that would have fetched the store a profitof 20% on the wholesale cost. What was the wholesale cost of the dress?

After reducing the listed price by 10% the dress was sold for a net profit of 10dollars.

A.

The dress was sold for 50 dollars.B.

[CAT 2002]

1) 1

2) 2

3) 3

4) 4


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Solution:Let 100x be the wholesale cost of the dress.

∴ List price of the dress = 120x

Consider statement A:

Selling Price = 0.9 × List Price = 0.9 × 120x = 108x

Now, Selling Price – Cost Price = Profit

∴ (108x) − (100x) = 10

∴ x = 10/8

∴ Wholesale Cost = 100x = Rs. 125



This gives the selling price of the dress but it is not mentioned whether anydiscount is provided on the list price or not.


Hence, option 1.

22.3 Marks



Is 500 the average (arithmetic mean) score of the GMAT?

Half of the people who take GMAT score above 500 and half of the people scorebelow 500.

A.

The highest GMAT score is 800 and the lowest score is 200.B.

[CAT 2002]


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1) 1

2) 2

3) 3

4) 4


This statement alone does not give sufficient information as we do not knowhow much above/below 500 these students scored.

For example, it is possible that one student scored 800, one scored 750, thethird scored 450, while the last scored 200.Then, average = (800 + 750 + 450 + 200)/4 = 550 ≠ 500


Using this statement alone, we cannot say whether 500 is the average scoreof GMAT. The previous example can be used here as well.

Combining both statements together:

Even now, we cannot determine the average. (Again, the above example canbe used.)

Hence, option 4.

23.3 Marks



Is |x − 2| < 1?

|x| > 1A.|x − 1| < 2B.

[CAT 2002]


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1) 1

2) 2

3) 3

4) 4

Solution:|x − 2| < 1


|x| > 1

x < −1 or x > 1

For x = 1.5, |x − 2| < 1 is true.

For x = 4, |x − 2| < 1 is false.



|x − 1| < 2

−2 < x − 1 < 2

−1 < x < 3

For −1 < x < 1, |x − 2| < 1 is false.

For 1 < x < 3, |x − 2| < 1 is true.


Consider both the statements:

We have, 1 < x < 3

For this range, |x − 2| < 1 is true.

∴ Both the statements combined together are sufficient to answer thequestion.

Hence, option 3.


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24.3 Marks



Members in a club either speak French or Russian or both. Find the numberof members in a club who speak only French.

There are 300 members in the club and the number of members who speak bothFrench and Russian is 196.

A.

The number of members who speak only Russian is 58.B.

[CAT 2002]

1) 1

2) 2

3) 3

4) 4

Solution:Let F represent the set of members speaking French and R represent the setof members speaking Russian.

Also, let x represent the number of members speaking only French.


Here, total number of members = 300


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∴ Number of members who speak only Russian = 300 – 196 – x = 104 – x

However, we cannot find the value of x.



We are given that the number of members speaking Russian = 58


Consider both statements together:

We have, 104 – x = 58

∴ Number of members speaking only French, x = 104 – 58 = 46

∴ The question can be answered using both statements together.

Hence, option 3.

25.3 Marks



A sum of Rs. 38,500 was divided among Jagdish, Punit and Girish. Whoreceived the minimum amount?


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Jagdish received 2/9 of what Punit and Girish together received.A.Punit received 3/11 of what Jagdish and Girish together received.B.

[CAT 2002]

1) 1

2) 2

3) 3

4) 4


Jagdish : (Punit + Girish) = 2 : 9

However, we don’t know the percentage distribution between Punit andGirish.



Punit : (Jagdish + Girish) = 3 : 11

However, we do not know the percentage distribution between Jagdish andGirish.


Consider both statements together:

Jagdish = 18.18% of the total amount

Punit = 21.4% of the total amount

Girish = 100 − 18.18 − 21.4 = 60.42% of the total amount

∴ Jagdish received the minimum amount.

Hence, option 3.


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26.3 Marks

In each question there are two statements: A and B.

Choose 1 if the question can be answered by one of the statements alone butnot by the other.

Choose 2 if the question can be answered by using either statement alone.

Choose 3 if the question can be answered by using both the statementstogether but cannot be answered using either statement alone.

Choose 4 if the question cannot be answered even by using both thestatements A and B.

F and M are father and mother of S, respectively. S has four uncles and threeaunts. F has two siblings. The siblings of F and M are unmarried. How manybrothers does M have?

F has two brothers.A.M has five siblings.B.


1) 1

2) 2

3) 3

4) 4

Solution:F and M have a total of four brothers and three sisters.

Statement A states that F has two brothers, which means M should have twobrothers.

∴ Statement A is alone sufficient.

Statement B is redundant as no additional information is provided.

Hence, option 1.

27.3 Marks




Choose 3 if the question can be answered by using both the statements


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together but cannot be answered using either statement alone.


A game consists of tossing a coin successively. There is an entry fee of Rs.10 and an additional fee of Re. 1 for each toss of the coin. The game isconsidered to have ended normally when the coin turns heads on twoconsecutive throws. In this case the player is paid Rs. 100. Alternatively, theplayer can choose to terminate the game prematurely after any of the tosses.Ram has incurred a loss of Rs. 50 by playing this game. How many times didhe toss the coin?

The game ended normally.A.The total number of tails obtained in the game was 138.B.


1) 1

2) 2

3) 3

4) 4

Solution:Let the number of tosses be x.

Total amount spent by Ram after x tosses = (10 + x × 1) = Rs. (10 + x)

We know that Ram incurs a loss of Rs. 50.

∴ We have two cases to evaluate:

If the game ends normally then Ram's net loss = Rs. (10 + x) − Rs. 100i.If he quits prematurely his loss = Rs. (10 + x)ii.

From statement A,

Ram's net loss = (10 + x) − 100

∴ 50 = (10 + x) − 100

∴ x = 140

∴ Statement A is alone sufficient.


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From statement B,

Ram gets 138 tails.

If his game ends prematurely, his loss = 10 + x = 50

∴ x = 40

This is not possibe as the number of tails > 40

∴ His game must have ended normally.

∴ 10 + x – 100 = 50

∴ x = 140

∴ Statement B is also sufficient.

Hence, option 2.

28.3 Marks






Each packet of SOAP costs Rs. 10. Inside each packet is a gift couponlabelled with one of the letters S, O, A, and P. If a customer submits foursuch coupons that make up the word SOAP, the customer gets a free SOAPpacket. Ms. X kept buying packet after packet of SOAP till she could get oneset of coupons that formed the word SOAP. How many coupons with label Pdid she get in the above process?

The last label obtained by her was S and the total amount spent was Rs. 210.A.The total number of vowels obtained was 18.B.


1) 1

2) 2

3) 3


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4) 4

Solution:From Statement A,

Also the last label obtained by her is S.

But this is not sufficient to get the number of P's.


From Statement B,

The number of O's and A's is 18.

But this is also not individually sufficient to arrive at the required answer.


After combining both the statements A and B, we can conclude that 18 out of21 coupons are O's and A's and that the 21st is an S.

∴This means that the remaining two are P's.

Hence, option 3.

29.3 Marks







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If A and B run a race, then A wins by 60 seconds. If B and C run the samerace, then B wins by 30 seconds. Assuming that C maintains a uniformspeed, what is the time taken by C to finish the race?

A and C run the same race and A wins by 375 metres.A.The length of the race is 1 km.B.


1) 1

2) 2

3) 3

4) 4

Solution:From the question, if A and C participate in a race, A will win by 90 seconds.

From statement A,

∵ A beats C by 375 m or 90 sec.

But the length of the track is not known.

∴ Statement A is not sufficient to find the time taken by C to complete therace.

From Statement B we cannot find the speed of C.


After combining both the statements A and B, the time taken by C tocomplete the race

Hence, option 3.

30.3 Marks

Each question is followed by two statements, A and B. Answer each questionusing the following instructions

Choose 1 if the question can be answered by using one of the statements


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alone but not by using the other statement alone.Choose 2 if the question can be answered by using either of the statementsalone.Choose 3 if the question can be answered by using both statements togetherbut not by either statement alone.Choose 4 if the question cannot be answered on the basis of the twostatements.

Is a44 < b11, given that a = 2 and b is an integer?

b is evenA.b is greater than 16B.


1) 1

2) 2

3) 3

4) 4

Solution:a44 < b11

But, a = 2

∴ a44 = 244

∴ a44 = 1611


b is an even integer. It may be less than or greater than 16.

So, we cannot answer the question using statement A alone.


b is greater than 16.

∴ b11 > 1611

∴ b11 > a44

So, we can answer the question using statement B alone.


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Hence, option 1.


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1.3 Marks

There were x pigeons and y mynahs in a cage. One fine morning p of themescaped to freedom. If the bird keeper, knowing only that the value of pwas 7, was able to figure out without looking into the cage that at least onepigeon had escaped, then which of the following does not represent apossible (x, y) pair?

1) (10, 8)

2) (7, 2)

3) (25, 6)

4) (12, 4)

Solution:7 birds escaped, out of which at least one was a pigeon.

For an (x, y) pair to be possible, there should be no chance that all the birdsthat escaped were mynahs.

If y ≥ 7, there is a possibility that all seven birds that escaped were mynahs.

Thus, for an (x, y) pair to be valid, y has to be less than 7.

Therefore, looking at the answer options (10, 8) cannot be a possible (x, y)pair.

This is because this pair has 8 mynahs which means that all 7 birds thatescaped can be mynahs. This violates the basic condition of the problem.

Hence, option 1.

2.3 Marks

Consider the following steps:

Put x = 1, y = 21.Replace x by xy2.Replace y by y + 13.If y = 5 then go to step 6 otherwise go to step 5.4.Go to step 25.Stop6.

Then the final value of x equals _____.

1) 1

Section I


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2) 24

3) 120

4) 720

Solution:Step 1:

x = 1 × 2 = 2; y = 2 + 1 = 3

y ≠ 5. So, go to step 5.

Step 2:

x = 2 × 3 = 6; y = 3 + 1 = 4

y ≠ 5. So, go to step 5.

Step 3:

x = 6 × 4 = 24; y = 4 + 1 = 5

Since y = 5, go to step 6 and stop.

When y = 5, x = 24

Thus, the final value of x = 24.

Hence, option 2.

3.3 Marks

116 people participated in a singles tennis tournament having a knock outformat. The players are paired up in the first round, the winners of the firstround are paired up in the second round, and so on till the final is playedbetween two players. If after any round, there are an odd number of playersleft, one player is given a bye, i.e., he skips that round and plays the nextround with the winners. Find the total number of matches played in thetournament.

1) 115

2) 53

3) 232

4) 116


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Solution:Consider Round 1 :

Since there are 116 players, 116/2 = 58 matches are played and 58 winnersare obtained.

Consider Round 2 :

58/2 = 29 matches are played and 29 winners are obtained.

Consider Round 3 :

Since there are 29 winners, 1 person gets a bye. The remaining 28people play 28/2 = 14 matches among themselves.

Thus, 14 winners are obtained.

Since one person has obtained a bye, 15 people go to the next round. Consider Round 4 :

Since there are 15 winners, 1 person gets a bye. The remaining 14people play 14/2 = 7 matches among themselves.

Thus, 7 winners are obtained.

Since one person has obtained a bye, 8 people go to the next round.

Consider Round 5 :


Consider Round 6 :


Consider Round 7 :

2/2 = 1 last match is played and the final winner is obtained.

∴ Total number of matches played = 58 + 29 + 14 + 7 + 4 + 2 + 1 = 115

Hence, option 1.

Alternatively,

The concept of a knockout tournament is that a person who loses goes out.


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Thus, if a person A wins the second round against B, he is considered to bebetter than 3 other players (B, the peron beaten by A in the first round andthe person beaten by B in the first round).

This is equivalent to winning 3 matches.

Thus, the person winning the tournament is considered to have won onceagainst every other player participating in the tournament.

Therefore, if there are n players participating in the tournament, it isequivalent to one player beating the remaining (n − 1) players exactly once.

Therefore, in a knockout tournament, if n players participate, (n – 1) matchesshould be played to decide the winner.

Hence, in a knockout tournament of 116 players, the total number of matchesplayed is 116 – 1 = 115.

Hence, option 1.

Group Question


The following questions relate to a game to be played by you and your friend. Thegame consists of a 4 x 4 board (see below) where each cell contains a positiveinteger. You and your friend make moves alternately. A move by any of the playersconsists of splitting the current board configuration into two equal halves andretaining one of them. In your moves you are allowed only to split theboard vertically and decide to retain either the left half or the right half. Yourfriend, in his/her moves, can only split the board horizontally and can retain eitherthe lower half or the upper half. After two moves by each player a single cell willremain which can no longer be split and the number in that cell will be treated asthe gain (in rupees) of the person who has started the game. A sample game isshown below.


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So your gain is Re.1. With the same initial board configuration as above andassuming that you have to make the first move, answer the following questions.

4.3 Marks

If you choose (retain right) (retain left) in your turns, the best movesequence for your friend to reduce your gain to a minimum will be_____.

1) (retain upper) (retain lower)

2) (retain lower) (retain upper)

3) (retain upper) (retain upper)

4) (retain lower) (retain lower)

Solution:The initial board is:


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Since your first move is (retain right), the board configuration after themove is as shown below

Since your next move is (retain left), your final profit will be one from (2,6, 3 and 8).

If the friend's first move is (retain lower), your possible profit will beeither Rs. 3 or Rs. 8.

If the friend's first move is (retain upper), your possible profit will beeither Rs. 2 or Rs. 6.

Since his objective is to minimise your gain, he will try and limit yourgain to the least value i.e. Rs. 2.

Hence, his first move will be (retain upper).


Since you have now selected (retain left), the numbers left for yourfriend are 2(upper) and 6(lower).

To minimise your gain, your friend will select (retain upper).

Your gain now will be Rs. 2.

Hence, the moves are (retain upper), (retain upper).


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Hence, option 3.

5.3 Marks

With the initial board configuration as shown in the question, if both ofyou select your moves intelligently then at the end of the game, yourgain will be _____.

1) Rs. 4

2) Rs. 3

3) Rs. 2

4) None of these

Solution:The initial board is:

Since both of you play intelligently, your objective is to get the maximumpossible gain while your friend's objective is to give you the minimumpossible gain.

Case I : You select (retain left).

Since your friend also plays intelligently, he will select (retain upper) sothat your gain does not cross Rs. 5. If he selects (retain lower), yourgain can possibly go up to Rs. 9

Now, you will again select (retain left) to get a maximum possible gain ofRs. 5

Finally, in order to minimise your gain, your friend will again select(retain upper).

This will limit your gain to Rs. 2

Thus, with intelligent moves, your maximum gain in this case is Rs. 2

Case II : You select (retain right).


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Now, if your friend selects (retain upper), the minimum profit you canearn is Rs. 2 and the maximum profit you can earn is Rs. 4

On the other hand, if your friend selects (retain lower), the minimumprofit you can earn is Rs. 2 and the maximum profit you can earn is Rs.3.

Since your friend also plays intelligently, he will select (retain lower) sothat your gain does not cross Rs. 3.

Now, you will again select (retain left) to get a maximum possible gain ofRs. 8

Finally, in order to minimise your gain, your friend will again select(retain upper).

This will limit your gain to Rs. 3

Thus, with intelligent moves, your maximum gain in this case is Rs. 3

Since you want to maximise your gain, your first intelligent move will be(retain right).

As per Case II, your gain will be Rs. 3.

Hence, option 2.

6.3 Marks

If your first move is (retain right), then whatever moves your friend mayselect, you can always force a gain of no less than _____.

1) Rs. 3

2) Rs. 6

3) Rs. 4

4) None of these

Solution:The first move will be as shown below.


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If your friend selects (retain upper), you will now select (retain right) totry and get a maximum gain of Rs. 7.

This means that your friend can now limit your gain to the minimum of(4, 7) i.e. Rs. 4

If my friend selects (retain lower), you will now select (retain left) to tryand get a maximum gain of Rs. 8.

This means that your friend can now limit your gain to the minimum of(3, 8) i.e. Rs. 3.

Thus, irrespective of your friend's move, you will never gain anythingless than Rs. 3.

Hence, option 1.

Group Question


The pages of a book are numbered 0, 1, 2 … upto M, M > 0. There are fourcategories of instructions that direct a person in positioning the book at aparticular page. The instruction types and their meanings are:

OPEN : Position the book at page No. 1 I.CLOSE : Position the book at page No. 0II.FORWARD, n : From the current page ,move forward by n pages; if, in this process, pagenumber M is reached, stop at M.

III.

BACKWARD, n : From the current page, move backward by n pages; if in this process, pagenumber 0 is reached, stop at page number 0.

IV.

In each of the following questions, you will find a sequence of instructions formedfrom the above categories. In each case, let n1 be the page number before theinstructions are executed and n2 be the page number at which the book ispositioned after the instructions are executed.


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7.3 Marks

FORWARD, 25; BACKWARD, 10. Which of the following statements isdefinitely true?

1) n1 = n2 if M = 10 and n1 = 0

2) M = 20 provided n1 > 0

3) n1 > 30 provided M = 900

4) n1 = 37 provided M = 25

Solution:The given instructions are: FORWARD 25, BACKWARD 10.

Option 1: Given M = 10, n1 = 0

Thus, after FORWARD 25, page number 10 will be reached (since M =10).

Now, after BACKWARD 10, page number 0 will be reached.

∴ n2 = 0 = n1

Hence, the given statement is definitely true.

Option 2: Given M = 20 provided n1 > 0

Assume n1 = 1.

For any M > 25, FORWARD 25 will lead to page number 26 (1 + 25)and then BACKWARD 10 will lead to page number 16 (26 − 10). This isvalid.

For any M ≤ 25, FORWARD 25 will lead to page number M andthen BACKWARD 25 will lead to page number (M − 10) or to page 0 (ifM ≤ 10). This is also valid

Thus, M may take any value.

Hence, the given statement may or may not be true.

Option 3: Given n1 > 30 provided M = 900

For n1 = 30, n2 = 30 + 25 − 10 = 45 (which is valid).

For n1 > 30 (say 40), n2 = 40 + 25 − 10 = 55 (which is also valid).


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Thus, it is not necessary that n1 should be greater than 30. Hence, the given statement may or may not be true.

Option 4: Given n1 = 37 provided M = 25

Since M is the number of pages in the book and n1 is the page fromwhere we start, n1 ≤ M.

Here, n1 > M Hence, the given statement is definitely false.

Hence, option 1.

8.3 Marks

BACKWARD, 5; FORWARD, 5. Which of the following statements isdefinitely true about the above set of instructions?

1) n1 = n2 provided n1 ≥ 5

2) n1 = n2 provided n1 > 0

3) n2 = 5 provided M > 0

4) n1 > n2 provided M > 0

Solution:The given instructions are: BACKWARD 5, FORWARD 5.

Option 1: Given n1 = n2 provided n1 ≥ 5

n1 ≥ 5

Thus, after BACKWARD 5, the intermediate position (n) is n = n1 – 5.

Hence, after FORWARD 5, the final position (n2) is n2 = n1 – 5 + 5 = n1.

∴ n1 = n2

Hence, the given statement is definitely true.

Option 2: Given n1 = n2 provided n1 > 0

Consider n1 = 3.

Thus, after BACKWARD 5, the intermediate position (n) is n = 0


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Now, after FORWARD 5, the final position (n2) is n2 = 0 + 5 = 5

∴ n1 ≠ n2

Now, consider n1 = 5.



∴ n1 = n2

Thus, the given statement may or may not be true.

Option 3: Given n2 = 5 provided M > 0

Let n1 = 2 and M = 4


Now, after FORWARD 5, the final position (n2) is n2 = 4

∴ n2 ≠ 5

Now, let n1 = 5 and M ≥ 5



∴ n2 = 5


Option 4: Given n1 > n2 provided M > 0.

Let n1 = 1 and M = 5:



∴ n1 < n2

Thus, the given statement is false.

Hence, option 1.


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NOTE : The second case in option 2 and 3 have been given to illustratethat the statement may or may not be true. Since the question asks fora “definitely true” condition, you can eliminate that option once it isproved that the statement has a possibility of being false. However, ifthe question had asked for a “possibly true” condition, you would haveneeded to check both cases as shown above.

9.3 Marks

FORWARD, 10; FORWARD, 10. Which of the following statementsabout the above instructions is true?

1) n2 – n1 = 20 only if n1 = 0

2) n2 – n1 = 20 if M > 20 and n1 = 1

3) n2 – n1 = 10 if M = 21 and n1 = 0

4) n2 > n1 if M > 0

Solution:The given instructions are: FORWARD 10, FORWARD 10.

Option 1: Given n2 – n1 = 20 only if n1 = 0

This is a restrictive condition as it means that n2 − n1 can be 20 only ifn1 = 0.

Thus, if it can be proved that n2 – n1 = 20 for n1 ≠ 0, the given statementbecomes false.

Let n1 = 1:

Thus, after FORWARD 10, the intermediate position (n) is n = 11

Now, after the second FORWARD 10, n2 = 11 + 10 = 21

∴ n2 – n1 = 21 − 1 = 20

Thus, the given statement is false.

Option 2: Given n2 – n1 = 20 if M > 20 and n1 = 1

Note that this not a restrictive condition like the one above. You justneed to prove that the equation is satisfied for the given values of n1and M.

n1 = 1. Let M = 21


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∴ n2 – n1 = 21 − 1 = 20

Thus, the given statement is true.

Option 3: Given n2 – n1 = 10 if M= 21 and n1 = 0

Again, you just need to prove that the equation is satisfied for the givenvalues of n1 and M.

Thus, after FORWARD 10, the intermediate position (n) is n = 0 + 10 =10


∴ n2 – n1 = 20 ≠ 10

Thus, this statement is false.

Option 4: Given n2 > n1 if M > 0

This statement need not be true in all cases.

For example, if n1 = 1 and M = 1:


Now, after the second FORWARD 10, n2 = 1

Here, n2 = n1.

Thus, this statement may or may not be true.

Hence, option 2.

10.3 Marks

FORWARD, 5; BACKWARD, 4. Which of the following statements aboutthe above instructions is definitely true?

1) n2 = n1 + 4 provided 1 < n1 < 7

2) n2 = n1 provided M < 6

3) n2 = n1 + 1 provided M – n1 > 5


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4) n2 – n1 < 0 provided M > 0

Solution:The given instructions are: FORWARD 5, BACKWARD 4.

Option 1: Given n2 = n1 + 4 provided 1 < n1 < 7


Let n1 = 2:


Now, after BACKWARD 4, n2 = 7 − 4 = 3

Here, n2 ≠ n1 + 4

Thus, the given statement is not definitely true.

Option 2: Given n2 = n1 provided M < 6


Let n1 = 3 and M = 5:


Now, after BACKWARD 4, n2 = 5 − 4 = 1

Here, n1 ≠ n2

Thus, the given statement is not definitely true.

Option 3: Given n2 = n1 + 1 provided M – n1 > 5

If M – n1 > 5, then M > n1 + 5.

Therefore, after FORWARD 5, the intermediate position (n) is n = n1 + 5and not n = M

Now, after BACKWARD 4, n2 = n1 + 5 – 4 = n1 + 1

Hence, the given statement is true.

Option 4: Given n2 – n1 < 0 provided M > 0


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Let n1 = 1 and M = 10:

Thus, after FORWARD 5, the intermediate position (n) is n = 1 + 5 = 6

Now, after BACKWARD 4, n2 = 6 – 4 = 2

∴ n2 − n1 = 2 – 1 = 1 > 0


Hence, option 3.

11.3 Marks

The last time Rahul bought Diwali cards, he found that the four types of cardsthat he liked were priced at Rs. 2.00, Rs. 3.50, Rs. 4.50 and Rs. 5.00 each.As Rahul wanted 30 cards, he took five each of two kinds and ten each of theother two, putting down an exact number of 10 rupees notes on the counterpayment. How many notes did Rahul give?

1) 8

2) 9

3) 10

4) 11

Solution:In all, there are 4 varieties of cards, of a price Rs 2, Rs 3.50, Rs 4.50 and Rs 5per card.

Rahul buys 30 cards and puts an amount which is a multiple of 10. Also, hebuys 5 cards each of two types and 10 cards each of the other two types.

Since two denominations are in terms of decimals, they will together give anumber that is an integer only if the same number of cards is bought for eachdenomination.

In such a case, the total cost of the Rs. 3.5 and the Rs. 4.5 cards will be 3.5x+ 4.5x = 8x. Here, x is the number of cards bought for each of these twotypes.

Now, if Rahul buys 10 cards each of these two denominations, he will buy 5cards each of the Rs. 2 and the Rs. 5 denomination.

Thus, the total cost will be 2(5) + 5(5) + 8(10) = 10 + 25 + 80 = Rs. 115


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Since the total amount has to be a multiple of 10, this is not possible.

Hence, Rahul buys 5 cards each of the Rs. 3.5 and the Rs. 4.5 denominationand 10 cards each of the Rs. 2 and the Rs. 5 denominations.

Thus, the total cost is 2(10) + 5(10) + 8(5) = 20 + 50 + 40 = Rs. 110.

Since Rahul places all Rs. 10 notes, he places 110/10 = 11 notes in all.

Hence, option 4.

12.3 Marks

I happened to be the judge in the all India Essay Competition on NylonDying, organized some time back by a dyestuff firm. Mill technicians wereeligible to enter the competition. My work was simplified in assessing theessays, which had to be done under five heads-Language, Coherence,Subject Matter, Machinery and Recent Developments. Marks were to be givenout of a maximum of 20 under each head. There were only five entriesresulting in a sole winner. The winner got 90 marks. Akhila got 13 inCoherence and Divya 10 in Machinery. Bhanu’s total was less than Akhila’s.Charulata has sent an entry. Ela had got as many marks as Divya. No one got20 under any head.

Who was the winner?

1) Divya and Ela

2) Charulata

3) Akhila

4) Bhanu

Solution:Consider the answer options.

Since Bhanu's total was less than Akhila's total, Bhanu cannot be the winner.


Ela and Divya had the same marks. However, there was a sole winner.

Thus, Ela and Divya could not have been combined winners.


Now, Akhila got 13 in Coherence and the winner's total marks were 90.

Thus, if Akhila was the winner, she should have scored 90 − 13 = 77 under


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the remaining 4 heads.

No person got 20 under any individual head. Thus, the maximum one couldhave got under any head was 19.

Even if Akhila got 19 in the remaining 4 heads, she would have scored 19 × 4= 76 in the remaining four heads.

Thus, her total marks would have been 76 + 13 = 89.

Hence, Akhil could not have been the winer.

Hence, Charulata was the winner.

Hence, option 2.

13.3 Marks

A player rolls a die and receives the same number of rupees as the numberof dots on the face that turns up. What should the player pay for each roll ifhe wants to make a profit of one rupee per throw of the die in the long run?

1) Rs. 2.50

2) Rs. 2

3) Rs. 3.50

4) Rs. 4

Solution:The possible outcome on one throw of a fair die is one from 1, 2, 3, 4, 5 and6.

Thus, the probability of each of these outcomes is 1/6.

Now, in the long run, since each outcome has an equal chance of appearing,the expected outcome from one roll of an ordinary (that is, fair) six-sided die

Thus, if the player wants to make a profit of one rupee per throw in the longrun, then the amount that should be paid by the player for each roll = 3.5 – 1= Rs. 2.5

Hence, option 1.

14.3 Marks

A calculator has two memory locations, A and B. The value ‘1’ is initiallystored in both memory locations. The following sequence of steps is carried


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out five times:Add 1 to B.Multiply A to B.Store the result in A.

What is the value stored in the memory location A at the end ofthis procedure?

1) 120

2) 450

3) 720

4) 250

Solution:

The calculations and the value in memory locations A and B at the end ofeach iteration are as shown in the table given above.

Thus, the value in the memory location A at the end of the 5th iteration is 720.

Hence, option 3.

15.3 Marks

X and Y are playing a game. There are eleven 50 paise coins on the tableand each player must pick up at least one coin but not more than five. Theperson picking up the last coin loses. X starts. How many coins should hepick up at the start to ensure a win no matter what strategy Y employs?

1) 4

2) 3

3) 2

4) 5

Solution:This problem can easily be solved by working backwards.

If X has to win the game, there has to be 1 coin left on the table after his turn.


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This means that B canot have the second last turn and that the last turn hasto be B's.

One player can pick a maximum of 5 coins in one turn.

Thus, A has to pick x coins at the start such that there 5 + 1 + 1 = 7 coins lefton the table.

Since there are 11 coins in all, A has to pick up 4 coins at the start.

Hence, option 1.

16.3 Marks

The money order commission is calculated as follows. From Rs. X to be sentby money order, subtract Rs. 0.01 and divide by 10. Add 1 to the quotientobtained. If the result is Rs. Y, the money order commission is Rs. 0.5Y. If aperson sends two money orders to Aurangabad and Bhatinda for Rs. 71 andRs. 48 respectively, the total commission is:

1) Rs. 7.00

2) Rs. 6.50

3) Rs. 6.00

4) Rs. 7.50

Solution:

When the money order amount is Rs. 71,

X − 0.01 = 70.99

The quotient when this is divided by 10 is 7.

∴ The commission = 0.5 × (7 + 1) = Rs. 4

When the money order amount is Rs. 48,

X − 0.01 = 47.99

The quotient when this divided by 10 is 4.


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∴ The commission = 0.5 × (4 + 1) = Rs. 2.5

∴ The total commission = 4 + 2.5 = Rs. 6.5

Hence, option 2.

17.3 Marks

The auto fare in Ahmedabad is calculated using the meter reading and thefollowing process. The meter reading (in paise) is rounded up to the multipleof 4 just greater than this reading. For instance, if the meter reading is 37paise, it is rounded up to 40 paise. The resultant is multiplied by 12. The finalresult is then rounded off to the nearest multiple of 25 paise. If 53 paise is themeter reading what will the actual fare be?

1) Rs. 6.75

2) Rs. 6.50

3) Rs. 6.25

4) Rs. 7.50

Solution:Since the meter reading is 53 paise, it is first rounded off to the next multipleof 4 i.e. 56 paise.

Now, 56 × 12 = 672 paise.

The multiple of 25 nearest to this value is 675.

Thus, the amount is rounded up to 675 paise.

Hence, the actual fare is Rs. 6.75

Hence, option 1.

18.3 Marks

Juhi and Bhagyashree were playing simple mathematical puzzles. Juhi wrotea two-digit number and asked Bhagyashree to guess what it was. Juhi alsoindicated that the number was exactly thrice the product of its digits. Whatwas the number that Juhi wrote?

1) 36

2) 24

3) 12

4) 48


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Solution:This can be solved very easily using the answer options and verifying theproduct of digits.

Option 1: 36 ≠ 3 × (3 × 6), so option 1 is incorrect.

Option 2: 24 = 3 × (2 × 4), so option 2 is correct



Thus, Juhi wrote the number 24.

Hence, option 2.

19.3 Marks

After paying all your bills, you find that you have Rs. 7.20 in your pocket. Youhave an equal number of 50 paise and 10 paise coins, but no other coins norany other currency notes. How many coins do you have?

1) 8

2) 24

3) 12

4) 30

Solution:Let the number of 50 paise coins be n.

Since the number of 50 paise coins and 10 paise coins is the same, thenumber of 10 paise coins is also n.

Since the total amount in your pocket is Rs. 7.20 and you have no other coinsor currency notes,

∴ 0.5n + 0.1n = 7.20

∴ 0.6n = 7.2

∴ n = 12

∴ The total number of coins = 2 × 12 = 24

Hence, option 2.


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Group Question


Alord has received a large order for stitching school uniforms from MayflowerSchool and Little Flower School. He has two cutters to cut the fabric, five tailors todo the stitching, and two assistants to stitch the buttons and buttonholes. Each ofthese nine persons work for exactly 10 hours a day. Each of the Mayfloweruniforms requires 20 minutes for cutting the fabric, one hour for stitching, and 15minutes for stitching the buttons and buttonholes. On the other hand, each LittleFlower uniform requires 30 minutes, 1 hour, and 30 minutes, respectively forcutting, stitching and stitching the buttons and buttonholes.

20.3 Marks

On a particular day, Alord decided to complete 20 Little Floweruniforms. How many Mayflower uniforms can he complete on that day?

1) 30

2) 40

3) 25

4) 0

Solution:Alord has 2 cutters who both work for 10 hours a day.

Each Little Flower uniform requires 30 minutes for cutting.

Thus, one cutter can cut 2 uniforms per hour.

Thus, both the cutters can together cut all 20 uniforms in 5 hours.

Similarly, each Little Flower uniform requires 30 minutes for stitchingbuttons and buttonholes.

Alord has 2 assistants who stitch buttons and buttonholes for 10 hoursa day.

Thus, as seen above, both the assitants can together finish 20 uniformsin 5 hours.

Finally, Alord has 5 tailors who work 10 hours a day.

Each Little Flower uniform requires 1 hour for stitching.

Thus, if all 5 tailors work together, the Little Flower uniforms can becompleted in 4 hours.


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Thus, at the end of 5 hours, all 20 Little Flower uniforms are complete.

Each Mayflower uniform requires 20 minutes for cutting, 1 hour forstitching and 15 minutes for stitching the buttons and buttonholes.

Thus, 2 cutters working together can complete 30 Mayflower uniforms inthe 5 hours left.

Similarly, 2 assistants working together can complete 40 Mayfloweruniforms left with them.

Finally, 5 tailors working together can complete 30 Mayflower uniformsin the 6 hours left with them.

Since the number of completed Mayflower uniforms is required, theminimum of the three values above is to chosen.

Thus, Alord can complete 30 Mayflower uniforms. Hence, option 1.

21.3 Marks

If Alord decides to complete 30 Little Flower uniforms only and donothing else on a particular day, how many total man-hours will be idle?

1) 20

2) 30

3) 5

4) 25

Solution:Each Little Flower uniform requires 30 minutes, 1 hour and 30 minutesfor cutting, stitching and stitching buttons and button holes respectively.

Also, Alord has 2 cutters, 5 tailors and 2 assistants to do these threerespective activities. Each person works for 10 hours a day.

Working together, both cutters can finish 4 uniforms per hour.

Thus, the time taken to complete Little Flower uniforms is 30/4 = 7.5hours.

Thus, each cutter has 2.5 hours left idle.

Therefore, the total idle man-hours for the cutters is 2.5 × 2 = 5 hours.


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Similarly, the total idle time man-hours for the tailors and the assistantscan be found as shown in the table below.

∴ Total idle man-hours = 20 + 5 + 5 = 30 hours

Hence, option 2.

22.3 Marks

What is the maximum number of Little Flower uniforms that Alord cancomplete in a day?

1) 50

2) 20

3) 40

4) 30

Solution:Number of uniforms cut in a day = Number of cutters × (Total number ofhours worked by each cutter/Time required by one cutter to cut oneuniform)

= 2 × (10/0.5)

= 40

Similarly, number of uniforms stitched in a day = 5 × (10/1)

= 50

Finally, number of uniforms with buttons and buttonholes stitched in a day= 2 × (10/0.5)

=40


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Since one uniform can be considered complete only if all three acitivitieshave been completed on it, the maximum number of Little Flower uniformsthat Alord can make in a day is equal to the smallest of the three numbersabove i.e. 40.

Thus, Alord can complete a maximum of 40 Little Flower uniforms in a day.

Hence, option 3.

23.3 Marks

Alord has the option to hire one more employee of any category. Whichcategory should he hire to get the maximum increase in productioncapacity assuming that he needs to stitch only Mayflower uniforms onthat day?

1) Tailor

2) Cutter

3) Assistant

4) Indeterminate

Solution:Each person has 10 man-hours available on a day.

One Mayflower uniform requires 20 minutes, 1 hour and 15 minutes tocut, stitch and put the buttons and buttonholes respectively.

Thus, 1 cutter, 1 tailor and 1 assitant can complete 30, 10 and 40Mayflower uniforms per day.

Alord has 2 cutters, 5 tailors and 2 assistants.

Therefore, 2 cutters, 5 tailors and 2 assitants can complete 60, 50 and80 Mayflower uniforms per day.

Since a uniform is considered complete only if all three activities havebeen completed, it can be said that Alord has 50 sets of the Mayfloweruniform ready. Thus, if Alord wants to increase the production capacity, he should hiremore tailors.

Hence, option 1.

24.3 Marks

If he hires one more assistant, what is the maximum number ofMayflower uniforms that he can complete in a day?


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1) 40

2) 50

3) 60

4) 30

Solution:Each person has 10 man-hours available on a day.

One Mayflower uniform requires 20 minutes, 1 hour and 15 minutes tocut, stitch and put the buttons and buttonholes respectively.

Thus, 1 cutter, 1 tailor and 1 assitant can complete 30, 10 and 40Mayflower uniforms per day.

Alord has 2 cutters, 5 tailors and 2 assistants.

Therefore, 2 cutters, 5 tailors and 2 assitants can complete 60, 50 and80 Mayflower uniforms per day.

Hence, if there are 3 assistants, they can complete 40 × 3 = 120uniforms per day.

However, only 50 uniforms have been stitched.

Thus, the maximum number of Mayflower uniforms that can becompleted is 50.

Hence, option 2.

25.3 Marks

139 persons have signed for an elimination tournament. All players are to bepaired up for the first round, but because 139 is an odd number one playergets a bye, which promotes him to the second round, without actually playingin the first round. The pairing continues in the next round, with a bye to anyplayer left over. If the schedule is planned so that a minimum number ofmatches is required to determine the champion, then the number of matcheswhich must be played is:

1) 136

2) 137

3) 138

4) 139


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Solution:The concept of a knockout competition comprising n players is that the winneris better than every other player.

Thus, the tournament is equivalent to one where the winner beats theremaining (n − 1) players.

To do so, the winner requires (n − 1) matches.

Hence, in a knockout tournament of n players, (n − 1) matches are requiredto determine the champion.

Since this tournament has 139 players, the number of matches that must beplayed is 138.

Hence, option 3.

26.3 Marks

There are ten 50 paise coins placed on a table. Six of these show tails andfour show heads. A coin is chosen at random and flipped over (not tossed).This operation is performed seven times. One of these coins is then covered.Of the remaining nine coins, five show tails and four show heads. Thecovered coin shows:

1) A head

2) A tail

3) More likely a head

4) More likely a tail

Solution:Assume that one coin, say one showing a tail, is flipped 7 times, instead of 7different coins. Then, it would show a head and there would be 5 heads and5 tails.

If by covering a coin, there are 5 tails and 4 heads to be seen, then thecovered coin is showing a head.

Hence, option 1.

Alternatively,

Assume that all four coins that now show heads are flipped coins. Hence,they originally showed tails.

Hence, the remaining two coins that originally showed tails still show tails.


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Now, since there are seven flips in all, only three coins that originally showedheads can be flipped.

Therefore, they will now show tails.

Thus, the number of coins now showing tails is 2 + 3 = 5.

Thus, the only coin that is now left shows a head.

Since five tails and four heads are visible, the remaining coin (the one that iscovered) shows a head.

Hence, option 1.

27.3 Marks

Along a road lie an odd number of stones placed at intervals of 10 m. Thesestones have to be assembled around the middle stone. A person can carryonly one stone at a time. A man carried out the job starting with the stone inthe middle, carrying stones in succession, thereby covering a distance of 4.8km. Then, the number of stones on the road is:

1) 30

2) 15

3) 29

4) 31

Solution:If the total distance covered is 4.8 km, the distance covered on each side ofthe middle stone is 2.4 km.

Assume that there are n stones on each side of the middle stone.

Each stone is kept at an interval of 10 m.

Thus, the man travels a distance of 10 + 10 = 20 m to carry the first stone andplace it around the middle stone.

Similarly, the man travels a distance of 20 + 20 = 40 m to carry the secondstone and place it around the middle stone.

Thus, the distance travelled by the man on one side forms a G.P. with a = 20and d = 20.

Since there are n stones on one side,

∴ (n/2) × [2a + (n − 1)d] = 2400


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∴ (n) × [40 + (n − 1)20] = 4800

∴ n × (n + 1) = 240

∴ n2 + n − 240 = 0

On solving this, you get, n = 15

Thus, there are 15 stones on one side of the road.

Therefore, the total number of stones = 15 + 1 + 15 = 31

Hence, option 4.

Group Question


Alphonso, on his death bed, keeps half his property for his wife and divides therest equally among his three sons Ben, Carl and Dave. Some years later Ben diesleaving half his property to his widow and the remaining to his brothers Carl andDave together, shared equally. When Carl makes his will he keeps half hisproperty for his widow and the rest he bequeaths to his younger brother Dave.When Dave dies some years later, he keeps half his property for his widow andthe remaining for his mother. The mother now has Rs. 15,75,000.

28.3 Marks

What was the total property worth?

1) Rs. 30 lakh

2) Rs. 8 lakh

3) Rs. 18 lakh

4) Rs. 24 lakh

Solution:Let the value of the property of Alphonso be Rs. x

Thus, Alphonso's wife gets Rs. x/2 and the three sons together get Rs.x/2.

Thus, each son gets Rs. x/6.

Now, when Ben dies, his wife gets [x/6]/2 = Rs. x/12.

Carl and Dave together get Rs. x/12 and individually get Rs. x/24


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Thus, the amount with Carl as well as Ben is Rs. [(x/6) + (x/24)]

Now, Carl leaves half of this property for his wife and the other half forDave.

Thus, Carl's wife gets Rs. [(x/12) + (x/48)]

Thus, the amount now available with Dave is [(x/6) + (x/24)] + (1/2) ×[(x/6) + (x/24)] i.e. Rs. (3/2) × [(x/6) + (x/24)]

Dave leaves half of this amount for his wife and the remaining for hismother.

Thus, Dave's wife gets Rs. (3/4) × [(x/6) + (x/24)]

Now, Dave's mother has a total amount of Rs. (x/2) + (3/4) × [(x/6) +(x/24)]

i.e. (x/2) + (x/8) + (x/32)

Thus, the total amount that Dave's mother has is 21x/32.

The amount received by each person at every stage is as shown in thetable below.

It is given that Dave's mother has Rs. 15,75,000 at the end.

∴ (21x/32) = 1575000

∴ x = (1575000 × 32)/21

= 75000 × 32

= 2400000


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Thus, the total property was worth Rs. 24 lakhs.

Hence, option 4.

29.3 Marks

What was Carl’s share when he made his will?

1) Rs. 4 lakh

2) Rs. 12 lakh

3) Rs. 6 lakh

4) Rs. 5 lakh

Solution:

So, the original share of Carl = 4 + 1 = 5 lakhs

Hence, option 4.

30.3 Marks

What was the ratio of the property owned by the widows of the threesons, in the end?

1) 7 : 9 : 13

2) 8 : 10 : 15

3) 5 : 7 : 9

4) 9 : 12 : 13

Solution:The worth of the total property x = 24 lakhs

The required ratio is = 2 : 2.5 : 3.75

This ratio is the same as 8 : 10: 15.


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Hence, option 2.


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Group Question


A, B, C, D, E, F and G are brothers. Two brothers had an argument and A said to B, “Youare as old as C was when I was twice as old as D, and will be as old as E was when hewas as old as C is now”. B said to A, “You may be older than F but G is as old as I waswhen you were as old as G is, and D will be as old as F was when F will be as old as G is”.

1.3 Marks

Who is the eldest brother?

1) A

2) E

3) C

4) Indeterminate

Solution:B is as old as C was when A was twice as old as D was.

Thus, C had reached B's age before B had.

∴ C > B; A > D … (i)

B will be as old as E was when he was as old as C is now.

∴ E > B; E > C … (ii)

A may be older than F but G is as old as B was when A was as old as G is.

∴ A > F; B > G; A = B … (iii)

D will be as old as F was when F will be as old as G is.

∴ F > D; G > F … (iv)

From (i), (ii), (iii) and (iv),

E > C > A = B > G > F > D.

Thus, the eldest brother is E.

Hence, option 2.

2.3 Marks

Who is the youngest brother?

1) B

Section I


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2) D

3) F

4) Indeterminate

Solution:From the solution to the first question, the youngest brother is D.

Hence, option 2.

3.3 Marks

Which two brothers are probably twins?

1) D and G

2) E and C

3) A and B

4) Indeterminate

Solution:From the solution to the first question, it can be seen that A and B are of thesame age.

Thus, they are the only pair that can possibly be twins.

Hence, option 3.

4.3 Marks

Which of the following statements is false?

1) G has 4 elder brothers.

2) A is older than G but younger than E.

3) B has 3 elder brothers.

4) There is a pair of twins among the brothers.

Solution:Refer to the order obtained in the solution to the first question.

E > C > A = B > G > F > D

Statement 1 : G has four elder brothers i.e. E, C, A and B.

Thus, statement 1 is true.

Statement 2 : From the order it is clear that A is older than G but younger than E.


Statement 3 : B has 3 elder brothers.


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From the order it can be seen that B has only two elder brothers i.e. E and C. Bhad one brother (A) who is of the same age.


Statement 4 : There is a pair of twins among the brothers.

Since A and B have the same age, they are twins.

Thus, there is a pair of twins among the brothers.


Hence, option 3.

Group Question


Four sisters Suvarna, Tara, Uma and Vibha were playing a game such that the loserdoubled the money of the other players from her share. They played four games and eachsister lost one game in the alphabetical order. At the end of fourth game each sister hadRs. 32 with her.

5.3 Marks

How many rupees did Suvarna start with?

1) 60

2) 34

3) 66

4) 28

Solution:Let the amounts held by Suvarna, Tara, Uma and Vibha at any stage be denotedby S, T, U and V respectively.

At the end of game 4, all of them have Rs 32 with them.

Since Vibha lost game 4, she would have doubled the other three players'amount.

Thus, at the end of the game 3 (or at the beginning of game 4), Suvarna, Taraand Uma would each have had Rs. 32/2 = Rs. 16.

Also, Vibha would have had 32 + 16 + 16 + 16 = Rs. 80

Similarly, the amount with each person at the end of each game can becalculated as shown in the table below.


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It is evident from the table that Suvarna started with 66 coins.

Hence, option 3.

6.3 Marks

Who started with the lowest amount?

1) Suvarna

2) Tara

3) Uma

4) Vibha

Solution:From the table in the solution to the first question, Vibha started with the leastamount (Rs. 10).

Hence, option 4.

7.3 Marks

Who started with the highest amount?

1) Suvarna

2) Tara

3) Uma

4) Vibha

Solution:From the table in the solution to the first question, it is clear that Suvarna startedwith the highest amount (i.e. Rs. 66)

Hence, option 1.

8.3 Marks

What was the amount with Uma at the end of the second game?

1) 36

2) 72

3) 16

4) None of these


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Solution:From the table in the solution to the first question, Uma had Rs. 72 at the end ofthe second game.

Hence, option 2.

Group Question


A salesman entered the quantity sold and the price into the computer. Both the numberswere two-digit numbers. But by mistake, both numbers were entered with their digitsinterchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventoryreduced by 54 units.

9.3 Marks

What is the actual price per article?

1) Rs. 82

2) Rs. 41

3) Rs. 14

4) Rs. 28

Solution:Total sales value = 1148 = Price × Quantity

To find the price and quantity, factorise 1148 in terms of two two-digit numbers.

1148 = 2 × 2 × 7 × 41

∴ 1148 = 14 × 82 = 28 × 41

Inventory is the amount of goods remaining in the store after the sale.

Since this has mistakenly reduced by 54 units, it means that the quantity hasbeen mistakenly shown to be more by 54 units.

82 = 28 + 54

Thus, actual number of units sold = 28

Thus, the original price has to be Rs. 41 and then after interchanging, it becomesRs. 14.

Thus, the actual price = Rs. 41

Hence, option 2.

10.3 Marks

What is the actual quantity sold?


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1) 28

2) 14

3) 82

4) 41

Solution:From the solution to the previous question, it is clear that the actual quantitysold is 28 units.

Hence, option 1.

11.3 Marks

Out of two-thirds of the total number of basketball matches scheduled, a team haswon 17 matches and lost 3. What is the maximum number of matches that the teamcan lose and still win more than three-fourths of the total number of matchesscheduled, if it is true that no match can end in a tie?

1) 4

2) 6

3) 5

4) 3

Solution:Matches played so far = 17 + 3 = 20

∴ Total number of matches scheduled = 20 × (3/2) = 30

If the team wants to win more than three-fourths of all the matches scheduled, theyhave to win at least (3/4) × 30 i.e. at least 22.5 matches.

Thus, the team will have to win at least 23 matches.

The team has already won 17 matches.

Thus, in the next 10 matches, (23 – 17) = 6 matches have to be won.

Hence, not more than (10 – 6) = 4 matches can be lost to maintain the required thewinning ratio.

Hence, option 1.

Group Question


The production pattern for a number of units (in cubic feet) per day:


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For a truck that can carry 2000 cubic feet, the hiring cost per day is Rs. 1,000. The storingcost per cubic feet is Rs. 5 per day.

12.3 Marks

If all the units have to be sent to the market, on which days should the truck behired to minimise the total cost?

1) 2nd, 4th, 6th, 7th

2) Only on 7th

3) 2nd, 4th, 5th and 7th

4) None of these

Solution:Hiring cost of truck per day = Rs 1,000.

Storage cost for each day of storage = Rs 5 per cubic feet.

Thus, hiring a truck is cheaper compared to storage for more than 200 cubic feet.

Thus, on all days when the number of units present is less than or equal to 200,hiring a truck is costlier than storing the goods. Thus, on such days, the unitsshould be stored and not sent out.

On the other hand, on all days when the number of units present is more than200, a truck should be hired to minimize the total cost.

The truck has to be hired on the 7th day because that is the last available day andall the units have to be sent to the market.

Hence, the truck is hired on the 2nd, 4th, 6th and the 7th days.

Hence, option 1.

13.3 Marks

If storage costs are reduced to Rs. 0.8 per cubic feet per day, then on which daysshould the trucks be hired to minimise the total cost?


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1) 2nd, 4th, 6th, 7th

2) Only on 7th

3) 2nd, 4th, 5th and 7th

4) None of these

Solution:Hiring cost of truck per day = Rs 1,000.

Storage cost for each day of storage = Rs 0.8 per cubic feet.

Thus, hiring a truck is cheaper compared to storage for more than (1000/0.8) i.e.1250 cubic feet.

Thus, on all days when the number of units present is less than or equal to 1250,hiring a truck is costlier than storing the goods. Thus, on such days, the units shouldbe stored and not sent out.

On the other hand, on all days when the number of units present is more than 1250, atruck should be hired to minimize the total cost.

If this quantity is not reached till the last day, then on the 7th day, the truck has to behired to transport all the units to the market.

Hence, the truck is hired only on the 7th day.

Hence, option 2.

Group Question


A, B, C and D collected one rupee coins as per the following conditions:Together they collected 100 coins.Each one of them collected an even number of coins.Each one of them collected at least 10 coins.No two of them collected the same number of coins.

14.3 Marks

The maximum number of coins collected by any one of them cannot exceed_____.


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1) 64

2) 36

3) 54

4) None of these

Solution:Each person collects an even number of coins such that the minimum number ofcoins with each person is 10.

To find the maximum possible number of coins collected by a single person,assume that the other three people collect the lowest possible number of coins.

No two people collect the same number of coins.

Therefore, assume that A, B and C collect 10, 12 and 14 coins respectively.

Thus, the maximum number of coins that the fourth person i.e. D can collect =100 − (10 + 12 + 14)

= 100− 36

= 64

Thus, the maximum number of coins collected by a person cannot exceed 64.

Hence, option 1.

15.3 Marks

If A collected 54 coins, then the difference in the number of coins between theone who collected the maximum number of coins and the one who collected thesecond-highest number of coins must be at least _____.

1) 12

2) 24

3) 30

4) None of these

Solution:The difference between the person who collected the most number of coins andthe one who collected the 2nd highest number of coins would be minimum whenthe 2nd highest collects the maximum number of coins possible for him.

Assume that the person who collects the 2nd highest number of coins is B.

Now, B can collect the maximum number of coins when C and D collect as fewcoins as possible.


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This can happen if one of C and D collects 10 coins while the other collects 12coins.

In such a case, B collects 100 − 54 − (10 + 12) i.e. 24 coins

Thus, the 2nd highest collector (assumed as B) can collect a maximum of 24coins.

Therefore, the difference between the highest and second highest person is atleast 54 − 24 i.e. 30 coins.

Hence, option 3.

16.3 Marks

If A collected 54 coins and B collected two more coins than the twice of thenumber of coins collected by C, then the number of coins collected by B couldbe _______.

1) 28

2) 20

3) 26

4) 22

Solution:Let the number of coins collected by A, B, C and D be a, b, c and d respectively.

Given that: a = 54, b = (2 × c) + 2

a + b + c + d = 100

∴ b + c + d = 100 – 54 = 46

∴ 2c + 2 + c + d = 46

∴ 3c + d = 44, where c ≥ 10 and d ≥ 10

Since the minimum value of d is 10, the maximum value of 3c is 34.

For this value, the maximum value of c can be 11.33

However, c has to be even and have a value of at least 10.

Only c = 10 satisfies all three conditions.

Consider c = 10, then d = 14 and b = 22

Thus, the number of coins collected by B would be 22.

Hence, option 4.


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17.3 Marks

A, B, C, D, … X, Y, Z are players who participated in a tournament. Everyone playedwith every other player exactly once. A win scores 2 points, a draw scores 1 point anda loss scores 0 points. None of the matches ended in a draw. No two players had thesame score. At the end of the tournament, the ranking list is published which is inaccordance with the alphabetical order. Then ...

1) M wins over N.

2) N wins over M.

3) M does not play with N.

4) None of these

Solution:Since no match ends in a draw and no two players have the same score, it means thatall players have won matches according to their rankings which correspond to thealphabetical order.

Since M takes precedence over N in the ranking order, M should have won over N.

Hence, option 1.

18.3 Marks

Three labeled boxes containing red and white cricket balls are all mislabeled. It isknown that one of the boxes contains only white balls and one only red balls. The thirdcontains a mixture of red and white balls. You are required to correctly label the boxeswith the labels red, white and red and white by picking a sample of one ball from onlyone box. What is the label on the box you should sample?

1) White

2) Red

3) Red and White

4) Not possible to determine from a sample of one ball

Solution:Let the red, white and red/white box be denoted by R, W and RW respectively.

Since each box is incorrectly named, the box labeled:

RW could actually be R or W

R could actually be W or RW

W could actually be R or RW.

Since the label RW is an incorrect label, the ball that comes out from that box will bethe actual colour of the balls in the box.

Hence, pick one ball from RW:


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Case 1:

i) If the ball is a red one, then re-label the box as R.

ii) Now, the box labelled W can be re-labelled only as RW.

iii) Finally, the box labelled R can be re-labelled as W.

Case 2:

i) If the ball is a white one, then re-label the box as W.

ii) Now, the box labeled R can be re-labelled only as RW.

iii) Finally, the box labeled W can be re-labelled only as R.

Thus, if you sample a ball from the box labelled red and white, you can correctly labelall the boxes.

Hence, option 3.

Group Question


Ten coins are distributed among four people P, Q, R and S such that one of them gets onecoin, another gets two coins, the third gets three coins and the fourth gets four coins. It isknown that Q gets more coins than P, and S gets fewer coins than R.

19.3 Marks

If the number of coins distributed to Q is twice the number distributed to P thenwhich one of the following is necessarily true?

1) R gets an even number of coins.

2) R gets an odd number of coins.

3) S gets an even number of coins.

4) S gets an odd number of coins.

Solution:Based on the given data, the number of coins with P, Q, R and S should be 1, 2,3 and 4 coins (not necessarily in that order).

Also, it is given that: P < Q, S < R.

Thus,

(i) Q, R cannot have 1 coin.

(ii) P, S cannot have 4 coins.

Given: Q = 2P


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i) If Q = 2, then P = 1, this implies that S = 3 (since S ≠ 4) and R = 4

ii) If Q = 4, then P = 2, this implies that R = 3 (since R ≠ 1) and S = 1

From the 2 possible cases shown above, it can be seen that S always gets anodd number of coins.

Hence, option 4.

20.3 Marks

If R gets at least two more coins than S, then which one of the following isnecessarily true?

1) Q gets at least two more coins than S.

2) Q gets more coins than P.

3) P gets more coins than S.

4) P and Q together get at least five coins.

Solution:Given: R ≥ (S + 2)

i) If R = 4, and if S = 2, this implies that Q = 3 (since Q ≠ 1) and P = 1

ii) If R = 4, and if S = 1, this implies that Q = 3 (since Q > P) and P = 2

iii) If R = 3, and if S = 1, this implies that Q = 4 (since P ≠ 4) and P = 2

From the 3 possible cases shown above, it can be seen that the statement‘Q gets more coins than P’ is always true.

Hence, option 2.

21.3 Marks

If Q gets fewer coins than R, then which one of the following is not necessarilytrue?

1) P and Q together get at least four coins.

2) Q and S together get at least four coins.

3) R and S together get at least five coins.

4) P and R together get at least five coins.

Solution:Given: Q < R → P < Q < R and S < R, thus R = 4

Possible cases (R = 4):

(i) P = 1, Q = 2, S = 3


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(ii) P = 1, Q = 3, S = 2

(iii) P = 2, Q = 3, S = 1

In all of the above cases, it can be seen that:

(Q + S) ≥ 4, (R + S) ≥ 5 and (P + R) ≥ 5

Thus, the only option that is not always true is (P + Q) ≥ 4 [Case (i)].

Hence, option 1.

Group Question


A young girl Roopa leaves home with x flowers and goes to the bank of a nearby river. Onthe bank of the river, there are four places of worship, standing in a row. She dips all the'x' flowers in the river. The number of flowers doubles. Then she enters the first place ofworship, offers 'y' flowers to the deity. She dips the remaining flowers into the river, andagain the number of flowers doubles. She goes to the second place of worship, offers 'y'flowers to the deity. She dips the remaining flowers into the river, and again the number offlowers doubles. She goes to the third place of worship, offers 'y' flowers to the deity. Shedips the remaining flowers into the river, and again the number of flowers doubles. Shegoes to the fourth place of worship, offers 'y' flowers to the deity. Now she is left with noflowers in hand.

22.3 Marks

If Roopa leaves home with 30 flowers, the number of flowers she offers to eachdeity is:

1) 30

2) 31

3) 32

4) 33

Solution:Let Roopa leave home with x flowers and offer y flowers to each deity.

After each dip, the number of flowers she has doubles and after offering flowersto each deity, the number of flowers decreases by y.


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Thus, from the table, it can be seen that 16x = 15y … (i)

Hence, option 3.

23.3 Marks

The minimum number of flowers that could be offered to each deity is:

1) 0

2) 15

3) 16

4) Indeterminate

Solution:From the solution to the first question, y = (x/15) × 16

Thus, it can be seen that y is a multiple of 16.

Hence, the minimum value of y = 16 when x = 15.

Hence, option 3.

24.3 Marks

The minimum number of flowers with which Roopa leaves home is:

1) 16

2) 15

3) 0

4) Indeterminate

Solution:From the solution to the first question, x = (y/16) × 15.

Thus, it can be seen that x is a multiple of 15.

Hence, the minimum value of x = 15 when y = 16.

Hence, option 2.

Group Question


There are m blue vessels with known volumes v1, v2, ... vm, arranged in ascending order ofvolume, where v1 > 0.5 litre, and vm < 1 litre. Each of these is full of water initially. Thewater from each of these is emptied into a minimum number of empty white vessels, each


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having volume of 1 litre. The water from a blue vessel is not emptied into a white vesselunless the white vessel has enough empty volume to hold all the water of the bluevessel. The number of white vessels required to empty all the blue vessels according to theabove rules was n.

25.3 Marks

Among the four values given below, which is the least upper bound on e, wheree is the total empty volume in the n white vessels at the end of the aboveprocess?

1) mvm

2) m(1 – vm)

3) mv1

4) m(1 – v1)

Solution:The upper bound is the least when the volumes in all the blue vessels is nearlyequal, i.e., v1 ≈ v2 ≈ … ≈ vm

Then, the empty volume in each white vessel = e1 ≈ (1 – v1) litres

Total empty value = e = m × (1 – v1)

Hence, option 4.

26.3 Marks

Let the number of white vessels needed be n1 for the emptying processdescribed above, if the volume of each white vessel is 2 liters. Among thefollowing values, which is the least upper bound on n1?

1)

2)

3) n

4)

Solution:Minimum number of blue vessels that can be emptied into each white vessel of2 litres capacity = 2

Hence, option 2.


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Group Question


There are 5 cities, A, B, C, D and E connected by 7 roads as shown in the figurebelow:

Design a route such that you start from any city of your choice and walk on eachof the 7 roads once and only once, not necessarily returning to the city from whichyou started.

1.3 Marks

For a route that satisfies the above restrictions, which of the followingstatements is true?

1) There is no route that satisfies the above restriction.

2) A route can either start at C or end at C, but not both.

3) D can be only an intermediate city in the route.

4) The route has to necessarily end at E.

Solution:

The route has to be created in such a way that you pass through eachroad exactly once and you do not need to end at the same city from

Section I


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where you started. Also, it is not mentioned that a particular city cannotbe visited more than once. This means that you can go through one citymore than once provided you do not go through the same road.

Keeping these conditions in mind, multiple routes such asDEBDCABC, CABCDBED and so on can be formed.

The statement in option 1 is false since it is clear that multipleroutes satisfy the given conditions.

The statement in option 2 is true as no valid route can start and end atC.

The statement in option 3 is false since the route DEBDCABC is a validroute and starts at D. Thus, D need not only be an intermediate city.

The statement in option 4 is false since the route DEBDCABC is a validroute and does not end at E.

Hence, option 2.

2.3 Marks

From how many different cities can one start such that the givenrestriction is satisfied?

1) One

2) Zero

3) Three

4) Two

Solution:To ensure that the given restriction is not violated, one can start eitherfrom D or from C.

If one starts from either of A, B or E, the given restriction gets violated.

Thus, one can start only from 2 possible cities.

Hence, option 4.

3.3 Marks

Fifty college teachers are surveyed as to their possession of colour TVs,VCRs and tape recorders. Of them, 22 own colour TVs, 15 own VCRs and 14own tape recorders. Nine of these college teachers own exactly two items ofthese three items; and, one college teacher owns all three. How many of the50 teachers own none of the three, colour TV, VCR or tape recorder?


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1) 4

2) 9

3) 10

4) 11

Solution:The given information can be represented as shown in the following Venndiagram:

In the above figure, the various letters represent the folowing:

a : Teachers who own only TV

b : Teachers who own only VCR

c : Teachers who own only tape recorders (TR)

x : Teachers who own a TV and VCR but not TR

y : Teachers who own a TV and TR but not VCR

z : Teachers who own a TR and VCR but not TV

r : Teachers who own all three items

d : Teachers who do not own any of the three items

From the data given:

a + b + c + x + y + z + r + d = 50 ... (i)

a + x + y + r = 22 ... (ii)

b + x + z + r = 15 ... (iii)


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c + y + z + r = 14 ... (iv)

Add (ii), (iii) and (iv)

a + b + c + 2(x + y + z) + 3r = 51 ... (v)

Now,

x + y + z = 9 ... (vi)

and, r = 1 ... (vii)

Substituting the values from (vi) and (vii) in (v),

a + b + c = 51 − 2(9) − 3(1)

= 51 − 18 − 3

= 30

Substituting these values in (i)

∴ 30 + 9 + 1 + d = 50

∴ d = 10

Thus, 10 teachers did not own even one of the three products.

Hence, option 3.

4.3 Marks

For the network given, what is the total number of ways in which one way canreach B from A?


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1) 12

2) 16

3) 20

4) 22

Solution:The number of ways in which one can reach B from A can be found bycounting as shown below.

A-c-g-l-B1.A-c-h-l-B2.A-c-h-k-B3.A-c-g-k-B4.A-d-g-l-B5.A-d-h-l-B6.A-d-h-k-B7.A-d-g-k-B8.A-e-i-k-B9.A-e-i-l-B10.A-e-j-l-B11.A-e-j-k-B12.A-f-i-k-B13.A-f-i-l-B14.A-f-j-l-B15.A-f-j-k-B16.

Thus, one can reach B from A in 16 different ways

Hence, option 2.

Alternatively,

In the network shown above, each junction is known as a node.


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For such a network, the total number of ways in which one can reach from Ato B can be calculated as the product of the number of routes emerging fromany node at a particular level.

i.e. There are 4 posssible routes from the origin (A) to the next level (i.e. to c,d, e or f).

Next, from each of c, d, e and f, there are 2 possible routes to the next level(i.e. to g, h or i, j)

Similarly, from each of g, h, i and j, there are 2 routes to the next level ( i.e. tok and l)

Finally, from both l and k, there is one route each available to go to thedestination (B).

∴ Total number of routes = 4 × 2 × 2 × 1 = 16

Hence, option 2.

Group Question


There were a hundred schools in a town. Of these, the number of schools havinga play-ground was 30, and these schools had neither a library nor a laboratory.The number of schools having a laboratory alone was twice the numberof schools having only a library. The number of schools having a laboratory aswell as a library was one-fourth the number of schools having a laboratory alone.The number of schools having either a laboratory or a library or both was 35.

5.3 Marks

How many schools had none of the three, viz., laboratory, library orplay-ground?

1) 20

2) 5

3) 30

4) 35

Solution:The town had 30 schools which had a playground. However, none ofthese 30 schools had either a library or a laboratory.

Thus, there was no school that had both; a playground and alaboratory or a playground and a library.


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Similarly, there was no school that had all three facilities.

The number of schools having a library and a laboratory was one-fourthof the number of schools having only a laboratory.

Let the number of schools having only a laboratory be 4x.

Thus, the number of schools with a laboratory as well as a library is x.

The number of schools having only a laboratory was twice the numberof schools having only a library.

Therefore, the number of schools having only a library is 2x.

Thus, the given data can now be represented as shown in the followingVenn diagram:

In the above Venn diagram, PG, LI and LA corresponds to the numberof schools with a playground, library and laboratory respectively.

The number of schools having either a library or a laboratory or bothwas 35.

∴ 2x + x + 4x = 35

∴ 7x = 35

∴ x = 5

Let the number of schools that did not have any of the three facilities i.e.playground, library and laboratory be y.

∴ 30 + 35 + y = 100


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∴ y = 35

Thus, 35 schools did not have any of the three facilities.

Hence, option 4.

6.3 Marks

What was the ratio of schools having a laboratory to those having alibrary?

1) 1 : 2

2) 5 : 3

3) 2 : 1

4) 2 : 3

Solution:Number of schools having a laboratory = 4x + x = 5x

Number of schools having a library = 2x + x = 3x

Thus, the required ratio = 5x : 3x, i.e. 5 : 3

Hence, option 2.

7.3 Marks

There are 3 clubs, A, B and C, in a town with 40, 50 and 60 membersrespectively. While 10 people are members of all 3 clubs, 70 people aremembers in exactly one club. How many people belong to exactly two clubs?

1) 20

2) 25

3) 50

4) 70

Solution:Let a, b, and c represent the number of people who are members of only clubA, only club B and only club C respectively.

∴ a + b + c = 70 ... (i)

Let the number of people who are members only in clubs A and B, but not inC be x.

Similarly, let the number of people who are members in only B and C be y


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and the number of people who are members in only C and A be z.

Thus, the number of people who belong to exactly two clubs is x + y + z

Club A has 40 members.

∴ a + x + z + 10 = 40 ... (ii)

Using similar information for clubs B and C, you can get,

b + x + y + 10 = 50 ... (iii)

c + y + z + 10 = 60 ... (iv)

Adding (i), (ii) and (iii)

(a + b + c) + 2(x + y + z) + 30 = 150

∴ 70 + 2(x + y + z) = 120

∴ x + y + z = 25

Thus, 25 people belong to exactly two clubs.

Hence, option 2.

8.3 Marks

A man starting at a point walks one km east, then two kms north, then onekm east, then one km north, then one km east and then one km north toarrive at the destination. What is the shortest distance from the starting pointto the destination?

1)

2) 7 km

3)

4) 5 km

Solution:The shortest distance between the starting point and the destination can befound by first finding the horizontal as well as the vertical distance travelledbetween the starting point and the destination and then applying Pythagoras'Theorem.

Since the man alternately walked towards the east and then towards thenorth, the horizontal distance will simply be the summation of the totaldistance travelled towards the east. Similarly, the vertical distance will be the


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summation of the total distance travelled towards the north.

Thus,

The total horizontal distance travelled by the man = 1 + 1 + 1 = 3 kms

The total vertical distance travelled by the man = 2 + 1 + 1 = 4 kms

Let A and B be the initial and final position of the man.

Hence, option 4.

9.3 Marks

If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 = ?

1) 10

2) 4

3) 6

4) 18

Solution:The actual sum of 8 and 12 is 20

The sum of the digits in 20 = 2 + 0 = 2

Using a similar logic, 7 + 14 = 21

The sum of the digits in 21 = 2 + 1 = 3

Now, 10 + 18 = 28

The sum of digits of 28 = 2 + 8 = 10

∴ 10 + 18 = 10

Hence, option 1.

10.3 Marks

Lata has the same number of sisters as she has brothers, but her brotherShyam has twice as many sisters as he has brothers. How many children arethere in the family?

1) 7

2) 6


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3) 5

4) 4

Solution:Let the number of girls and boys in the family be G and B respectivley.

Lata has the same number of sisters as she has brothers. This implies thatthe number of girls reduced by 1 is the same as the number of boys.

∴ G − 1 = B … (i)

Lata’s brother Shyam has twice as many sisters as he has brothers. Thisimplies that the number of boys reduced by 1 is half the number of girls.

∴ G = 2(B – 1) … (ii)

Substituting (i) in (ii), you get

G = 2(G − 2)

∴ G = 4

∴ B = 3

G + B = 4 + 3 = 7

Thus, there are 7 children in the family.

Hence, option 1.

11.3 Marks

A cube is made into a number of cubelets by dividing each edge into fourequal parts. The top face of the cube is a square ABCD. Take the diagonalAC and push a knife downwards so that the cube is cut into two prisms ofequal size. How many cubelets are cut by the knife in this operation?

1) 16

2) 48

3) 4

4) 8

Solution:When the cube is cut into four equal parts on each edge, the total number ofcublets formed is 4 × 4 × 4 = 64 (length × breadth × depth)


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The top face of the cube can be represented as given below. The numbers 1,2, 3 and 4 represent the four cubelets whose top face forms the diagonal ACof the square ABCD.

Consider cubelet 1. It is evident that there are 3 more cubelets exactly belowit (because the depth is 4).

Similarly, cubelets 2, 3 and 4 also have 3 cubelets each under them.

Thus, when the knife cuts downwards through cubelet 1, it actually cutscubelet 1 and the three cubelets exactly below it i.e. a total of 4 cubelets.

Similarly, it cuts 4 cubelets each when it cuts through cubelets 2, 3 and 4.

Thus, it cuts a total of 4 × 4 = 16 cubelets.

Hence, option 1.

12.3 Marks

If m # n = m + n + mn, then 2 # 3 = ?

1) 0

2) 6

3) 11

4) 20

Solution:m # n = m + n + mn

∴ 2 # 3 = 2 + 3 + (2 × 3) = 11

Hence, option 3.

13.3 Marks

If m # n = m + n + mn and for any m, there is a number q such that m # q =m, then q = ?

1) 0


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2) –1

3) 1

4) q does not exist

Solution:m # n = m + n + mn

It is given that m # q = m

∴ m + q + mq = m

∴ q(1 + m) = 0

∴ q = 0 or 1 + m = 0

∴ q = 0 or m = −1

It is given that m can take any value.

∴ q = 0

Hence, option 1.

14.3 Marks

100 Management students who read at least one of three available businessmagazines are surveyed to observe the readership pattern. It is found that 80students read Business India, 50 read Business World, and 30 read BusinessToday. Five students read all the three magazines. How many read exactlytwo magazines?

1) 50

2) 10

3) 95

4) 25

Solution:Since all 100 students read at least one of the three available magazines,there is no student who does not read any of the three magazines.

The general Venn diagram for this survey can be as shown below where BI,BW and BT represent Business India, Business World and Business Todayrespectively.


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From the given information, it can be noted that:

(a + b + c) + (x + y + z) + r = 100 ... (i)

a + x + y + r = 80 ... (ii)

b + x + z + r = 50 ... (iii)

c + y + z + r = 30 ... (iv)

r = 5 ... (v)

Adding (ii), (iii) and (iv), you get:

(a + b + c) + 2(x + y + z) + 3r = 160 … (vi)

∴ a + b + c + 2(x + y + z) = 145 ... (vii)

Subtracting (i) from (vii), and substiuting the value of r, you get

x + y + z = 50

Thus, the number of people who read exactly 2 magazines = x + y + z = 50

Hence, option 1.

15.3 Marks

A young girl counted the fingers of her left hand in the following manner. Shestarted calling the thumb 1, the index finger 2, middle finger 3, ring finger4 and little finger 5; then reversed the direction, calling the ring finger 6,middle finger 7, index finger 8, thumb 9 and then back to the index finger for10, middle finger for 11, and so on. She counted up to 1994. She ended onher..

1) Thumb

2) Index finger


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3) Middle finger

4) Ring finger

Solution:Note that all five fingers were counted in the first iteration while only fourfingers were counted in every iteration after that.

The girl started with the thumb at 1 before reaching the thumb again at 9.

Similarly, she would reach the thumb again at 17, 25 and so on after every 8counts.

Thus, the number assigned to the thumb would always be of the form 8n + 1.

Similarly, the number assigned to the index finger would be of the form 8n +2, for the middle finger would be 8n + 3 and so on.

1994 = 8(249) + 2

Thus, 1994 is of the form 8n + 2

Hence, 1994 would represent the index finger.

Hence, she stopped at the index finger.

Hence, option 2.

16.3 Marks

Out of 100 families in a certain neighbourhood, 45 own radios, 75 own TVswhile 25 have VCRs. Only 10 families have all three appliances and eachVCR owner also has a TV. If 25 families have only a radio, how many familiesown only a TV?

1) 30

2) 35

3) 40

4) 45

Solution:Each VCR owner also has a TV. This implies that there is no family that ownsonly a VCR.

Similarly, there is no family that owns only a VCR and radio, but not a TV.

Number of families that own a VCR = 25


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Number of families that own all three appliances = 10

Families that own a VCR = Families that own only a VCR + Families that ownonly TV and VCR + Families that own only VCR and radio + Families that ownall three appliances.

∴ 25 = 0 + Number of families that own only TV and VCR + 0 + 10

∴ Number of families that own only TV and VCR = 15

Similarly, number of families that own only TV and radio = 45 − (25 + 10 + 0)= 10

∴ Families with only TV = Families with TV − (Families with only TV and radio+ Families with only TV and VCR + Families with all three appliances)

= 75 − (10 + 15 + 10)

= 40

Hence, option 3.

Group Question


85 children went to an amusement park where they could ride on the merry-go-round, roller coaster or Ferris wheel. It is known that 20 of them took all threerides, and 55 of them took at least two of the three rides. Each ride costs Re. 1and the total receipts of the amusement park were Rs. 145.

17.3 Marks

How many children did not try any of the rides?

1) 5

2) 10

3) 15

4) 20

Solution:The number of children that took atleast 2 rides = 55

The number of children that took all three rides = 20

Therefore, the number of children that took exactly 2 rides = 55 – 20 =35


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Each ride costs Re. 1 and the total collections were Rs. 145

Total collections = (No. of children who took exactly 1 ride × 1) + (No.of children who took exactly 2 rides × 2) + (No. of children who took all3 rides × 3)

If the number of children that took exactly 1 ride is n, then

145 = n + (35 × 2) + (20 × 3)

∴ n = 15

Thus, the number of children who took at least one ride = 15 + 35 + 20= 70

∴ Number of children who did not take even a single ride = 85 − 70 =15

Hence, option 3.

18.3 Marks

How many children took exactly one ride?

1) 5

2) 10

3) 15

4) 20

Solution:From the solution to the previous question, the number of children thattook exactly 1 ride = 15

Hence, option 3.

Group Question


“Kya-Kya” is an island in the South Pacific. The inhabitants of “Kya-Kya” alwaysanswer any question with two sentences, one of which is always true and theother is always false.

19.3 Marks

You are walking on a road and come to a fork. You ask the inhabitantsRam, Laxman and Lila, “Which road will take me to the village?"Ram says, “I never speak to strangers. I am new to these parts.”


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Laxman says, “I am married to Lila. Take the left road.”Lila says, “I am married to Ram. He is not new to this place.”Which of the following statements is true?

1) The left road takes you to the village

2) The right road takes you to the village

3) Lila is married to Laxman

4) None of these

Solution:Since Ram is talking to you, he speaks to strangers. This implies thathis first statement is False.

Therefore, Ram's second statement is True i.e. he is new to these parts.

This makes Lila's second statement False and her first statement Truei.e. Lila is married to Ram.

Finally, this means that Laxman's first statement becomes False andsecond becomes True i.e. “Take the left road” is a True statement.

Thus, the left road takes you to the village.

Hence, option 1.

20.3 Marks

You find that your boat is stolen. You question three inhabitants of theisland and they reply as follows:John says, “I didn’t do it. Matthew didn’t do it.”Matthew says, “I didn’t do it. Krishna didn’t do it.”Krishna says, “I didn’t do it. I don’t know who did it.”Who stole your boat?

1) John

2) Matthew

3) Krishna

4) None of them

Solution:If the second statement of Matthew and first statement of Krishna istrue, then Matthew has stolen the boat which implies that his firststatement is false. So, the first statement of John is true and his secondstatement is false.


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Hence, option 2.

21.3 Marks

You want to speak to the chief of the village. You question threeinhabitants, Amar, Bobby and Charles. Only Bobby is wearing a redshirt.Amar says, “I am not Bobby’s son. The chief wears a red shirt.”Bobby says, “I am Amar’s father, Charles is the chief.”Charles says, “The chief is one among us. I am the chief.”Who is the chief?

1) Amar

2) Bobby

3) Charles

4) None of them

Solution:Since it is mentioned in two places that “Charles is the chief”, start byassuming that this statement is True.

Thus, if Charles is the chief, the chief is definitely one among Amar,Bobby and Charles.

Thus, Charles' first statement also turns out to be True.

Thus, both the statements made by Charles become True, which is notpossible as per the condition of the problem.

Thus, Charles' second statement has to be definitely False.

This makes Bobby's second statement also False, and consequently,Bobby's first statement True.

Thus, Bobby is Amar's father.

Therefore, Amar's first statement is False and second statement has tobe True.

Thus, the chief has to be a person wearing a red shirt.

Since Bobby is the only person wearing a red shirt, Bobby has to be thechief.

Hence, option 2.

22. There is only one pilot on the island. You interview three men; Koik,


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3 Marks Lony and Mirna. You also notice that Koik is wearing a cap.Mirna says, “Lony’s father is the pilot. Lony is not the priest’s son.”Koik says, “I am the priest. On this island, only priests can wear caps.”Lony says, “I am the priest’s son. Koik is not the priest.”Which of the following statements is true?

1) Lony is not Koik’s son

2) Koik is the pilot

3) Mirna is the pilot

4) Lony is the priest

Solution:Consider Koik's statements.

If his second statement is true, then as he is wearing a cap, his firststatement also is true, which is not possible.

Therefore, Koik's second statement is false and hence he is the priest.

This makes Lony's second statement false and first statement true,which in turn makes Mirna's second statement false and first statementtrue.

Thus we can see that Lony's father, Koik is the priest as well as thepilot.

Hence, option 2.

Group Question


There are three different cable channels, namely Ahead, Luck and Bang. In asurvey it was found that 85% of the viewers respond to Bang, 20% to Luck, and30% to Ahead. 20% of the viewers respond to exactly two channels and 5% tonone.

23.3 Marks

What percentage of the viewers responded to all three channels?

1) 10

2) 12

3) 14

4) None of these


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Solution:A general Venn diagram can be drawn to represent the given data asshown under:

Assume the total number of viewers to be 100.

Since 5% viewers do not respond to any channel, the number of viewerswho respond to at least one channel is 95.

∴ (a + b + c) + (x + y + z) + r = 95 ... (i)

The number of viewers who respond to Ahead, Bang and Luck is 30, 85and 20 respectively.

∴ a + x + y + r = 30 ... (ii)

b + x + z + r = 85 ... (iii)

c + y + z + r = 20 ... (iv)

Adding (ii), (iii) and (iv),

(a + b + c) + 2(x + y + z) + 3r = 135 ... (v)

Now, there are 20 users who respond to exactly 2 channels.

∴ x + y + z = 20 ... (vi)

Substituting the value from (vi) in (i) and (v), you get

(a + b + c) + r = 75 ... (vii)

and, (a + b + c) + 3r = 95 ... (viii)

(viii) − (vii) gives, r = 10


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∴ a + b + c = 65

Thus, 10 out of 100 viewers responded to all three channels.

Thus, 10% of the viewers responded to all three channels.

Hence, option 1.

24.3 Marks

Assuming 20% respond to Ahead and Bang and 16% respond to Bangand Luck, what is the percentage of viewers who watch only Luck?

1) 20

2) 10

3) 16

4) None of these

Solution:Using the terminology and the values obtained in the solution to theprevious question,

x + r = 20

and

z + r = 16

Using the value of r = 10 in the two equations above, you get:

x = 10 and z = 6

x + y + z = 20

∴ y = 4

The number of viewers who followed Luck = c + y + z + r = 20

∴ c + 4 + 6 + 10 = 20

∴ c = 0

Thus, no viewer follows only Luck.

Hence, option 4.


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Group Question


In a locality, there are five small cities, A, B, C, D and E. The distances of thesecities from each other are as follows:

AB = 2 km AC = 2 km AD > 2 km AE > 3 km BC = 2 km

BD = 4 km BE = 3 km CD = 2 km CE = 3 km DE > 3 km

25.3 Marks

If a ration shop is to be set up within a maximum of 2 km of each city,how many ration shops will be required?

1) 2

2) 3

3) 4

4) 5

Solution:Given distances between the points:

AB = 2 km, AC = 2 km, AD > 2 km, AE > 3 km, BC = 2 km, BD = 4 km,BE = 3 km, CD = 2 km, CE = 3 km, DE > 3 km.

Consider the above conditions:

(i) AB = AC = BC = 2 km. Hence it can be seen that A, B and C form anequilateral triangle of side 2 km.

(ii) BD = 4 km, CD = 2 km. Hence it can be seen that point D lies on theextended straight line connecting B and C and at a distance of 2 kmfrom C.

(iii) BE = CE = 3 km, AE > 3 km. Hence point E should lie on theperpendicular bisector of the line BC. Point A lies on one side, hence Eshould lie on the other side of the line BC.

Thus, the overall arrangement is as shown in the figure below:


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City C is at a distance of 2 km from A, B as well as D.

Thus, one ration shop at C can suffice for A, B, C as well as D.

However, city E is 3 km away from city C.

Thus, the ration shop at city C cannot serve city E.

Therefore, a separate ration shop is required for city E.

Thus, all the 5 cities can be properly served using just 2 ration shops.

Hence, option 1.

26.3 Marks

If a ration shop is to be set up within 3 km of each city, how many rationshops will be required?

1) 1

2) 2

3) 3

4) 4

Solution:Using the figure obtained in the solution to the previous question; if aration shop is required within 3 km of each city, then a single rationshop at city C can serve all the cities under consideration.

Hence, option 1.

27.3 Marks

A cube of sides 12 cm is painted red on all the faces and then cut intosmaller cubes, each of sides 3 cm. What is the total number of smaller cubes


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having none of their faces painted?

1) 16

2) 8

3) 12

4) 24

Solution:Number of smaller cubes on each side (n) = 12/3 = 4

Thus, the total number of smaller cubes formed = 43 = 64

If one wants the side of a cube to not be painted, one has to ignore one smallcube exactly in front of that side.

Thus, when one wants a small cube that has none of its sides painted, onehas to ignore one cube from each side. In other words, one has to ignore twosmall cubes in each dimension. Thus, the number of small cubes that have none of their sides painted = (n –2)3 = 23 = 8

Hence, option 2.

28.3 Marks

In a locality, two-thirds of the people have cable-TV, one-fifth have VCRs, andone-tenth have both. What is the fraction of people having either cable-TV or aVCR?

1)

2)

3)

4)

Solution:Fraction of people having either cable-TV or VCR = Fraction of people havingcable-TV + Fraction of people having VCR − Fraction of people having both


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Hence, option 4.

Group Question


A survey of 200 people in a community who watched at least one of the threechannels - BBC, CNN, DD - showed that 80% of the people watched Doordarshan(DD), 22% watched BBC, and 15% watched CNN.

29.3 Marks

What is the maximum percent of people who can watch all threechannels?

1) 12.5

2) 8.5

3) 15

4) Insufficient data

Solution:All 200 people watched at least one channel. This implies that therewas no one who did not watch any of the three channels.

The general Venn diagram for the channels can be drawn as shownbelow.

The percentage of people who can watch all three channels can bemaximum only if all the people watching one particular channel alsowatch the other two channels.

Note that since only 15% people watch CNN, all of the 80% people whowatch DD cannot watch CNN.


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Thus, the percentage can be maximum if all the people who watch thechannel with the least viewership also watch the other two channelsthat have a higher viewership.

Thus, the percentage can be maximum if the 15% people who watchCNN also watch BBC as well as DD.

Thus, the maximum percentage of people who can wacth all threechannels is 15%.

Hence, option 3.

30.3 Marks

If 5% of the people watched DD and CNN, 10% watched DD and BBC,then what percent of the people watched BBC and CNN only?

1) 2%

2) 5%

3) 8.5%

4) Indeterminate

Solution:Consider the Venn diagram made in the previous solution as well as thedata given in the question.

80% people watched DD, 22% watched BBC and 15% watched CNN.

Thus, the actual number of people watching DD, BBC and CNN was160, 44 and 30 respectively.

∴ d + x + y + r = 160 ... (i)

b + x + z + r = 44 ... (ii)

c + y + z + r = 30 ... (iii)

Now, 5% of the people watched DD and CNN while 10% watched DDand BBC

Thus, 10 people watched DD and CNN while 20 people watched DDand BBC.

∴ y + r = 10 ... (iv)

and


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x + r = 20 ... (v)

The number of people watching BBC and CNN only is z.

Now, every person watched at least one channel.

∴ (b + c + d) + (x + y + z) + r = 200 ... (vi)

Adding (i), (ii) and (iii), you get,

(b + c + d) + 2(x + y + z) + 3r = 234 ... (vii)

(vii) − (vi) gives

x + y + z + 2r = 34

∴ (x + r) + (y + r) + z = 34

Substituting the values from (iv) and (v) in the above equation, you get,

20 + 10 + z = 34

∴ z = 4

Thus, 4 people out of 200 watch only BBC and CNN.

Thus, 2% of the people watch only BBC and CNN.

Hence, option 1.

31.3 Marks

Referring to the previous question, how many percent of the peoplewatched all the three channels?

1) 3.5%

2) 0%

3) 8.5%

4) Indeterminate

Solution:The percentage of people who watched all three channels can be foundif the value of r can be found.

With the given data, it is not possible to find r.

Hence, option 4.


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Group Question


a # b = a + b, if a and b both are positive, else a # b = 1

a ∇ b = (ab)a + b, if ab is positive, else a ∇ b = 1

32.3 Marks

1)

2) 1

3)

4) 3

Solution:(i) a # b = a + b, if a, b > 0; else a # b = 1

(ii) a ∇ b = (ab)a + b, if ab > 0; else a ∇ b = 1

Therefore,

Hence, option 3.

33.3 Marks

1)

2)

3)

4) None of these


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Solution:log10 0.1 = log10 (10)−1 = −1

Thus, one of the parts of the second term of the numerator is negativeand so this second term becomes 1 (as per the alternate condition)

Thus,

Hence, option 1.

34.3 Marks

1) X = 1, Y = 2

2) X > 0, Y < 0

3) Both X and Y are positive.

4) Both X and Y are negative.

Solution:If X and Y lie on the same side of the number line, the numerator aswell as denominator both have one term that is negative.

Thus, the value of the numerator as well as the denominator becomes1.

Thus, the value of the expression becomes 1 for the case where both Xand Y are positive as well as for the case where both X and Y arenegative.

Hence, options 3 and 4 do not yield the desired value, andconsequently, can be eliminated.

The values in option 1 are a specific case of option 3 and so, they alsoyield a value of 1 for the expression.

Hence, option 1 can also be eliminated.

Consider option 2: X > 0, Y < 0

The numerator now has both terms positive and becomes X + Y


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On the other hand, the denominator has both terms negative andbecomes (XY)−(X + Y)

Thus, the value of the expression becomes (X + Y)/(XY)−(X + Y) i.e. (X +Y) × (XY)(X + Y)

Among the options given, this is the only option that give the value ofthe expression as 3/8.

Hence, option 2.

35.3 Marks

In a survey of political preference, 78% of those asked were in favor of at leastone of the proposals: I, II and III. 50% of those asked favored proposal I, 30%favored proposal II, and 20% favored proposal III. If 5% of those askedfavored all three of the proposals, what percentage of those asked favoredmore than one of the 3 proposals?

1) 10

2) 12

3) 17

4) 22

Solution:The information given can be expressed as a general Venn Diagram asshown below.

Let the number of respondents be 100.

Thus, 78 respondents favored at least one proposal.

∴ (a + b + c) + (x + y + z) + r = 78 ... (i)


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The number of people who favored proposals I, II, and III was respectively 50,30 and 20.

∴ a + x + y + r = 50 ... (ii)

b + x + z + r = 30 ... (iii)

c + y + z + r = 20 ... (iv)

(ii) + (iii) + (iv) gives,

(a + b + c) + 2(x + y + z) + 3r = 100 ... (v)

(v) − (i) gives,

(x + y + z) + 2r = 22 ... (vi)

5 people favored all three proposals.

∴ r = 5 ... (vii)

Substitute the value of r in (vi)

∴ (x + y + z) = 12 ... (viii)

The number of people who favored more than one of the three proposals = (x+ y + z) + r

= 12+ 5

= 17

Thus, 17 out of 100 people favored more than one of the three proposals.

Hence, 17% people favored more than one of the three proposals.

Hence, option 3.

Group Question


A robot moves on a graph sheet with x and y-axes. The robot is moved by feedingit a sequence of instructions. The different instructions that can be used in movingit are:


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36.3 Marks

The robot reaches point (6, 6) when a sequence of three instructions isexecuted, the first of which is a GOTO (x, y) instructions, the second isWALK X(2) and the third is WALK Y(4). What is the value of x and yrespectively?

1) 2, 4

2) 0, 0

3) 4, 2

4) 2, 2

Solution:The final position of the robot is (6, 6) after the instruction WALK Y(4).

Therefore, the position of the robot just before this instruction and afterthe instruction WALK X(2) is (6, 2).

Similarly, the position of the robot just before the instruction WALK X(2)is (4, 2).

This is also the position of the robot after the GOTO (x, y) instruction

According to the conditions, if the robot receives a GOTO (x, y), itdirectly reaches the position (x, y).

Since the robot is at (4, 2) after the GOTO instruction, it must havereceived the instruction as GOTO (4, 2).

∴ x = 4 and y = 2

Hence, option 3.

37.3 Marks

The robot is initially at (x, y), x > 0 and y < 0. The minimum number ofinstructions needed to be executed to bring it to the origin (0, 0) if youare prohibited from using the GOTO instruction is:


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1) 2

2) 1

3) x + y

4) 0

Solution:Since the x as well as y co-ordinate is not zero and GOTO is notallowed, each co-ordinate has to be separately brought to zero.

This can be done using a total of two instructions (one WALK X and oneWALK Y).

The two instructions required are:

WALK X(−x)

WALK Y(+y)

Hence, option 1.


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Group Question


There are three bottles of water, A, B, C, whose capacities are 5 litres, 3 litres, and2 litres respectively. For transferring water from one bottle to another and to drainout the bottles, there exists a piping system. The flow thorough these pipes iscomputer controlled. The computer that controls the flow through these pipes canbe fed with three types of instructions, as explained below

Initially, A is full with water, and B and C are empty.

[CAT 2000]

1.3 Marks

After executing a sequence of three instructions, bottle A contains onelitre of water. The first and the third of these instructions are shownbelow

First instruction FILL (C, A)

Third instruction FILL (C, A)

Then which of the following statements about the instructions is true?

1) The second instruction is FILL (B, A)

2) The second instruction is EMPTY (C, B)

3) The second instruction transfers water from B to C

4) The second instruction involves using the water in bottle A.

Solution:Instruction 1: FILL (C, A)

Section I


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2 litres of water is transferred from A to C

∴ A has 3 litres of water left and C has 2 litres of water.

Instruction 3: FILL (C, A)

2 litres of water is transferred from A to C

∴ A has 1 litres of water left and C has 2 litres of water.

Since the third instruction again transfers water from A to C, C shouldbe empty before the third operation. Thus, instruction 2 should be either“EMPTY (C, B)” or “DRAIN (C)”.

Hence, option 2.

2.3 Marks

Consider the same sequence of three instructions and the same initialstate mentioned above. Three more instructions are added at the end ofthe above sequence to have A contain 4 litres of water. In this totalsequence of six instructions, the fourth one is DRAIN (A). This is theonly DRAIN instruction in the entire sequence. At the end of theexecution of the above sequence, how much water (in litres) iscontained in C?

1) One

2) Two

3) Zero

4) None of these

Solution:After third instruction A has 1 litre, B has 2 litres and C has 2 litres ofwater.

Instruction 4: DRAIN A

Instruction 5: EMPTY (B, A)

Instruction 6: EMPTY (C, A)

After 6th instruction, C has no water as all 2 litres have been transferredto A.

Hence, option 3.


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3.3 Marks

There is a vertical stack of books marked 1, 2, and 3 on Table-A, with 1 at thebottom and 3 on top. These are to be placed vertically on Table-B with 1 atthe bottom and 2 on the top, by making a series of moves from one table tothe other. During a move, the topmost book, or the topmost two books, or allthe three, can be moved from one of the tables to the other. If there are anybooks on the other table, the stack being transferred should be placed on topof the existing books, without changing the order of books in the stack that isbeing moved in that move. If there are no books on the other table, the stackis simply placed on the other table without disturbing the order of books in it.What is the minimum number of moves in which the above task can beaccomplished?

[CAT 2000]

1) One

2) Two

3) Three

4) Four

Solution:In four moves the task can be accomplished.One of the ways is given below.

Initial state: Table A: 3(on top) 2(in middle) 1(bottom)

Step 1: Move book 3 from table A to table B

Step 2: Move book 2 from table A to table B

Step 3: Move books 2(on top) and 3(below book 2) from table B to table A onbook 1(bottommost)

Step 4: Move books 2, 3 and 1 from table A to table B.

Hence, option 4.

4.3 Marks

ABCDEFGH is a regular octagon. A and E are opposite vertices of theoctagon. A frog starts jumping from vertex to vertex, beginning from A. Fromany vertex of the octagon except E, it may jump to either of the two adjacentvertices. When it reaches E, the frog stops and stays there. Let an be thenumber of distinct paths of exactly n jumps ending in E. Then what is thevalue of a2n – 1?

[CAT 2000]


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1) Zero

2) Four

3) 2n – 1


Solution:The frog has to jump at least four times to reach E.

i.e. a4 = 2

(i.e. (i)A-B, B-C,C-D and D-E; (ii) A-H, H-G, G-F and F-E).

If the frog keeps jumping on left (right) hand side vertices it will not take morethan four jumps.

If it jumps on right vertex and then keeps on jumping left vertices then it willtake 6 jumps to reach E.

∴ We will not find any path such that the frog takes 5 jumps and reaches E.

∴ a5 = 0

Similarly, we find that only for even values of n the frog can reach E.

2n − 1 is an odd number

∴ No route is possible with odd number of jumps.

Hence, option 1.

Group Question


The following sketch shows the pipelines carrying material from one location toanother. Each location has a demand for material. The demand at Vaishali is 400,at Jyotishmati is 400, at Panchal is 700, and at Vidisha is 200. Each arrowindicates the direction of material flow through the pipeline. The flow from Vaishalito Jyotishmati is 300. The quantity of material flow is such that the demands at allthese locations are exactly met. The capacity of each pipeline is 1000.

[CAT 2001]


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5.3 Marks

The quantity moved from Avanti to Vidisha is

1) 200

2) 800

3) 700

4) 1000

Solution:

Demand at Panchal = 700

∴ Quantity of material flowing in the pipeline from Jyotishmati toPanchal = 700

Also, Flow from Vaishali to Jyotishmati + Flow from Vidisha toJyotishmati = Demand at Jyotishmati + Demand at Panchal

∴ 300 + Flow from Vidisha to Jyotishmati = 400 + 700 = 1100

∴ Flow from Vidisha to Jyotishmati = 1100 − 300 = 800


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Now, Flow from Avanti to Vaishali = Demand at Vaishali + Flow fromVaishali to Jyotishmati

∴ Flow from Avanti to Vaishali = 300 + 400 = 700

Also, Flow from Avanti to Vidisha = Demand at Vidisha + Flow fromVidisha to Jyotishmati

∴ Flow from Avanti to Vidisha = 200 + 800 = 1000

The diagram above shows the flow of the material in the pipelines andthe demand at the respective points.

∴ Quantity of material moved from Avanti to Vidisha = 1000

Hence, option 4.

6.3 Marks

The free capacity available at the Avanti-Vaishali pipeline is

1) 0

2) 100

3) 200

4) 300

Solution:From the flow diagram, we have,

Each pipeline has a capacity of 1000 and the flow in the Avanti-Vaishalipipeline is 700.

∴ Free capacity available = 1000 − 700 = 300

Hence, option 4.

7.3 Marks

What is the free capacity available in the Avanti-Vidisha pipeline?

1) 300

2) 200

3) 100

4) 0


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Solution:From the flow diagram, the Avanti-Vidisha pipeline carries 1000.

∴ The Avanti-Vidisha pipeline has no free capacity.

Hence, option 4.

8.3 Marks

While Balbir had his back turned, a dog ran into his butcher shop, snatched apiece of meat off the counter and ran out. Balbir was mad when he realisedwhat had happened. He asked three other shopkeepers, who had seen thedog, to describe it. The shopkeepers really didn't want to help Balbir. So eachof them made a statement which contained one truth and one lie.

Shopkeeper Number 1 said: "The dog had black hair and a long tail."A.Shopkeeper Number 2 said: "The dog has a short tail and wore a collar."B.Shopkeeper Number 3 said: "The dog had white hair and no collar."C.

Based on the above statements, which of the following could be a correctdescription?

[CAT 2001]

1) The dog had white hair, short tail and no collar.

2) The dog had white hair, long tail and a collar.

3) The dog had black hair, long tail and a collar.

4) The dog had black hair, long tail and no collar.

Solution:According to the statement of the shopkeeper number 1, the dog had eitherblack hair or a long tail, but definitely not both.

∴ Options 3 and 4 can be eliminated.

According to the statement of shopkeeper number 3, the dog had either whitehair or wore a collar, but not both.

∴ Option 1 can be eliminated.

Hence, option 2.

9.3 Marks

Eight people carrying food baskets are going for a picnic on motorcycles.Their names A, B, C, D, E, F, G, and H. They have four motorcycles, M1, M2,M3 and M4 among them. They also have four food baskets O, P, Q and R of


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different sizes and shapes and each can be carried only on motorcycles M1,M2, M3, or M4, respectively. No more than two persons can travel on amotorcycle and no more than one basket can be carried on a motorcycle.There are two husband-wife pairs in this group of eight people and each pairwill ride on a motorcycle together. C cannot travel with A or B. E cannot travelwith B or F. G cannot travel with F or H or D. The husband-wife pairs mustcarry baskets O and P. Q is with A and P is with D. F travels on M1 and Etravels on M2 motorcycles. G is with Q, and B cannot go with R. Who istravelling with H?

1) A

2) B

3) C

4) D

Solution:As, O, P, Q, R are on motorcycle M1, M2, M3, M4 respectively. Hence we get,

Now, A is with Q and G is with Q hence A is with G on motorcycle M3.

And F is on M1 and E is on M2.

P is with D hence D is with E.

As B cannot go with R hence he has to go with F on motorcycle M1.

Hence C and H go together on motorcycle M4.

Hence we get,

Hence C goes with H.


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Hence, option 3.

10.3 Marks

In a family gathering there are two males who are grandfathers and fourmales who are fathers. In the same gathering there are two females who aregrandmothers and four females who are mothers. There is at least onegrandson or a granddaughter present in this gathering. There are twohusband-wife pairs in this group. These can either be a grandfather and agrandmother, or a father and a mother. The single grandfather (who wife isnot present) has two grandsons and a son present. The single grandmother(whose husband is not present) has two granddaughters and a daughterpresent. A grandfather or a grandmother present with their spouses does nothave any grandson or granddaughter present. What is the minimum numberof people present in this gathering?

[CAT 2001]

1) 10

2) 12

3) 14

4) 16

Solution:

Here "-" represents the Husband-Wife pair.

∵ We want the minimum number of people, let us assume that the twograndfathers and two grandmothers have already been counted as fathersand mothers respectively.

∴ We have 4 fathers, 4 mothers, 2 grandsons and 2 granddaughters.

∴ Minimum number of people present = 4 + 4 + 2 + 2 = 12

Hence, option 2.

Group Question


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A and B are two sets (e.g. A = mothers, B = women). The elements that couldbelong to both the sets (e.g. women who are mothers) is given by the set C = A.B.The elements which could belong to either A or B, or both, is indicated by the setD = A ∪ B. A set that does not contain any elements is known as a null set,represented by ϕ (for example, if none of the women in the set B is a mother, theyC = A.B is a null set, or C = ϕ).

Let 'V' signify the set of all vertebrates; 'M' the set of all mammals; 'D' dogs; 'F'fish; 'A' Alsatian and 'P', a dog named Pluto.

[CAT 2001]

11.3 Marks

Given that X = M.D is such that X = D, which of the following is true?

1) All dogs are mammals.

2) Some dogs are mammals.

3) X = ϕ

4) All mammals are dogs.

Solution:X = M.D implies some dogs are mammals and X = D implies the set ofdogs.

This implies all dogs are mammals.

Hence, option 1.

12.3 Marks

If Y = F. (D.V), is not a null set, it implies that

1) All fish are vertebrates

2) All dogs are vertebrates

3) Some fish are dogs


Solution:Y = F.(D.V) implies some vertebrates are dogs and some vertebratedogs are fishes.

∴ Some fishes are dogs.


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Hence, option 3.

13.3 Marks

If Z = (P.D) ∪ M, then

1) The elements of Z consist of Pluto the dog or any othermammal.

2) Z implies any dog or mammal.

3) Z implies Pluto or any dog that is a mammal.

4) Z is a null set.

Solution:Z = (P.D) ∪ M

P.D means a dog called Pluto and P ∪ M means Pluto the dog and theother mammals.

Hence, option 1.

14.3 Marks

If P.A = ϕ and P ∪ A = D, then which of the following is true?

1) Pluto and Alsatians are dogs.

2) Pluto is an Alsatian.

3) Pluto is not an Alsatian.

4) D is a null set.

Solution:P. A = ϕ means that "Pluto is not an Alsatian".

Hence, option 3.

Group Question


In a country, the following signals are applicable:


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A man headed towards north and follows the given signals as:

[CAT 2002]

15.3 Marks

What is the total distance covered by the man till the last signal?

1) 90 km

2) 120 km

3) 110 km

4) 84 km

Solution:The movement can be tabulated as below:

= 10 + 10 + 20 + 40 + 10


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= 90 km

Hence, option 1.

16.3 Marks

What is his net displacement with respect to the starting point?

1) 40 km towards South West

2) 50 km towards North East

3) 40 km towards North East

4) 60 km towards South West

Solution:The map of his movements is as shown below:

∴ The net displacement with respect to the starting point

Hence, option 2.


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17.3 Marks

If the first signal after the starting point, is 1 Red and 2 Green lights,then what is the total distance covered by the man till the last signal?

1) 90 km

2) 50 km

3) 40 km

4) 80 km

Solution:Since only the direction of the man has changed, the total distancecovered by him will still remain the same.

∴ Total distance = 90 km

Hence, option 1.

18.3 Marks

Instead of heading North, if the man was heading South, then by theend of the journey, he was

1) 50 km towards South, 50 km towards West from his startingpoint.

2) 50 km towards North, 50 km towards West from his startingpoint.

3) 60 km towards North, 40 km towards West from his startingpoint.

4) 40 km towards South, 30 km towards West from his startingpoint.

Solution:If instead of North, the man headed for South, the map given in thesolution of the second question in the set will get inverted and flipped.

∴ He will end up south-west of his starting position, instead ofnorth-east.

∴ He ends up at 30 km West and 40 km South of his starting point.

Hence, option 4.

19.3 Marks

In each of the following questions there are two blanks marked I & II. Thewords to fill in these blanks are given against I as (A, B, C, D) and II as (P, Q,R, S). The right words to fill in these blanks are given as four alternatives. The


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words on either side of the sign (::) have a similar relationship. That alternativewhich signifies this relationship is your answer.

For what reason Purohit did not get the offer of employment?

Statement:

Purohit passed the interview.I.Purohit's friend passed the medical test who passed the interview along withPurohit.

II.

Purohit's father did not want him to take the job.III.Purohit has another employment offer from another company.IV.Purohit did not clear the mandatory medical test.V.

[CAT 2002]

1) III and IV only

2) III, IV and V only

3) I, III and IV only

4) V only

Solution:Non-clearance of the mandatory medical test is the reason for not getting theoffer of employment.

Hence, option 4.

20.3 Marks

Each question given below is followed by five statements numbered I, II, III, IVand V. The answer choice given below each question consists of one or morestatements. You have to choose the choice which gives more relevant / usefulinformation in answering the question correctly. Read all the statementstogether with the question and choose your answer

What were the possible reasons due to which DESCO incurred losses for thelast two years?

Statement:

The company's shares are not registered in the stock exchange.I.The company does not export its products.II.The company has an inefficient labour force.III.The price of its product has fallen in the last two years due to competitive market.IV.Entry of similar foreign goods at a cheaper rate.V.

[CAT 2002]


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1) Only III, IV and V

2) Only II, III and IV

3) Only IV and V

4) Only I and II

Solution:Inefficient labour forces, fall in product price, and entry of similar foreigngoods at lower rates are the possible reasons for incurring losses by DESCO.

Hence, option 1.

21.3 Marks

Each question given below is followed by five statements numbered I, II, III, IVand V. The answer choice given below each question consists of one or morestatements. You have to choose the choice which gives more relevant / usefulinformation in answering the question correctly. Read all the statementstogether with the question and choose your answer

On which day of the week did Sunil get his letter of promotion?

Statement:

Sunil purchased a new shirt on FridayI.Sunil was given a party that Saturday.II.Sunil was given the letter of promotion on the day before he purchased the shirt.III.Tuesday being his birthday, Sunil gave a party to all his friends.IV.Sunil's friend was promoted on Friday.V.

[CAT 2002]

1) I and II only

2) II, III and IV only

3) I and III only

4) II, III and V only

Solution:Sunil purchased a new shirt on Friday and he got the letter of promotion oneday before.

∴ Sunil got his letter of promotion on Thursday. Hence, option 3.

Group Question


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New Age Consultants have three consultants Gyani, Medha and Buddhi. The sumof the number of projects handled by Gyani and Buddhi individually is equal tothe number of projects in which Medha is involved. All three consultants areinvolved together in 6 projects. Gyani works with Medha in 14 projects. Buddhihas 2 projects with Medha but without Gyani and 3 projects with Gyani butwithout Medha. The total number of projects for New Age Consultants is one lessthan twice the number of projects in which more than one consultant is involved.


22.3 Marks

What is the number of projects in which Gyani alone is involved?

1) Uniquely equal to zero

2) Uniquely equal to 1


4) Cannot be determined uniquely

Solution:

Let a be the number of projects in which only Gyani is involved, g be thenumber of projects in which only Buddhi is involved and c be thenumber of projects in which only Medha is involved.

From the data, d = 6

b + d = 14

∴ b = 8

Also, e = 3 and f = 2

It is given that


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a + g = b + c + d + f

∴ a − c + g = 16 … (i)

Number of projects involving more than 1 consultant = 6 + 8 + 2 + 3 =19

∴ Total number of projects = 2 × 19 − 1 = 37

a + b + c + d + e + f + g = 2 × (b + d + e + f) − 1

∴ a + c + g = 19 − 1 = 18 … (ii)

Solving (i) and (ii), we get,

c = 1 and a + g = 17

∴ a cannot be determined uniquely.

Hence, option 4.

23.3 Marks

What is the number of projects in which Medha alone is involved?

1) Uniquely equal to zero



4) Cannot be determined uniquely

Solution:From the solution to the previous question, we get, c = 1

∴ Number of projects in which Medha alone is involved = 1

Hence, option 2.

Group Question


Shown below is a layout of major streets in a city.

Two days (Thursday and Friday) are left for campaigning before a major election,and the city administration has received requests from five political parties fortaking out their processions along the following routes.


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Congress: A-C-D-EBJP: A-B-D-ESP: A-B-C-EBSP: B-C-ECPM: A-C-D

Street B-D cannot be used for a political procession on Thursday due to areligious procession. The district administration has a policy of not allowing morethan one procession to pass along the same street on the same day. However, theadministration must allow all parties to take out their procession during these twodays.

[CAT 2003 Re-Test]

24.3 Marks

Congress procession can be allowed:

1) Only on Thursday.

2) Only on Friday.

3) On either day.

4) Only if the religious procession is cancelled.

Solution:

∵ Route BD cannot be used on Thursday.

∴ BJP has to take out its procession on Friday.

∵ Route DE is common to BJP and Congress.

∴ Congress should take out its procession on Thursday.


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∵ Route AB is common to SP and BJP.

∴ SP should take out its procession on Thursday.

∴ BSP and CPM have to take out their processions on Friday.

∴ Congress procession can be allowed only on Thursday.

Hence, option 1.

25.3 Marks

Which of the following is not true?

1) Congress and SP can take out their processions on the sameday.

2) The CPM procession cannot be allowed on Thursday.

3) The BJP procession can only take place on Friday.

4) Congress and BSP can take out their processions on thesame day.

Solution:From the explanation given in the solution of the first question we getthat,

Congress takes out a procession on Thursday and BSP on Friday.

∴ Only option 4 is not true.

Hence, option 4.

26.3 Marks

70 percent of the employees in a multinational corporation have VCD players,75 percent have microwave ovens, 80 percent have ACs and 85 percent havewashing machines. At least what percentage of employees has all fourgadgets?

[CAT 2003 Re-Test]

1) 15%

2) 5%

3) 10%



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Solution:70% have VCD Players.

∴ 30% do not have VCD Players.

75% have microwave ovens.

∴ 25% do not have microwave ovens.

80% have ACs.

∴ 20% do not have ACs.

85% have washing machines.

∴ 15% do not have washing machines.

∴ 30 + 25 + 15 + 20 = 90% of employees do not have at least 1 gadget.

∴ Minimum percentage of employees who has all the four gadgets

= 100 – 90 = 10%

Hence, option 3.

Alternatively,

Minimum percentage of employees which possess both VCDs andMicrowaves

= 70% + 75% – 100%

= 45%

Minimum percentage of employees which possess both ACs and Washingmachines

= 80% + 85% – 100%

= 65%

∴ Minimum percentage of employees which possess all the four gadgets

= 45% + 65% – 100%

= 10%


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Hence, option 3.

Group Question


The seven basic symbols in a certain numeral system and their respective valuesare as follows:

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000

In general, the symbols in the numeral system are read from left to right, startingwith the symbol representing the largest value; the same symbol cannot occurcontinuously more than three times; the value of the numeral is the sum of thevalues of the symbols.

For example, XXVII = 10 + 10 + 5 + 1 + 1 = 27.

An exception to the left-to-right reading occurs when a symbol is followedimmediately by a symbol of greater value; then, the smaller value is subtractedfrom the larger.

For example, XLVI = (50 – 10) + 5 + 1 = 46.

[CAT 2003 Re-Test]

27.3 Marks

The value of the numeral MDCCLXXXVII is:

1) 1687

2) 1787

3) 1887

4) 1987

Solution:The expression MDCCLXXXVII is expanded as,

1000 + 500 + 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1

= 1787

Hence, option 2.

28.3 Marks

The value of the numeral MCMXCIX is

1) 1999


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2) 1899

3) 1989

4) 1889

Solution:The expression MCMXCIX is expanded as, 1000 + (1000 – 100) + (100 – 10) + (10 – 1)

= 1000 + 900 + 90 + 9

= 1999

Hence, option 1.

29.3 Marks

Which of the following can represent the numeral for 1995?

MCMLXXVa.MCMXCVb.MVDc.MVMd.

1) Only (a) and (b)

2) Only (c) and (d)

3) Only (b) and (d)

4) Only (d)

Solution:Option (a): MCMLXXV

= 1000 + (1000 – 100) + 50 + 10 + 10 + 5

= 1000 + 900 + 50 + 25 = 1975

Option (b): MCMXCV

= 1000 + (1000 – 100) + (100 – 10) + 5

= 1000 + 900 + 90 + 5 = 1995

Option (c): MVD


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= 1000 + (500 – 5) = 1000 + 495 = 1495

Option (d): MVM

= 1000 + (1000 – 5) = 1000 + 995 = 1995

Options (b) and (d) give 1995.

Hence, option 3.

Group Question


A study was conducted to ascertain the relative importance that employees in fivedifferent countries assigned to five different traits in their Chief Executive Officers.The traits were compassion (C), decisiveness (D), negotiation skills (N), publicvisibility (P), and vision (V). The level of dissimilarity between two countries is themaximum difference in the ranks allotted by the two countries to any of the fivetraits. The following table indicates the rank order of the five traits for eachcountry.

[CAT 2004]

30.3 Marks

Three of the following four pairs of countries have identical levels ofdissimilarity. Which pair is the odd one out?

1) Malaysia and China

2) China and Thailand

3) Thailand and Japan

4) Japan and Malaysia

Solution:Let us consider the options:

1. Malaysia and China: The maximum level of dissimilarity is 4 for ‘V’ or


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‘N’.

2. China and Thailand: The maximum level of dissimilarity is 4 for ‘V’.

3. Thailand and Japan: The maximum level of dissimilarity is 4 for ‘D’.

4. Japan and Malaysia: The maximum level of dissimilarity is 3 for ‘V’ or‘N’.

Hence, option 4.

31.3 Marks

Which amongst the following countries is most dissimilar to India?

1) China

2) Japan

3) Malaysia

4) Thailand

Solution:

The table gives levels of dissimilarity between India and the othercountries for all traits.

Clearly, Japan is most dissimilar to India (since its level of dissimilarity is4).

Hence, option 2.

32.3 Marks

Which of the following countries is least dissimilar to India?

1) China

2) Japan

3) Malaysia

4) Thailand

Solution:


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From the above table, China is least dissimilar to India (since its level ofdissimilarity is only 2).

Hence, option 1.

33.3 Marks

Which of the following pairs of countries are most dissimilar?

1) China and Japan

2) India and China

3) Malaysia and Japan

4) Thailand and Japan

Solution:Consider the levels of dissimilarities for the four options.

China and Japan ≡ 3 (for 'D')

India and China ≡ 2 (for 'N')

Malaysia and Japan ≡ 3 (for 'N' or 'V')

Thailand and Japan ≡ 4 (for 'D')

Hence, option 4.

Group Question


Help Distress (HD) is an NGO involved in providing assistance to people sufferingfrom natural disasters. Currently, it has 37 volunteers. They are involved in threeprojects: Tsunami Relief (TR) in Tamil Nadu, FloodRelief (FR) in Maharashtra, andEarthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress hasto be involved in at least one relief work project.

A Maximum number of volunteers are involved in the FR project. Among them, thenumber of volunteers involved in FR project alone is equal to the volunteers havingadditional involvement in the ER project.The number of volunteers involved in the ER project alone is double the number of


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volunteers involved in all the three projects.17 volunteers are involved in the TR project.The number of volunteers involved in the TR project alone is one less than the number ofvolunteers involved in ER Project alone.Ten volunteers involved in the TR project are also involved in at least one more project.

[CAT 2005]

34.3 Marks

Based on the information given above, the minimum number ofvolunteers involved in both FR and TR projects, but not in the ERproject is:

1) 1

2) 3

3) 4

4) 5

Solution:

17 volunteers are involved in the TR project and 10 in TR are alsoinvolved in other projects. Thus, 7 volunteers are involved only in TR.

∴ 8 volunteers are involved in ER alone.

∴ 4 volunteers are involved in all the three projects.

Let x people be involved in FR alone.

∴ Number of people involved in FR and ER but not TR = x – 4

Now, a + b + 4 = 10


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∴ a + b = 6

Also, 7 + a + b + 4 + x + x – 4 + 8 = 37

∴ 2x = 16 or x = 8

Number of Volunteers involved in FR > Number of Volunteers involved inTR

And Number of Volunteers involved in FR > Number of Volunteersinvolved in ER

∴ 16 + a > 17 and 16 + a > 16 + b or a > b

∴ a and b can be (6, 0), (5, 1), (4, 2)

The minimum number of volunteers involved in both FR and TRprojects, but not in the ER Project = minimum value of a = 4

Hence, option 3.

35.3 Marks

Which of the following additional information would enable to find theexact number of volunteers involved in various projects?

1) Twenty volunteers are involved in FR.

2) Four volunteers are involved in all the three projects.

3) Twenty three volunteers are involved in exactly one project.

4) No need for any additional information.

Solution:We can obtain the information in options 2 and 3 from the initial data.

Based on the information given in the explanation to the first question,the information in option 1 will give us the value of a, which in turn willgive us the value of b. Thus, option 1 would enable us to find the exactnumber of volunteers involved in various projects.

Hence, option 1.

36.3 Marks

After some time, the volunteers who were involved in all the threeprojects were asked to withdraw from one project. As a result, one ofthe volunteers opted out of the TR project, and one opted out of the ERproject, while the remaining ones involved in all the three projects optedout of the FR project. Which of the following statements, then,


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necessarily follows?

1) The lowest number of volunteers is now in TR project.

2) More volunteers are now in FR project as compared to ERproject.

3) More volunteers are now in TR project as compared to ERproject.


Solution:

After the volunteers withdraw as mentioned, the number of volunteersworking on different projects is as shown.

∴ Number of volunteers working on TR = 7 + 6 + 3 = 16

Number of volunteers working on FR = 14 + a

Number of volunteers working on ER = 15 + b

Considering the possible values of a and b, 14 + a > 15 + b

∴ More volunteers are now in FR than in ER

Hence, option 2.

37.3 Marks

After the withdrawal of volunteers, as indicated in Question 89, somenew volunteers joined the NGO. Each one of them was allotted onlyone project in a manner such that, the number of volunteers working in


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one project alone for each of the three projects became identical. At thatpoint, it was also found that the number of volunteers involved in FRand ER projects was the same as the number of volunteers involved inTR and ER projects. Which of the projects now has the highest numberof volunteers?

1) ER

2) FR

3) TR


Solution:Let m volunteers be added to TR project and n be added to each of FRand ER projects.

Then, 7 + m = 8 + n

∴ m = n + 1

Also, b + 2 = 5

∴ b = 3 and a = 3

Number of volunteers working on TR = 7 + n + 1 + 4 + 5 = 17 + n

Number of volunteers working on FR = 17 + n

Number of volunteers working on ER = 18 + n

Thus, ER has the highest number of volunteers.

Hence, option 1.

38.3 Marks

Three Englishmen and three Frenchmen work for the same company. Each ofthem knows a secret not known to others. They need to exchange thesesecrets over person-to-person phone calls so that eventually each personknows all six secrets. None of the Frenchmen knows English, and only oneEnglishman knows French. What is the minimum number of phone callsneeded for the above purpose?

[CAT 2005]

1) 5


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2) 10

3) 9

4) 15

Solution:Let E1, E2 and E3 be the three Englishmen and F1, F2 and F3 be the threeFrenchmen.

Let E3 be the only Englishman knowing French.

Now, Let A ↔ B denote a phone call between A and B, where they both telleach other their secrets.The following phone calls will ensure that all sixpersons know all the six secrets.

1. E1 ↔ E2

2. E2 ↔ E3 (Now E3 knows all the secrets with the Englishmen)

3. F1 ↔ F2

4. F2 ↔ F3 (Now F3 knows all the secrets with the Frenchmen)

5. F3 ↔ E3 (Now F3 and E3 know all the secrets)

6. E3 ↔ E2

7. E2 ↔ E1

8. F3 ↔ F2

9. F2 ↔ F1

Thus, a minimum of 9 calls are needed to pass all the secrets to all the sixpersons.

Hence, option 3.

Group Question


A significant amount of traffic flows from point S to point T in the one-way streetnetwork shown below. Points A, B, C, and D are junctions in the network, and thearrows mark the direction of traffic flow. The fuel cost in rupees for travelling alonga street is indicated by the number adjacent to the arrow representing the street.


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Motorists travelling from point S to point T would obviously take the route forwhich the total cost of travelling is the minimum. If two or more routes have thesame least travel cost, then motorists are indifferent between them. Hence, thetraffic gets evenly distributed among all the least cost routes.

The government can control the flow of traffic only by levying appropriate toll ateach junction. For example, if a motorist takes the route S-A-T (using junction Aalone), then the total cost of travel would be Rs. 14 (i.e. Rs. 9 + Rs. 5) plus thetoll charged at junction A.

[CAT 2006]

39.3 Marks

If the government wants to ensure that all motorists travelling from S toT pay the same amount (fuel costs and toll combined) regardless of theroute they choose and the street from B to C is under repairs (andhence unusable), then a feasible set of toll charged (in rupees) atjunctions A, B, C, and D respectively to achieve this goal is:

1) 2, 5, 3, 2

2) 0, 5, 3, 1

3) 1, 5, 3, 2

4) 2, 3, 5, 1

5) 1, 3, 5, 1

Solution:Let the toll charged at junctions A, B, C and D be a, b, c and drespectively.

Since the cost of travel including toll on routes S-A-T, S-D-T, S-B-A-Tand S-D-C-T is the same,

∴ 14 + a = 13 + d = 9 + a + b = 10 + c + d

Thus, b = 5, d – a = 1, c = 3


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If a = 0, d = 1, If a = 1, d = 2 and if a = 2, d = 3

Hence, both options 2 and 3 satisfy the given criteria.

Note: The question makers took care of this inconsistency whilecalculating scores.

40.3 Marks

If the government wants to ensure that no traffic flows on the street fromD to T, while equal amount of traffic flows through junctions A and C,then a feasible set of toll charged (in rupees) at junctions A, B, C, and Drespectively to achieve this goal is:

1) 1, 5, 3, 3

2) 1, 4, 4, 3

3) 1, 5, 4, 2

4) 0, 5, 2, 3

5) 0, 5, 2, 2

Solution:Since the cost of travel including toll on routes S-A-T, S-B-C-T, S-B-A-Tand S-D-C-T is the same,

∴ 14 + a = 7 + b + c = 9 + a + b = 10 + c + d

∴ b = 5, d = 2, c – a = 2

Only option 5 satisfies these criteria.

Hence, option 5.

41.3 Marks

If the government wants to ensure that all routes from S to T get thesame amount of traffic, then a feasible set of toll charged (in rupees) atjunctions A, B, C, and D respectively to achieve this goal is:

1) 0, 5, 2, 2

2) 0, 5, 4, 1

3) 1, 5, 3, 3

4) 1, 5, 3, 2

5) 1, 5, 4, 2


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Solution:Since the cost of travel including toll on all routes is the same.

∴ 14 + a = 7 + b + c = 13 + d = 9 + a + b = 10 + c + d

∴ b = 5, d = 2, c = 3 and a = 1

Hence, option 4.

42.3 Marks

If the government wants to ensure that the traffic at S gets evenlydistributed along streets from S to A, from S to B, and from S to D, thena feasible set of toll charged (in rupees) at junctions A, B, C, and Drespectively to achieve this goal is:

1) 0, 5, 4, 1

2) 0, 5, 2, 2

3) 1, 5, 3, 3

4) 1, 5, 3, 2

5) 0, 4, 3, 2

Solution:If we make the cost of travelling on all the routes equal, traffic along S-Bwill be twice that along S-A.

But we want traffic along S-A, S-B and S-D to be the same.

As routes lead to C from both B and D, we can increase the toll at C sothat the cost of travelling along S-B-C-T and S-D-C-T is more than thatalong the other three routes.

Now, 14 + a = 9 + b = 13 + d

∴ a = 0, b = 5 and d =1

Also, 7 + b + c > 14 and 10 + d + c > 14

∴ c > 3

Hence, option 1.

43.3 Marks

The government wants to devise a toll policy such that the total cost tothe commuters per trip is minimized. The policy should also ensure thatnot more than 70 per cent of the total traffic passes through junction B.


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The cost incurred by the commuter travelling from point S to point Tunder this policy will be:

1) Rs. 7

2) Rs. 9

3) Rs. 10

4) Rs. 13

5) Rs. 14

Solution:If toll charges at all junctions are made 0, 100% traffic will pass throughS-B-C-T. This is not possible.

If toll charges at A and B are made 0, then 100% traffic will passthrough S-B-A-T. This is also not possible.

If toll charges at C and D are made 0, that at B are made Rs. 3, thenthe traffic will get equally divided between S-D-C-T and S-B-C-T.

Thus, the cost incurred will be Rs. 10.

Hence, option 3.

44.3 Marks

A survey was conducted of 100 people to find out whether they had readrecent issues of Golmal, a monthly magazine. The summarized informationregarding readership in 3 months is given below:

Only September: 18; September but not August: 23; September and July:8; September: 28; July: 48; July and August: 10; None of the three months:24.

What is the number of surveyed people who have read exactly twoconsecutive issues (out of the three)?

[CAT 2006]

1) 7

2) 9

3) 12

4) 14

5) 17


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Solution:

100 – 24 = 76 had read at least one issue.

If x people read all the three issues, then (8 – x) people read only theSeptember and July issues.

23 people read the September issue but not the August issue.

∴ 18 + 8 – x = 23

∴ x = 3

As 28 people read the September issue, [28 – (8 – 3) – 3 – 18] = 2 peopleread only the August and September issues.

As 10 people read the July and August issues, 10 – 3 = 7 people read onlythe July and August issues.

∴ The number of people who have read exactly two consecutive issues = 7 +2 = 9

Hence, option 2.


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http://www.time4education.com/onlinecattests/forprint.asp?ar=LDI&tn=1

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PAST CAT PAPER – 2002 Page 1

Directions for questions 1 to 6: Answer the questions independently.Four students — Ashish, Dhanraj, Felix and Sameer sat for the Common Entrance Exam for Management(CEEM). One student got admission offers from three NIMs (National Institutes of Management), anotherfrom two NIMs, the third from one NIM, while the fourth got none. Below are some of the facts about whogot admission offers from how many NIMs and what is their educational background.

I. The one who is an engineer didn’t get as many admissions as Ashish.II. The one who got offer for admissions in two NIMs isn’t Dhanraj nor is he a chartered accountant.III. Sameer is an economist.IV. Dhanraj isn’t an engineer and received more admission offers than Ashish.V. The doctor got the most number of admission offers.

1. Which one of the following statements is necessarily true?1. Ashish is a chartered accountant and got offer for admission in three NIMs.2. Dhanraj is a doctor and got admission offer in one NIM.3. Sameer is an economist who got admission offers in two NIMs.4. Felix who is not an engineer did not get any offer for admission.

2. Five boys went to a store to buy sweets. One boy had Rs. 40. Another boy had Rs. 30. Two otherboys had Rs. 20 each. The remaining boy had Rs. 10. Below are some more facts about the initialand final cash positions.I. Alam started with more than Jugraj.II. Sandeep spent Rs. 1.50 more than Daljeet.III. Ganesh started with more money than just only one other person.

IV. Daljeet started with 2

3 of what Sandeep started with.

V. Alam spent the most, but did not end with the least.VI. Jugraj spent the least and ended with more than Alam or Daljeet.VII. Ganesh spent Rs.3.50.VIII. Alam spent 10 times more than what Ganesh did.

In the choices given below, all statements except one are false. Which one of the following statementscan be true?1. Alam started with Rs. 40 and ended with Rs. 9.502. Sandeep started with Rs. 30 and ended with Re. 13. Ganesh started with Rs. 20 and ended with Rs. 44. Jugraj started with Rs. 10 and ended with Rs. 7

PAST CAT PAPER � 2002Instructions:

1. The Test Paper contains 150 questions. The duration of the test is 120 minutes.

2. The paper is divided into three sections. Section-I: 50 Q:, Section-II: 50 Q:, Section-III: 50 Q.

3. Wrong answers carry negative marks. There is only one correct answer for each question.

Section � 1

PAST CAT PAPER – 2002Page 2

3. In a hospital there were 200 diabetes, 150 hyperglycaemia and 150 gastro-enteritis patients.Of these, 80 patients were treated for both diabetices and hyperglycaemia. Sixty patients weretreated for gastro-enteritis and hyperglycaemia, while 70 were treated for diabetes and gastro-enteritis. Some of these patients have all the three diseases. Dr. Dennis treats patients with onlygastro-enteritis. Dr. Paul is a generalist. Therefore, he can treat patients with multiple diseases.Patients always prefer a specialist for their disease. If Dr. Dennis had 80 patients, then the otherthree doctors can be arranged in terms of the number of patients treated as:1. Paul > Gerard > Hormis 2. Paul > Hormis > Gerard3. Gerard > Paul > Hormis 4. None of these

4. Three children won the prizes in the Bournvita Quiz contest. They are from the schools: Loyola,Convent and Little Flowers, which are located at different cities. Below are some of the facts aboutthe schools, the children and the city they are from.I. One of the children is Bipin.II. Loyola School’s contestant did not come first.III. Little Flower’s contestant was named Riaz.IV. Convent School is not in Hyderabad.V. The contestant from Pune is not from Loyola School.VI. The contestant from Bangalore did not come first.VII. Convent School’s contestant’s name is not Balbir.

Which of the following statements is true?1. 1st prize: Riaz (Little Flowers), 2nd prize: Bipin (Convent), 3rd prize: Balbir (Loyola)2. 1st prize: Bipin (Convent), 2nd prize: Riaz (Little Flowers), 3rd prize: Balbir (Loyola)3. 1st prize: Riaz (Little Flowers), 2nd prize: Balbir (Loyola), 3rd prize: Bipin (Convent)4. 1st prize: Bipin (Convent), 2nd prize: Balbir (Loyola), 3rd prize: Riaz (Litttle Flowers)

5. Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boyis equal to the cube root of the product of the age of the two boys. If we place the digit representingthe age of the younger boy to the left of the digit representing the age of the elder boy, we get the ageof father of the younger boy. Similarly, if we place the digit representing the age of the elder boy tothe left of the digit representing the age of the younger boy and divide the figure by 2, we get the ageof mother of the younger boy. The mother of the younger boy is younger to his father by 3 years.Then, what is the age of the younger boy?1. 3 2. 4 3. 2 4. None of these

6. Flights A and B are scheduled from an airport within the next one hour. All the booked passengersof the two flights are waiting in the boarding hall after check-in. The hall has a seating capacity of200, out of which 10% remained vacant. 40% of the waiting passengers are ladies. When boardingannouncement came, passengers of flight A left the hall and boarded the flight. Seating capacity ofeach flight is two-third of the passengers who waited in the waiting hall for both the flights puttogether. Half the passengers who boarded flight A are women. After boarding for flight A, 60% of thewaiting hall seats became empty. For every twenty of those who are still waiting in the hall for flightB, there is one air hostess in flight A. What is the ratio of empty seats in flight B to the number ofair hostesses in flight A?1. 10 : 1 2. 5 : 1 3. 20 : 1 4. 1 : 1


Directions for questions 7 to 10: Answer the questions based on the information given below.A country has the following types of traffic signals.3 red lights = stop2 red lights = turn left1 red light = turn right3 green lights = go at 100 km/hr speed2 green lights = go at 40 km/hr speed1 green light = go at 20 km/hr speedA motorist starts at a point on a road and follows all traffic signals. His car is heading towards the north.He encounters the following signals (the time mentioned in each case below is applicable after crossingthe previous signal).Starting point - 1 green lightAfter half an hour, 1st signal - 2 red and 2 green lightsAfter 15 min, 2nd signal - 1 red lightAfter half an hour, 3rd signal - 1 red and 3 green lightsAfter 24 min, 4th signal - 2 red and 2 green lightsAfter 15 min, 5th signal - 3 red lights

7. The total distance travelled by the motorist from the starting point till the last signal is1. 90 km 2. 100 km 3. 120 km 4. None of these

8. What is the position (radial distance) of the most motorist when he reaches the last signal?1. 45 km directly north of the starting point2. 30 km directly to the east of the starting point3. 50 km away to the north-east of the starting point4. 45 km away to the north-west of the starting point

9. After the starting point if the 1st signal were 1 red and 2 green lights, what would be the final positionof the motorist?1. 30 km to the west and 20 km to the south 2. 30 km to the west and 40 km to the north3. 50 km to the east and 40 km to the north 4. Directly 30 km to the east

10. If at the starting point, the car was heading towards south, what would be the final position of themotorist?1. 30 km to the east and 40 km to the south 2. 50 km to the east and 40 km to the south3. 30 km to the west and 40 km to the south 4. 50 km to the west and 20 km to the north


Directions for questions 11 to 13: Answer these questions based on the table given below.The following table provides data on the different countries and location of their capitals. (the data may notmatch the actual Latitude, Longitudes) Answer the following questions on the basis of this table.

S.No. Country Capital Latitude Longitude

1 Argentina Buenos Aires 34.30 S 58.20 E

2 Australia Canberra 35.15 S 149.08 E

3 Austria Vienna 48.12 N 16.22 E

4 Bulgaria Sofia 42.45 N 23.20 E

5 Brazil Brasilia 15.47 S 47.55 E

6 Canada Ottawa 45.27 N 75.42 E

7 Cambodia Phnom Penh 11.33 N 104.55 E

8 Equador Quito 0.15 S 78.35 E

9 Ghana Accra 5.35 N 0.6 E

10 Iran Teheran 35.44 N 51.30 E

11 Ireland Dublin 53.20 N 6.18 E

12 Libya Tripoli 32.49 N 13.07 E

13 Malaysia Kuala Lumpur 3.9 N 101.41 E

14 Peru Lima 12.05 S 77.0 E

15 Poland Warsaw 52.13 N 21.0 E

16 New Zealand Wellington 41.17 S 174.47 E

17 Saudi Arabia Riyadh 24.41 N 46.42 E

18 Spain Madrid 40.25 N 3.45 W

19 Sri Lanka Colombo 6.56 N 79.58 E

20 Zambia Lusaka 15.28 S 28.16 E

11. What percentage of cities located within 10 E° and 40 E° (20° East and 40° East) lie in the SouthernHemisphere?1. 15% 2. 20% 3. 25% 4. 30%

12. The number of cities whose names begin with a consonant and are in the Northern Hemisphere inthe table1. exceeds the number of cities whose names begin with a consonant and are in the southern

hemisphere by 12. exceeds the number of cities whose names begin with a consonant and are in the southern

hemisphere by 23. is less than the number of cities whose names begin with a consonant and are in the east of the

meridian by 14. is less than the number of countries whose name begins with a consonant and are in the east

of the meridian by 3

13. The ratio of the number of countries whose name starts with vowels and located in the southernhemisphere, to the number of countries, the name of whose capital cities starts with a vowel in thetable above is1. 3 : 2 2. 3 : 3 3. 3 : 1 4. 4 : 3


Directions for questions 14 to 21: Each item is followed by two statements, A and B. Answer eachquestion using the following instructions.

Choose 1 if the question can be answered by one of the statement alone but not by the other.Choose 2 if the question can be answered by using either statement alone.Choose 3 if the question can be answered by using both the statements together, but cannot beanswered by using either statement alone.Choose 4 if the question cannot be answered by either of the statements.

14. In a hockey match, the Indian team was behind by 2 goals with 5 min remaining. Did they win thematch?A. Deepak Thakur, the Indian striker, scored 3 goals in the last 5 min of the match.B. Korea scored a total of 3 goals in the match.1. 1 2. 2 3. 3 4. 4

15. Four students were added to a dance class. Would the teacher be able to divide her students evenlyinto a dance team (or teams) of 8?A. If 12 students were added, the teacher could put everyone in teams of 8 without any leftovers.B. The number of students in the class is currently not divisible by 8.1. 1 2. 2 3. 3 4. 4

16. Is x = y?

A.1 1

(x y) 4x y

+ + =

B. 2 2(x 50) (y 50)− = −1. 1 2. 4 3. 3 4. 4

17. A dress was initially listed at a price that would have given the store a profit of 20% of the wholesalecost. What was the wholesale cost of the dress?A. After reducing the listed price by 10%, the dress sold for a net profit of $10.B. The dress is sold for $50.1. 1 2. 2 3. 3 4. 4

18. Is 500 the average (arithmetic mean) score in the GMAT?A. Half of the people who take the GMAT score above 500 and half of the people score below 500.B. The highest GMAT score is 800 and the lowest score is 200.1. 1 2. 2 3. 3 4. 4

19. Is |x – 2| < 1?A. |x| < 1B. |x – 1| < 21. 2 2. 1 3. 3 4. 4

20. People in a club either speak French or Russian or both. Find the number of people in a club whospeak only French.A. There are 300 people in the club and the number of people who speak both French and Russian

is 196.B. The number of people who speak only Russian is 58.1. 1 2. 2 3. 3 4. 4


21. A sum of Rs. 38,500 was divided among Jagdish, Punit and Girish. Who received the minimumamount?

A. Jadgish received 2

9 of what Punit and Girish received together.

B. Punit received 3

11 of what Jadgish and Girish received together.

1. 1 2. 2 3. 3 4. 4

Directions for questions 22 to 25: Answer the questions based on the following information.The following table gives details regarding the total earnings of 15 employees and the number of days theyhave worked on complex, medium and simple operation in the month of June 2002. Even though theemployees might have worked on an operation, they would be eligible for earnings only if they have minimumlevel of efficiency.

Emp. No Complex Medium Simple Total Complex Medium Simple Total

2001147 82.98 636.53 719.51 3.00 0.00 23.00 26.002001148 51.53 461.73 513.26 3.33 1.67 16.00 21.002001149 171.1 79.10 250.81 5.50 4.00 8.50 18.00

2001150 100.47 497.47 597.95 6.00 4.67 7.33 18.002001151 594.43 159.64 754.06 9.67 13.33 0.00 23.00

2001156 89.70 89.70 8.00 0.00 1.00 9.002001158 472.31 109.73 582.04 1.39 9.61 0.00 11.002001164 402.25 735.22 213.67 1351.14 5.27 12.07 0.67 18.00

2001170 576.57 576.57 21.00 0.00 0.00 21.002001171 286.48 6.10 292.57 8.38 4.25 0.38 13.002001172 512.10 117.46 629.56 10.00 8.50 3.50 22.00

2001173 1303.88 1303.88 25.50 0.00 0.50 26.002001174 1017.94 1017.9 26.00 0.00 0.00 26.002001179 46.56 776.19 822.75 2.00 19.00 0.00 21.00

2001180 116.40 1262.79 1379.19 5.00 19.00 0.00 24.00

Total Earnings Total Days

22. The number of employees who have earned more than Rs. 50 per day in complex operations is1. 4 2. 3 3. 5 4. 6

23. The number of employees who have earned more than Rs. 600 and having more than 80% attendance(there are 25 regular working days in June 2002; some might be coming on overtime too) is1. 4 2. 5 3. 6 4. 7

24. The employee number of the person who has earned the maximum earnings per day in mediumoperation is1. 2001180 2. 2001164 3. 2001172 4. 2001179

25. Among the employees who were engaged in complex and medium operations, the number ofemployees whose average earning per day in complex operations is more than average earning perday in medium operations is1. 2 2. 3 3. 5 4. 7


Directions for questions 26 to 33: Answer the questions based on the table given below:

The following table shows the revenue and expenses in millions of Euros (European currency) associatedwith REPSOL YPF company’s oil and gas producing activities in operations in different parts of the worldfor 1998-2000.

REPSOL YPF’S Operations of Oil and Gas Producing Activities

S. No. Item Year Total

World

Spain North

Africa &

Middle

East

Argentina Rest of

Latin

America

Far

East

North

Sea

Rest of

the

World

1998 916 70 366 281 34 82 78 5

1999 3374 55 666 2006 115 301 140 91

2000 8328 394 1290 5539 482 603 0 20

1998 668 39 255 187 57 63 52 15

1999 1999 48 325 1168 131 204 65 58

2000 3709 43 530 2540 252 311 0 33

Income

before1998 248 31 111 94 –23 19 26 –10

Taxes &

Charges1999 1375 7 341 838 –16 97 75 33

(Revenue-

Expenses)

=[(1)-(2)]

2000 4619 351 760 2999 230 292 0 –13

1998 152 6 104 33 –3 9 6 –3

1999 561 3 169 338 –6 39 21 –3

2000 1845 126 404 1150 61 103 0 1Net

Income 1998 96 25 7 61 –20 10 20 –7

Taxes

Charges1999 814 4 172 500 –10 58 54 36

[=(3)-(4)] 2000 2774 225 356 1849 169 189 0 –14

Revenue

Expenses

5

Taxes &

Charges

1

2

3

4

26. How many operations (Spain, North Africa and Middle East,..) of the company accounted for lessthan 5% of the total revenue earned in 1999?1. 2 2. 3 3. 4 4. None of these

27. How many operations (Spain, North Africa and Middle East…) of the company witnessed more than200% revenue from 1999 to 2000?1. 1 2. 2 3. 3 4. None of these

28. How many operations registered a sustained yearly increase in income before taxes and chargesfrom 1998 to 2000?1. 3 2. 4 3. 5 4. None of these


29. Ignoring the loss making operations of the company in 1998, for how many operations was thepercentage increase in net income before taxes and charges higher than the average from 1998 to1999?1. 0 2. 1 3. 2 4. None of these

30. If profitability is defined as the ratio of net income after taxes and charges to expense, which of thefollowing statements is true?1. The Far East operations witnessed its highest profitability in 19982. The North Sea operations increased its profitability from 1998 to 19993. The operations in Argentina witnessed a decrease in profitability from 1998 to 19994. Both 2 and 3 are true

31. In 2000, which among the following countries had the best profitability?1. North Africa and Middle East 2. Spain3. Rest of Latin America 4. Far East

32. If efficiency is defined as the ratio of revenue to expenses, which operation was the least efficient in2000?1. Spain 2. Argentina 3. Far East 4. None of these

33. Of the following statements, which one is not true?1. The operations in Spain had the best efficiency in 20002. The Far East operations witnessed an efficiency improvement from 1999 to 20003. The North Sea operations witnessed an efficiency improvement from 1998 to 19994. In 1998, the operations in Rest of Latin America were the least efficient

Directions for questions 34 and 35: Answer the questions based on the pie charts given below.

Chart 1

China

15%Turkey

16%

India

20%

Sw itzerland

20%

Pakistan

12%

USA

17%

Chart 2

China

17%

Turkey

15%India

26%

Sw itzerland

11%Pakistan

16%USA

15%

Chart 1 shows the distribution by value of top 6 suppliers of MFA Textiles in 1995. Chart 2 shows thedistribution by quantity of top 6 suppliers of MFA Textiles in 1995. The total value is 5760 millionEuro (European currency). The total quantity is 1.055 million tonnes.

34. The country which has the highest average price is1. USA 2. Switzerland 3. Turkey 4. India


35. The average price in Euro per kilogram for Turkey is roughly1. 6.20 2. 5.60 3. 4.20 4. 4.80

Directions for questions 36 to 41: Answer these questions based on the tables given below:

There are 6 refineries, 7 depots and 9 districts. The refineries are BB, BC, BD, BE, BF and BG. The depotsare AA, AB, AC, AD, AE, AF and AG. The districts are AAA, AAB, AAC, AAD, AAE, AAF, AAG, AAH, andAAI. Table A gives the cost of transporting one unit from refinery to depot. Table B gives the cost oftransporting one unit from depot to a district.

Table A

BB BC BD BE BF BG

AA 928.2 537.2 567.8 589.9 589.9 800.1

AB 311.1 596.7 885.7 759.9 759.9 793.9

AC 451.1 0 320.1 780.1 720.7 1000.1

AD 371.1 150.1 350.1 750.1 650.4 980.1

AE 1137.3 314.5 0 1157.7 1157.7 1023.4

AF 617.1 516.8 756.5 1065.9 1065.9 406.3

AG 644.3 299.2 537.2 1093.1 1093.1 623.9

Table B

AA AB AC AD AE AF AG

AAA 562.7 843.2 314.5 889.1 0 754.8 537.2

AAB 532.7 803.2 284.5 790.5 95.2 659.6 442

AAC 500.7 780.2 0 457.3 205.7 549.1 331.5AAD 232.9 362.1 286.2 275.4 523.6 525.3 673.2

AAE 345.1 268.6 316.2 163.2 555.9 413.1 227.8

AAF 450.1 644.3 346.2 372.3 933.3 402.9 379.1

AAG 654.5 0 596.7 222.7 885.7 387.6 348.5

AAH 804.1 149.6 627.2 360.4 1035.3 537.2 498.1AAI 646 255 433.5 137.7 698.7 112.2 161.5

36. What is the least cost of sending one unit from any refinery to any district?1. 95.2 2. 0 3. 205.7 4. 284.5

37. What is the least cost of sending one unit from any refinery to the district AAB?1. 0 2. 284.5 3. 95.2 4. None of these

38. What is the least cost of sending one unit from refinery BB to any district?1. 284.5 2. 311.1 3. 451.1 4. None of these

39. What is the least cost of sending petrol from refinery BB to district AAA?1. 765.6 2. 1137.3 3. 1154.3 4. None of these


40. How many possible ways are there for sending petrol from any refinery to any district?1. 63 2. 42 3. 54 4. 378

41. The largest cost of sending petrol from any refinery to any district is1. 2172.6 2. 2193.0 3. 2091.0 4. None of these

Directions for questions 42 to 47: Answer the questions based on the chart given below.The chart given below indicates the annual sales tax revenue collections (in rupees in crores) of sevenstates from 1997 to 2001. The values given at the top of each bar represents the total collections in thatyear.

3526 4728 5251

40264402 4796

540035103829 4265

483972907826

8067

10284

12034

53415604

6113

7000

3473

39354458

5270

2704

2844

72026055

6300

5413

8015

6375

3118

3500

4300

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

1996-97 1997-98 1998-99 1999-2000 2000-01

W B

UP

TN

MA

KA

GU

A P

UP Uttar Prdes h

TN Tamil Nadu

MA Maharas htra

KA Karnataka

GU Gujarat

A P A ndhra Prades h

W B W es t Bengal

29.870

33.16836.068

42.348

49.638

42. If for each year, the states are ranked in terms of the descending order of sales tax collections,how many states do not change the ranking more than once over the five years?1. 1 2. 5 3. 3 4. 4

43. Which of the following states has changed its relative ranking most number of times when yourank the states in terms of the descending volume of sales tax collections each year?1. Andhra Pradesh 2. Uttar Pradesh 3. Karnataka 4. Tamil Nadu

44. The percentage share of sales tax revenue of which state has increased from 1997 to 2001?1. Tamil Nadu 2. Karnataka 3. Gujarat 4. Andhra Pradesh

45. Which pair of successive years shows the maximum growth rate of tax revenue in Maharashtra?1. 1997 to 1998 2. 1998 to 1999 3. 1999 to 2000 4. 2000 to 2001


46. Identify the state whose tax revenue increased exactly by the same amount in two successive pairof years?1. Karnataka 2. West Bengal 3. Uttar Pradesh 4. Tamil Nadu

47. Which state below has been maintaining a constant rank over the years in terms of its contributionto total tax collections?1. Andhra Pradesh 2. Karnataka 3. Tamil Nadu 4. Uttar Pradesh

Directions for questions 48 to 50: Answer the questions based on the table given below.The table below gives information about four different crops, their different quality, categories and theregions where they are cultivated. Based on the information given in the table answer the questions below.

Type of Crop Quality Region

High R1, R2, R3, R4, R5

Medium R6, R7, R8

Low R9, R10, R11

High R5, R8, R12

Medium R9, R13

Low R6, R7, R8

High R2, R6, R7. R13

Medium R3, R9, R11

Low R1, R4

High R3, R10, R11

Medium R1, R2, R4

Low R5, R9

Crop - 1

Crop - 2

Crop - 3

Crop - 4

48. How many regions produce medium qualities of Crop-1 or Crop-2 and also produce low quality ofCrop-3 or Crop-4?1. Zero 2. One 3. Two 4. Three

49. Which of the following statements is true?1. All medium quality Crop-2 producing regions are also high quality Crop-3 producing regions.2. All high quality Crop-1 producing regions are also medium and low Crop-4 producing regions.3. There are exactly four Crop-3 producing regions, which also produce Crop-4 but not Crop-2.4. Some Crop-3 producing regions produce Crop-1, but not high quality Crop-2.

50. How many low quality Crop-1 producing regions are either high quality Crop-4 producing regions ormedium quality Crop-3 producing regions?1. One 2. Two 3. Three 4. Zero

CAT PAPER – 2003 (Leaked)Page 18

DIRECTIONS for Questions 51 to 53: In each question, there are two statements: A and B, either ofwhich can be true or false on the basis of the information given below.

A research agency collected the following data regarding the admission process of a reputed manage-ment school in India.

Year Gender

Number bought

application

forms

Number

appeared for

written test

Number

called for

interviews

Number

selected for

the course

Male 61205 59981 684 171

Female 19236 15389 138 48

Male 63298 60133 637 115

Female 45292 40763 399 84

2002

2003

Choose (1) if only A is true

Choose (2) if only B is true

Choose (3) if both A and B are true

Choose (4) if neither A nor B is true

51. Statement A: The success rate of moving from written test to interview stage for males was worse

than for females in 2003.

Statement B: The success rate of moving from written test to interview stage for females was better

in 2002 than in 2003.

52. Statement A: In 2002, the number of females selected for the course as a proportion of the number

of females who bought application forms, was higher than the corresponding proportion for males.

Statement B: In 2002, among those called for interview, males had a greater success rate than

females.

53. Statement A: The percentage of absentees in the written test among females decreased from 2002

to 2003.

Statement B: The percentage of absentees in the written test among males was larger than among

females in 2003.

Section � 1I

CAT PAPER – 2003 (Leaked) Page 19

DIRECTIONS for Questions 54 to 57: Answer the questions on the basis of the information given below.

The length of an infant is one of the measures of his/her development in the early stages of his/her life.

The figure below shows the growth chart of four infants in the first five months of life.

45

50

55

60

65

0 1 2 3 4 5

Month

Le

ng

th (

cm

) Seeta

Geeta

Ram

Shyam

54. After which month did Seeta's rate of growth start to decline?

1. Second month 2. Third month 3. Fourth month 4. Never

55. Who grew at the fastest rate in the first two months of life?

1. Geeta 2. Seeta 3. Ram 4. Shyam

56. The rate of growth during the third month was the lowest for


57. Among the four infants, who grew the least in the first five months of life?




The table below provides certain demographic details of 30 respondents who were part of a survey. The

demographic characteristics are: gender, number of children, and age of respondents. The first number in

each cell is the number of respondents in that group. The minimum and maximum age of respondents in

each group is given in brackets. For example, there are five female respondents with no children and

among these five, the youngest is 34 years old, while the oldest is 49.

No. of children Male Female Total

0 1 (38, 38) 5 (34, 49) 6

1 1 (32, 32) 8 (35, 57) 9

2 8 (21, 65) 3 (37, 63) 11

3 2 (32, 33) 2 (27, 40) 4

Total 12 18 30

58. The percentage of respondents aged less than 40 years is at least

1. 10% 2. 16.67% 3. 20.0% 4. 30%

59. Given the information above, the percentage of respondents older than 35 can be at most

1. 30% 2. 73.33% 3. 76.67% 4. 90%

60. The percentage of respondents that fall into the 35 to 40 years age group (both inclusive) is at least

1. 6.67% 2. 10% 3. 13.33% 4. 26.67%


Spam that enters our electronic mailboxes can be classified under several spam heads. The following table

shows the distribution of such spam worldwide over time. The total number of spam emails received during

December 2002 was larger than the number received in June 2003. The total number of spam emails

received during September 2002 was larger than the number received in March 2003. The figures in the

table represent the percentage of all spam emails received during that period, falling into those respective

categories.

Category Sep-02 Dec-02 Mar-03 Jun-03

Adult 38 33 19 17

Financial 25 30 37 45

Health 11 19 5 18

Internet 5 3 10 6

Products 3 7 10 11

Scams 5 6 11 2

Others 13 2 8 1

61. In which category was the percentage of spam emails increasing but at a decreasing rate?

1. Financial 2. Scams 3. Products 4. None of the above


62. In the health category, the number of spam emails received in December 2002 as compared to

June 2003.

1. was larger 2. was smaller 3. was equal 4. cannot be determined

63. In the financial category, the number of spam emails received in September 2002 as compared to

March 2003.

1. was larger 2. was smaller 3. was equal 4. cannot be determined


One of the functions of the Reserve Bank of India is to mobilize funds for the Government of India by issuing

securities. The following table shows details of funds mobilized during the period July 2002 - July 2003.

Notice that on each date there were two rounds of issues, each with a different maturity.

Date of

issue

Notified

amountMaturity

Competitive

bids

received

Non-

competitive

bids

received

Total

amount

mobilized

Coupon

rate %

Implicit

yield %

Rs. Crore Years No. No. No. Value No. Value Rs. Crore

17-Jul-02 40 15 229 23 66 15.21 23 0.37 16 8.07 7.80

17-Jul-02 30 10 145 12 90 29.88 12 0.12 30 6.72 6.72

5-Aug-02 50 9 324 13 105 49.68 13 0.33 50 9.39 7.24

5-Aug-02 20 24 163 9 34 19.81 9 0.19 20 10.18 7.93

28-Aug-02 50 15 260 26 157 48.92 26 1.08 50 7.46 7.46

28-Aug-02 20 30 119 15 67 19.61 15 0.39 20 7.95 7.95

11-Sep-02 40 15 261 22 152 38.93 22 1.07 40 7.46 7.44

11-Sep-02 30 20 131 20 98 29.44 20 0.56 30 8.35 7.70

9-Oct-02 40 11 361 26 119 39.22 26 0.78 40 7.27 7.14

9-Oct-02 30 30 91 15 39 29.52 15 0.48 30 7.95 7.89

7-Nov-02 40 17 245 14 20 39.71 14 0.29 40 10.03 7.26

7-Nov-02 30 24 166 11 49 29.70 11 0.31 30 10.18 7.48

9-Apr-03 40 20 245 25 65 39.53 25 1.47 40 6.30 6.30

9-Apr-03 50 11 236 24 201 49.40 24 0.60 50 7.37 5.98

23-Apr-03 50 15 319 26 134 48.98 26 1.02 50 6.25 6.10

23-Apr-03 20 29 131 19 9 19.39 19 0.61 20 7.95 6.33

5-May-03 60 10 314 14 98 59.69 14 0.31 60 7.27 5.97

5-May-03 30 20 143 14 118 29.58 14 0.42 30 6.30 6.35

4-Jun-03 30 25 187 19 15 28.50 19 1.50 30 6.13 6.13

4-Jun-03 60 9 378 21 151 59.09 21 0.91 60 6.85 5.76

2-Jul-03 50 11 298 20 116 49.05 20 0.95 50 7.37 5.76

2-Jul-03 30 25 114 20 45 28.64 20 1.36 30 6.31 6.10

16-Jul-03 60 17 371 29 115 57.00 29 3.10 60 6.35 5.97

16-Jul-03 30 29 134 22 12 29.32 22 0.68 30 7.95 6.20

Total 930 906

Competitive bids

accepted

Non-

competitive

bids accepted

64. How many times was the issue of securities under-subscribed, i.e., how often did the total amount

mobilized fall short of the amount notified?

1. 0 2. 1 3. 2 4. 3


65. Which of the following is true?

1. The second round issues have a higher maturity than the first round for all dates.

2. The second round issue of any date has a lower maturity only when the first round notified

amount exceeds that of the second round.

3. On at least one occasion, the second round issue having lower maturity received a higher

number of competitive bids.

4. None of the above three statements is true.

66. Which of the following statements is NOT true?

1. Competitive bids received always exceed non-competitive bids received.

2. The number of competitive bids accepted does not always exceed the number of non-competitive

bids accepted.

3. The value of competitive bids accepted on any particular date is never higher for higher maturity.

4. The value of non-competitive bids accepted in the first round is always greater than that in the

second round.


Each point in the graph below shows the profit and turnover data for a company. Each company belongs

to one of the three industries: textile, cement and steel.

Profit

400

300

200

100

1000 2000 3000 4000

Turnover

TextileCem entSteel

67. For how many companies does the profit exceed 10% of turnover?

1. 8 2. 7 3. 6 4. 5

68. For how many steel companies with a turnover of more than 2000 is the profit than 300?

1. 0 2. 1 3. 2 4. 7

69. An investor wants to buy stock of only steel or cement companies with a turnover more than

1000 and profit exceeding 10% of turnover. How many choices are available to the investor?

1. 4 2. 5 3. 6 4. 7



Details of the top 20 MBA schools in the US as ranked by US News and World Report, 1997 are given

below.

School Overall

ranking

Ranking by

Academics

Ranking

by

recruiters

Ranking by

placement

Median

starting

salary

%

employed

Annual

tuition fee

Stanford University 1 1 3 1 $82,000 98.9 $23,100

Harvard University 2 1 2 4 $80,000 96.4 $23,840

University of

Pennsylvania3 1 4 2 $79,000 100.0 $24,956

Massachusetts Institute

of Technology4 1 4 3 $78,000 98.8 $23,900

University of Chicago 5 1 8 10 $65,000 98.4 $23,930

Northwestern University 6 1 1 11 $70,000 93.6 $23,025

Columbia University 7 9 10 5 $83,000 96.2 $23,830

Dartmouth College 8 12 11 6 $70,000 98.3 $23,700

Duke Univrsity 9 9 7 8 $67,500 98.5 $24,380

University of

California—Berkeley10 7 12 12 $70,000 93.7 $18,788

University of Virginia 11 12 9 9 $66,000 98.1 $19,627

University of

Michigan—Ann Arbor12 7 6 14 $65,000 99.1 $23,178

New York University 13 16 19 7 $70,583 97 $23,554

Carnegie Mellon

University14 12 18 13 $67,200 96.6 $22,200

Yale University 15 18 17 22 $65,000 91.5 $23,220

Univ. of North

Carolina—Chapel Hill16 16 16 16 $60,000 96.8 $14,333

University of

California—Los Angeles17 9 13 38 $65,000 82.2 $19,431

University of

Texas—Austin18 18 13 24 $60,000 97.3 $11,614

Indiana

University—Bloomington19 18 20 17 $61,500 95.2 $15,613

Cornell University 20 12 15 36 $64,000 85.1 $23,151

70. Madhu has received admission in all schools listed above. She wishes to select the highest overall

ranked school whose a) annual tuition fee does not exceed $23,000 and b) median starting salary is

at least $70,000. Which school will she select?

1. University of Virginia. 2. University of Pennsylvania

3. Northwestern University 4. University of California - Berkeley


71. In terms of staring salary and tuition fee, how many schools are uniformly better (higher median

starting salary AND lower tuition fee) than Dartmouth College?

1. 1 2. 2 3. 3 4. 4

72. How many schools in the list above have single digit rankings on at least 3 of the 4 parameters

(overall ranking, ranking by academics, ranking by recruiters and ranking by placement)?

1. 10 2. 5 3. 7 4. 8


Table A below provides data about ages of children in a school. For the age given in the first column, the

second column gives the number of children not exceeding the age. For example, first entry indicates that

there are 9 children aged 4 years or less. Tables B and C provide data on the heights and weights respec-

tively of the same group of children in a similar format. Assuming that an older child is always taller and

weighs more than a younger child, answer the following questions.

Age (years) Number Height (cm.) Number Weight (kg.) Number

4 9 115 6 30 8

5 12 120 11 32 13

6 22 125 24 34 17

7 35 130 36 36 28

8 42 135 45 38 33

9 48 140 53 40 46

10 60 145 62 42 54

11 69 150 75 44 67

12 77 155 81 46 79

13 86 160 93 48 91

14 100 165 100 50 100

Table A Table B Table C

73. What is the number of children of age 9 years of less whose height does not exceed 135 cm?

1. 48 2. 45 3. 3 4. Cannot be determined

74. How many children of age more than 10 years are taller than 150 cm and do not weigh more than

48 kg?


75. Among the children older than 6 years but not exceeding 12 years, how many weigh more than

38 kg.?




An industry comprises four firms (A, B, C, and D). Financial details of these firms and of the industry as a

whole for a particular year are given below. Profitability of a firm is defined as profit as a percentage of sales.

Figures in Rs. A B C D Total

Sales 24568 25468 23752 15782 89570

Operating costs 17198 19101 16151 10258 62708

Interest costs 2457 2292 2850 1578 9177

Profit 4914 4075 4750 3946 17684

76. Which firm has the highest profitability?

1. A 2. B 3. C 4. D

77. If firm A acquires firm B, approximately what percentage of the total market (total sales) will they

corner together?

1. 55% 2. 45% 3. 35% 4. 50%


A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one

accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is

married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the

accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

78. Which of the following is one of the married couples?

1. A & B 2. B & E 3. D & E 4. A & D

79. What is E's profession?

1. Engineer 2. Lawyer 3. Professor 4. Accountant

80. How many members of the group are males?



DIRECTIONS for Questions 81 and 82: Answer the questions on the basis of the information given below.

The Head of a newly formed government desires to appoint five of the six elected members A, B, C, D, E

and F to portfolios of Home, Power, Defence, Telecom and Finance. F does not want any portfolio if D gets

one of the five. C wants either Home or Finance or no portfolio. B says that if D gets either Power or

Telecom then she must get the other one. E insists on a portfolio if A gets one.

81. Which is a valid assignment?

1. A-Home, B-Power, C-Defence, D-Telecom, E-Finance.

2. C-Home, D-Power, A-Defence, B-Telecom, E-Finance.

3. A-Home, B-Power, E-Defence, D-Telecom, F-Finance.

4. B-Home, F-Power, E-Defence, C-Telecom, A-Finance.

82. If A gets Home and C gets Finance, then which is NOT a valid assignment of Defense and Telecom?

1. D-Defence, B-Telecom. 2. F-Defence, B-Telecom.

3. B-Defence, E-Telecom. 4. B-Defence, D-Telecom.


Rang Barsey Paint Company (RBPC) is in the business of manufacturing paints. RBPC buys RED, YELLOW,

WHITE, ORANGE, and PINK paints. ORANGE paint can be also produced by mixing RED and YELLOW

paints in equal proportions. Similarly, PINK paint can also be produced by mixing equal amounts of RED

and WHITE paints. Among other paints, RBPC sells CREAM paint, (formed by mixing WHITE and YELLOW

in the ratio 70:30) AVOCADO paint (formed by mixing equal amounts of ORANGE and PINK paint) and

WASHEDORANGE paint (formed by mixing equal amounts of ORANGE and WHITE paint). The following

table provides the price at which RBPC buys paints.

Color Rs./litre

RED 20

YELLOW 25

WHITE 15

ORANGE 22

PINK 18

83. The cheapest way to manufacture AVOCADO paint would cost

1. Rs. 19.50 per litre. 2. Rs. 19.75 per litre

3. Rs. 20.00 per litre. 4. Rs. 20.25 per litre.

84. WASHEDORANGE can be manufactured by mixing

1. CREAM and RED in the ratio 14:10.

2. CREAM and RED in the ratio 3:1.

3. YELLOW and PINK in the ratio 1:1.

4. RED, YELLOW, and WHITE in the ratio 1:1:2.


85. Assume that AVOCADO, CREAM and WASHEDORANGE each sells for the same price. Which

of the three is the most profitable to manufacture?

1. AVOCADO 2. CREAM

3. WASHEDORANGE 4. Sufficient data is not available.


Seven varsity basketball players (A, B, C, D, E, F, and G) are to be honoured at a special luncheon. The

players will be seated on the dais in a row. A and G have to leave the luncheon early and so must be seated

at the extreme right. B will receive the most valuable player's trophy and so must be in the centre to

facilitate presentation. C and D are bitter rivals and therefore must be seated as far apart as possible.

86. Which of the following cannot be seated at either end?1. C 2. D 3. F 4. G

87. Which of the following pairs cannot be seated together?

1. B & D 2. C & F 3. D & G 4. E & A

88. Which of the following pairs cannot occupy the seats on either side of B?

1. F & D 2. D & E 3. E & G 4. C & F

DIRECTIONS for Questions 89 to 92: In each question there are two statements: A and B.

Choose (1) if the question can be answered by one of the statements alone but not by the other.

Choose (2) if the question can be answered by using either statement alone.

Choose (3) if the question can be answered by using both the statements together but cannot be answered

using either statement alone.

Choose (4) if the question cannot be answered even b using both the statements A and B.

89. F and M are father and mother of S, respectively. S has four uncles and three aunts. F has two

siblings. The siblings of F and M are unmarried. How many brothers does M have?

A. F has two brothers.

B. M has five siblings.

90. A game consists of tossing a coin successively. There is an entry fee of Rs. 10 and an additional fee

of Re. 1 for each toss of coin. The game is considered to have ended normally when the coin turns

heads on two consecutive throws. In this case the player is paid Rs. 100. Alternatively, the player

can choose to terminate the game prematurely after any of the tosses. Ram has incurred a loss of

Rs. 50 by playing this game. How many times did he toss the coin?

A. The game ended normally.

B. The total number of tails obtained in the game was 138.


91. Each packet of SOAP costs Rs. 10. Inside each packet is a gift coupon labelled with one of theletters S, O, A and P. If a customer submits four such coupons that make up the word SOAP, thecustomer gets a free SOAP packets. Ms. X kept buying packet after packet of SOAP till she couldget one set of coupons that formed the word SOAP. How many coupons with label P did she get inthe above process?

A. The last label obtained by her was S and the total amount spent was Rs. 210.B. The total number of vowels obtained was 18.

92. If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30seconds. Assuming that C maintains a uniform speed what is the time taken by C to finish therace?

A. A and C run the same race and A wins by 375 metres.B. The length of the race is 1 km.


Some children were taking free throws at the basketball court in school during lunch break. Below aresome facts about how many baskets these children shot.

i. Ganesh shot 8 baskets less than Ashish.ii. Dhanraj and Ramesh together shot 37 baskets.iii. Jugraj shot 8 baskets more than Dhanraj.iv. Ashish shot 5 baskets more than Dhanraj.v. Ashish and Ganesh together shot 40 baskets.

93. Which of the following statements is true?1. Ramesh shot 18 baskets and Dhanraj shot 19 baskets.2. Ganesh shot 24 baskets and Ashish shot 16 baskets.3. Jugraj shot 19 baskets and Dhanraj shot 27 baskets.4. Dhanraj shot 11 baskets and Ashish shot 16 baskets.

94. Which of the following statements is true?1. Dhanraj and Jugraj together shot 46 baskets.2. Ganesh shot 18 baskets and Ramesh shot 21 baskets.3. Dhanraj shot 3 more baskets than Ramesh.4. Ramesh and Jugraj together shot 29 baskets.


DIRECTIONS for Questions 95 to 97: Answer the questions on the basis of the information given below.Five women decided to go shopping to M.G. Road, Bangalore. They arrived at the designated meetingplace in the following order: 1. Archana, 2. Chellamma, 3. Dhenuka, 4. Helen, and 5. Shahnaz. Eachwoman spent at least Rs. 1000. Below are some additional facts about how much they spent during theirshopping spree.

i. The woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193.ii. One woman spent Rs. 1340 and she was not Dhenuka.iii. One woman spent Rs. 1378 more than Chellamma.iv. One woman spent Rs. 2517 and she was not Archana.v. Helen spent more than Dhenuka.vi. Shahnaz spent the largest amount and Chellamma the smallest.

95. What was the amount spent by Helen?1. Rs. 1193 2. Rs. 1340 3. Rs. 2234 4. Rs. 2517

96. Which of the following amounts was spent by one of them?1. Rs. 1139 2. Rs. 1378 3. Rs. 2571 4. Rs. 2718

97. The woman who spent Rs. 1193 is1. Archana 2. Chellamma 3. Dhenuka 4. Helen

DIRECTIONS for Questions 98 to 100: Answer the questions on the basis of the information given below.Five friends meet every morning at Sree Sagar restaurant for an idli-vada breakfast. Each consumes adifferent number of idlis and vadas. The number of idlis consumed are 1, 4, 5, 6, and 8, while the number ofvadas consumed are 0, 1, 2, 4, and 6. Below are some more facts about who eats what and how much.

i. The number of vadas eaten by Ignesh is three times the number of vadas consumed by the personwho eats four idlis.

ii. Three persons, including the one who eats four vadas eat without chutney.iii. Sandeep does not take any chutney.iv. The one who eats one idli a day does not eat any vadas or chutney. Further, he is not Mukesh.v. Daljit eats idli with chutney and also eats vada.vi. Mukesh, who does not take chutney, eats half as many vadas as the person who eats twice as

many idlis as he does.vii. Bimal eats two more idlis than Ignesh, but Ignesh eats two more vadas than Bimal.

98. Which one of the following statements is true?1. Daljit eats 5 idlis 2. Ignesh eats 8 idlis3. Bimal eats 1 idli. 4. Bimal eats 6 idlis.

99. Which of the following statements is true?1. Sandeep eats 2 vadas. 2. Mukesh eats 4 vadas.3. Ignesh eats 6 vadas. 4. Bimal eats 2 vadas.

100. Which of the following statements is true?1. Mukesh eats 8 idlis and 4 vadas but no chutney.2. The person who eats 5 idlis and 1 vada does not take chutney.3. The person who eats equal number of vadas and idlis also takes chutney.4. The person who eats 4 idlis and 2 vadas also takes chutney.

CAT PAPER – 2003(Leaked) ExplanationsPage 4

a teacher's situation, so (2) is out. are in (4) also indicatea compulsive situation which is not evident in thesentence, so (4) is out.

50. 4 Negative reinforcements foster negative behavior. (1),(2) and (3) are easily ruled out as giving, bestowing orconferring rewards cannot possibly encouragenegative behaviour. Withholding and fostering thuspresents the right situation here.

51. 4 From the data both statements are false.

52. 4 From the data both statements are false.

53. 1 From the data statement "A" is true.

54. 2 It is evident from graph Seeta's growth rate decreasedfrom third month as this is the first time the slope hasdecreased.

55. 1 Geeta grew at fastest rate in first two months (theslope of the line in this period is steepest for Geeta).

56. 1 Geeta grew lowest in third month (during this period,the slope was least for Geeta).

57. 4 Seeta increased 7cm on 50 and shyam 7cm on 53cm,Hence Shyam grew least.

58. 49

100 30%30

× =

59. 323

100 76.67%30

× =

60. 34

100 13.33%30

× =

61. 3 Incase of Products, percentage of spam emails isincreasing but at decreasing rate, from Sep 2002 to

Dec 2002 products increased by 7 3

133%3

−≈ and in

Mar 2003 about 7 4

43%7

−≈ and in Jun 2003

11 1010%

10

− ≈

62. 1 Since percentage of spam is Dec 2002 is higher thanJune 2003, and the number of total e-mails received ishigher, hence number received in Dec 2002 is higher.

63. 4 Cannot be determined as in Sept 2002 percentage islower as compared to March 2003, however the totalnumber of emails received in Sept 2003 is higher thanthat in March 2002. Thus we cannot say anything.

64. 2 It happened only once i.e; on 17-Jul-02

65. 3 From the table we can see that for issue dated,04 June-03, the 2nd round issue has a lower maturityand the competitive bids received are higher.

66. 4 For any issue the value of non-competitive bids in 2ndround is greater than the 1st round.

67. 2 Just draw a diagonal line from bottom left point to topright point. All companies lying above this line haveprofit in excess of 10% of turnover.From the graph there are 7 companies, has the profit10% of turnover.

68. 3 From the graph there are 2 steel companies with aturnover of more than 2000 and profit less than 300.

69. 2 From the graph there are 5 companies.

70. 4 By looking up the table, in University of California -Berkeley median starting salary is $70,000 and annualtuition fee is $18,788.

71. 2 By looking up the table, the number of schools, uniformlybetter than Dartmouth College is 2.

72. 4 By counting from the table, eight rows of first ninerow schools satisfy the given condition.

73. 2 There are 45 children of height not exceeding 135 and48 children of age not exceeding 9 yrs. Consider thetallest child of the 45 children with height not exceeding135. We can be very sure that his age is less than9 yrs as taller children have higher weights. Thus all45 children of heights not exceeding 135 will haveage not exceeding 9 yrs.

74. 1 Using the same logic as above, there are 25 childrentaller than 150 cms and more than 10 years of age.There are 9 children of weights more than 48. These9 children are surely included in the 25 children tallerthan 150 cms and more than 10 years of age becauseof the assumption given. Thus 25 – 9 = 16 childrensatisfy the condition.

75. 3 There are 55 children not exceeding 12 years butolder than 6 years. Again 33 children weigh less thanor equal to 38. Of these, 22 are those who are lessthan 6 years of age. Thus 11 of the 55 students weighless than or equal to 38 kg.So the answer is 55 – 11 = 44.

76. 4 Profitability is defined as percentage of sales.Approximately Firm A has 25% profit, B has 16.66%, Chas 20% and D has approximately 30% profit.

CAT PAPER – 2003(Leaked) Explanations Page 5

77. 124568 25468

100 55%89570

+× =

For questions 78 to 80:

(+) - Male(-) - Female

A(Lawyer)(+)-----Couple ------ D (Housewife)(-)C (Accountant)(+)-----Couple-----F(Professor)(-)(Or) F (Professor)(+)-----Couple-----C(Accountant)(-)

(B)(Housewife)(-)(E)(Engineer)(+)

78. 4

79. 1

80. 3

For questions 81 and 82:

If D gets portfolio F does not or vice-versa.C wants only Home or Finance or noneIf D gets Power B must get Telecom or D - Telecom then B mustget PowerIf A gets a portfolion E should get.

81. 2 (1) gets eliminated because C can have either homeor finance.(3) gets eliminated because F and D cannot be in thesame team.(4) gets eliminated because C cannot have telecomportfolio.Hence (2) is correct.

82. 4 B-Defence, D - Telecom because if D gets Telcom thenB must get Power.

83. 2 AVOCADO paint is mixture of ORANGE and PINK inequal quantities.If ORANGE is made using RED and YELLOW, then the

cost of ORANGE would be 20 25

22.52

+= which is

greater than the cost of the ORANGE.If we make PINK by RED and WHITE, the cost of PINK

would be 20 15

17.52

+= which is less than the cost

of the PINK paint.

Hence, the cost of the AVOCADO is 22 17.5

19.752

+=

84. 4 Mixing equal amounts of ORANGE and WHITE canmake WASHEDORANGE, ORANGE can be made bymixing equal amounts of RED and YELLOW. So theratio of RED, YELLOW and WHITE is 1 : 1 : 2

85. 2 If cost of AVOCADO paint is Rs.19.75

The cost of the CREAM is 7 15 3 75

Rs.1810

× + ×=

And cost of WASHEDORANGE is Rs.18.50So CREAM is the most profitable.


1 2 3 4 5 6 7

C B D A G

D B C A G

D B C G A

D B C G A

86. 3 From given options F is the only possibility.

87. 4 If we look at the options D & G can sit together, C & Fcan sit together, B & D can sit together and E & A is theonly option which is not possible.

88. 3 E & G is the only possibility.

89. 1 S has 4 uncles and from statement A. F has twobrothers. Hence, the other 2 uncles of S must be thebrothers of M. Statement B does not give any additionalinformation.

90. 2 From both statements individually. If x is the number oftosses he took, from statement I we get the equation10 + x – 100 = 50. Thus x = 140.From statement II individually, we have x > 138.Thus we are sure he has paid up more than 148. If heincurs a loss of only Rs. 50, the game has to endnormally. Thus the above state of his taking 150 shotswith first 138 as tails and 139 and 140 throw as headsis the scenario. With no other scenario will a loss ofjust 50 and 138 tails show up.

91. 3 Since Ms. X bought 21 packets out of which there are18 O’s and A’s in total. Since she got one S, there hasto be 2 P’s which she bought. Hence, both thestatements are required.

CAT PAPER – 2003(Leaked) ExplanationsPage 6

92. 3 If A takes X seconds then B takes (x + 60) seconds torun 1000 m.Ratio of speeds of A and C = 1000 : 625 = 8 : 5Ratio of times taken by A and C = 5 : 8If B takes y second then C takes y + 30 seconds to run1000 m.Hence 5 (y + 30) = 8x …(i)

and1000 1000

x 60 y=

+ …(ii)

Solving we get the values of x and y.Hence both statements are required.


G + 8 = AD + R = 37J = D + 8A = D + 5A + G = 40Solving we get2G = 32, G = 16, A = 24D = 19, j = 27, R = 18

93. 1

94. 1 D + J = 46


Five shopping women spending various amounts withconditions

One of the women spent 2517 – 1378 = 1139 who isChellamma. This is the only possibility as if we add 1378 evento the least amount of 1193, we will not be able to satisfy all theconditions given simultaneously.

A C D H S

2234 1139 1193 1340 2517

95. 2 96. 1 97. 3


Shree Sagar restaurant and idli-vada breakfast

Idli Vada

Ignesh 6 6

Sandeep 1 0

Mukesh 4 2

Daljit 5 1

Bimal 8 4

98. 1

99. 3

100. 3


S, M and R in all spend 1248 bahts.Initially M pays 211 bahts and R pays 92 bahts.Remaining is paid by S i.e; 945 bahtsIf 1248 is divided equally among S, M & R and each has tospend 415 bahtsHence M has to pay S 205 bahts which is 5 Dollars.And R has to pay 324 bahts to S.

101. 4

102. 3

103. 4 Putting the value of M in either equation, we getG + B = 17.Hence neither of two can be uniquely determined.

104. 2 As per the given data we get the following:

G M

B

8

36

2

G iani M edha

Buddhi

G + B = M + 16Also, M + B + G + 19 = (2 × 19) – 1i.e. (G + B) = 18 – MThus, M + 16 = 18 – Mi.e. M = 1

105. 3 2x – x – 1 = 0⇒ 2x – 1 = xIf we put x = 0, then this is satisfied and if we putx = 1, then also this is satisfied.Now we put x = 2, then this is not valid.

106. 2 For the curves to intersect, log10 x = x–1

Thus,x

101

log x or x 10x

= =

This is possible for only one value of x (2 < x < 3).

107. 4 The surface area of a sphere is proportional to thesquare of the radius.

Thus, B

A

S 4

S 1= (S. A. of B is 300% higher than A)

B

A

r 2

r 1∴ =

CAT PAPER - 1999 Page 31

Directions for questions 111 to 120: Each question consists of five statements followed by options

consisting of three statements put together in a specific order. Choose the option which indicates a valid

argument, that is, where the third statement is a conclusion drawn from the preceding two statements.

Example:

A. All cigarettes are hazardous to health.

B. Brand X is a cigarette.

C. Brand X is hazardous to health.

ABC is a valid option, where statement C can be concluded from statements A and B.

111. A. All software companies employ knowledge workers.

B. Tara Tech employs knowledge workers.

C. Tara Tech is a software company.

D. Some software companies employ knowledge workers.

E. Tara Tech employs only knowledge workers.

a. ABC b. ACB c. CDB d. ACE

112. A. Traffic congestion increases carbon monoxide in the environment.

B. Increase in carbon monoxide is hazardous to health.

C. Traffic congestion is hazardous to health.

D. Some traffic congestion does not cause increased carbon monoxide.

E. Some traffic congestion is not hazardous to health.

a. CBA b. BDE c. CDE d. BAC

113. A. Apples are not sweets.

B. Some apples are sweet.

C. All sweets are tasty.

D. Some apples are not tasty.

E. No apple is tasty.

a. CEA b. BDC c. CBD d. EAC

114. A. Some towns in India are polluted.

B. All polluted towns should be destroyed.

C. Town Meghana should be destroyed.

D. Town Meghana is polluted.

E. Some towns in India should be destroyed.

a. BDE b. BAE c. ADE d. CDB

115. A. No patriot is a criminal.

B. Bundledas is not a criminal.

C. Bundledas is a patriot.

D. Bogusdas is not a patriot.

E. Bogusdas is a criminal.

a. ACB b. ABC c. ADE d. ABE

Section � III

CAT PAPER - 1999

116. A. Anteaters like ants.

B. Boys are anteaters.

C. Balaram is an anteater.

D. Balaram likes ants.

E. Balaram may eat ants.

a. DCA b. ADC c. ABE d. ACD

117. A. All actors are handsome.

B. Some actors are popular.

C. Ram is handsome.

D. Ram is a popular actor.

E. Some popular people are handsome.

a. ACD b. ABE c. DCA d. EDC

118. A. Modern industry is technology-driven.

B. BTI is a modern industry.

C. BTI is technology-driven.

D. BTI may be technology-driven

E. Technology driven industry is modern.

a. ABC b. ABD c. BCA d. EBC

119. A. All Golmal islanders are blue-coloured people.

B. Some smart people are not blue-coloured people.

C. Some babies are blue-coloured.

D. Some babies are smart.

E. Some smart people are not Golmal islanders.

a. BCD b. ABE c. CBD d. None of these

120. A. MBAs are in great demand.

B. Ram and Sita are in great demand.

C. Ram is in great demand.

D. Sita is in great demand.

E. Ram and Sita are MBAs.

a. ABE b. ECD c. AEB d. EBA

Directions for questions 121 to 124: Each question has a main statement followed by four statements

labelled A, B, C and D. Choose the ordered pair of statements where the first statement implies the

second, and the two statements are logically consistent with the main statement.

121. Either the orangutan is not angry, or he frowns upon the world.

A. The orangutan frowns upon the world.

B. The orangutan is not angry.

C. The orangutan does not frown upon the world.

D. The orangutan is angry.

a. CB only b. DA only c. AB only d. CB and DA


122. Either Ravana is a demon, or he is a hero.

A. Ravana is a hero.

B. Ravana is a demon.

C. Ravana is not a demon.

D. Ravana is not a hero.

a. CD only b. BA only c. CD and BA d. DB and CA

123. Whenever Rajeev uses the Internet, he dreams about spiders.

A. Rajeev did not dream about spiders.

B. Rajeev used the Internet.

C. Rajeev dreamt about spiders.

D. Rajeev did not use the Internet.

a. AD b. DC c. CB d. DA

124. If I talk to my professors, then I do not need to take a pill for headache.

A. I talked to my professors.

B. I did not need to take a pill for headache.

C. I needed to take a pill for headache.

D. I did not talk to my professors.

a. AB only b. DC only c. CD only d. AB and CD

Directions for questions 125 to 134: Each question has a set of four statements. Each statement has

three segments. Choose the alternative where the third segment in the statement can be logically deduced

using both the preceding two, but not just from one of them.

125. A. No cowboys laugh. Some who laugh are sphinxes. Some sphinxes are not cowboys.

B. All ghosts are florescent. Some ghost do not sing. Some singers are not florescent.

C. Cricketers indulge in swearing. Those who swear are hanged. Some who are hanged are not

cricketers.

D. Some crazy people are pianists. All crazy people are whistlers. Some whistlers are pianists.

a. A and B b. C only c. A and D d. D only

126. A. All good people are knights. All warriors are good people. All knights are warriors.

B. No footballers are ministers. All footballers are tough. Some ministers are players.

C. All pizzas are snacks. Some meals are pizzas. Some meals are snacks.

D. Some barkers are musk deer. All barkers are sloth bears. Some sloth bears are musk deer.

a. C and D b. B and C c. A only d. C only

127. A. Dinosaurs are prehistoric creatures. Water-buffaloes are not dinosaurs. Water-buffaloes are not

prehistoric creatures.

B. All politicians are frank. No frank people are crocodiles. No crocodiles are politicians.

C. No diamond is quartz. No opal is quartz. Diamonds are opals.

D. All monkeys like bananas. Some GI Joes like bananas. Some GI Joes are monkeys.

a. C only b. B only c. A and D d. B and C

CAT PAPER - 1999

128. A. All earthquakes cause havoc. Some landslides cause havoc. Some earthquakes cause landslides.

B. All glass things are transparent. Some curios are glass things. Some curios are transparent.

C. All clay objects are brittle. All XY are clay objects. Some XY are brittle.

D. No criminal is a patriot. Ram is not a patriot. Ram is a criminal.

a. D only b. B only c. C and B d. A only

129. A. MD is an actor. Some actors are pretty. MD is pretty.

B. Some men are cops. All cops are brave. Some brave people are cops.

C. All cops are brave. Some men are cops. Some men are brave.

D. All actors are pretty ; MD is not an actor ; MD is not pretty.

a. D only b. C only c. A only d. B and C

130. A. All IIMs are in India. No BIMs are in India. No IIMs are BIMs.

B. All IIMs are in India. No BIMs are in India. No BIMs are IIMs.

C. Some IIMs are not in India. Some BIMs are not in India. Some IIMs are BIMs.

D. Some IIMs are not in India. Some BIMs are not in India. Some BIMs are IIMs.

a. A and B b. C and D c. A only d. B only

131. A. Citizens of Yes Islands speak only the truth. Citizens of Yes Islands are young people. Young

people speak only the truth.

B. Citizens of Yes Islands speak only the truth. Some Yes Islands are in Atlantic. Some citizens of

Yes Islands are in the Atlantic.

C. Citizens of Yes Islands speak only the truth. Some young people are citizens of Yes Islands.

Some young people speak only the truth.

D. Some people speak only the truth. Some citizens of Yes Islands speak only the truth. Some

people who speak only the truth are citizens of Yes Islands.

a. A only b. B only c. C only d. D only

132. A. All mammals are viviparous. Some fish are viviparous. Some fish are mammals.

B. All birds are oviparous. Some fish are not oviparous. Some fish are birds.

C. No mammal is oviparous. Some creatures are oviparous and some are not. Some creatures are

not mammals.

D. Some creatures are mammals. Some creatures are viviparous. Some mammals are viviparous.

a. A only b. B only c. C only d. D only

133. A. Many singers are not writers. All poets are singers. Some poets are not writers.

B. Giants climb beanstalks. Some chicken do not climb beanstalks. Some chicken are not giants.

C. All explorers live in snowdrifts. Some penguins live in snowdrifts. Some penguins are explorers.

D. Amar is taller than Akbar. Anthony is shorter than Amar. Akbar is shorter than Anthony.

a. A only b. B only c. B and C d. D only

134. A. A few farmers are rocket scientists. Some rocket scientists catch snakes. A few farmers catch

snakes.

B. Poonam is a kangaroo. Some kangaroos are made of teak. Poonam is made of teak.


C. No bulls eat grass. All matadors eat grass. No matadors are bulls.

D. Some skunks drive Cadillacs. All skunks are polar bears. Some polar bears drive Cadillacs.

a. B only b. A and C c. C only d. C and D

Directions for questions 135 to 138: Answer the questions based on the following information.

The figure below represents sales and net profit in Rs. crore of IVP Ltd. for five years from 1994-95 to

1998-99. During this period the sales increased from Rs. 100 crore to Rs. 680 crore. Correspondingly, the

net profit increased from Rs. 2.5 crore to Rs. 12 crore. Net profit is defined as the excess of sales over total

costs.

680

290300

250

100

128.5

6

4.52.5

0

100

200

300

400

500

600

700

1994-95 1995-96 1996-97 1997-98 1998-99

0

2

4

6

8

10

12

14

Sales Net profit

135. The highest percentage of growth in sales, relative to the previous year, occurred in

a. 1995-96 b. 1996-97 c. 1997-98 d. 1998-99

136. The highest percentage growth in net profit, relative to the previous year, was achieved in

a. 1998-99 b. 1997-98 c. 1996-97 d. 1995-96

137. Defining profitability as the ratio of net profit to sales, IVP Ltd., recorded the highest profitability in

a. 1998-99 b. 1997-98 c. 1994-95 d. 1996-97

138. With profitability as defined in question 137, it can be concluded that

a. profitability is non-decreasing during the five years from 1994-95 to 1998-99.

b. profitability is non-increasing during the five years from 1994-95 to 1998-99.

c. profitability remained constant during the five years from 1994-95 to 1998-99.

d. None of the above

Directions for questions 139 to 142: Answer the questions based on the following information

Consider the information provided in the figure below relating to India’s foreign trade in 1997-98 and the first

eight months of 1998-99. Total trade with a region is defined as the sum of exports and imports from that

region. Trade deficit is defined as the excess of imports over exports. Trade deficit may be negative.

A. USA G. Other East European countries

B. Germany H. OPEC

C. Other EU I. Asia

D. UK J. Other LDCs

E. Japan K. Others

F. Russia

CAT PAPER - 1999

Source of imports

1997-98 1998-99Imports into India $40,779 million Imports into India (April-November)

$28,126 million

A

9% B

5%

C

12%

D

6%

E

5%

F

2%

G

19%

H

23%

I

14%

K

1%

J

4%

A

9% B

5%

C

14%

D

6%

E

5%

F

1%

G

21%

H

17%

I

16%

J

5%

K

1%

Destination of exports

1997-98 1998-99Exports from India: $33,979 million Exports from India (April-November)

$21,436 million

A

19%

B

6%

C

14%

D

6%E

6%

F

3%

G

10%

H

10%

I

20%

J

5%

K

1% A

23%

B

6%

C

14%D

5%

E

5%

F

2%

G

12%

H

10%

I

17%

J

5%

K

1%

139. What is the region with which India had the highest total trade in 1997-98?

a. USA b. Other EU countries c. OPEC d. Others

140. In 1997-98 the amount of Indian exports, million US dollars, to the region with which India had the

lowest total trade, is approximately

a. 750 b. 340 c. 220 d. 440

141. In 1997-98, the trade deficit with respect to India, billion US dollars, for the region with the highest

trade deficit with respect to India, is approximately equal to

a. 6.0 b. 3.0 c. 4.5 d. 7.5


142. What is the region with the lowest trade deficit with India in 1997-98?

a. USA b. Asia c. Others d. Other EU countries

Directions for questions 143 and 144: Answer the questions based on the following information.

Assume that the average monthly exports from India and imports to India during the remaining four months

of 1998-99 would be the same as that for the first eight months of the year.

143. What is the region to which India’s exports registered the highest percentage growth between

1997-98 and 1998-99?

a. Other East European countries b. USA

c. Asia d. Exports have declined, no growth

144. What is the percentage growth rate in India’s total trade deficit between 1997-98 and 1998-99?

a. 43 b. 47 c. 50 d. 40


These questions are based on the price fluctuations of four commodities — arhar, pepper, sugar and gold

during February-July 1999 as described in the figures below.

Pri

ce

(Rs

.p

er

qu

inta

l)

1900

1300

1500

1700

2100

2300

2500

Arhar (Friday quotations)

Weeks (1999)

F1 F4 M 3 A2 A5 M 3 JN2 JL1

Pri

ce

(Rs

.p

er

qu

inta

l)

18500

17000

17500

18000

19000

19500

20000

Pepper (Friday quotations)

Weeks (1999)

F1 F4 M 3 A2 A5 M 3 JN2 JL1

3700

3800

3900

4000

4100

4200

4300

Gold (Friday quotations)

Weeks (1999)F1 F4 M 3 A2 A5 M 3 JN2 JL1

1400

1420

1440

1460

1480

1500

1520

Sugar (Friday quotations)

Weeks (1999)

F1 F4 M 3 A2 A5 M 3 JN2 JL1

Pri

ce

(Rs

.p

er

qu

inta

l)

Pri

ce

(Rs

.p

er

10

g)

145. Price change of a commodity is defined as the absolute difference in ending and beginning prices

expressed as a percentage of the beginning. What is the commodity with the highest price change?

a. Arhar b. Pepper c. Sugar d. Gold

CAT PAPER - 1999

146. Price volatility (PV) of a commodity is defined as follows:

PV = (Highest price during the period – Lowest price during the period)/Average price during the

period. What is the commodity with the lowest price volatility?

a. Arhar b. Pepper c. Sugar d. Gold

147. Mr X, a fund manager with an investment company invested 25% of his funds in each of the four

commodities at the beginning of the period. He sold the commodities at the end of the period. His

investments in the commodities resulted in

a. 17% profit b. 5.5% loss c. No profit, no loss d. 5.4% profit

148. The price volatility(PV) of the commodity with the highest PV during the February-July period is

approximately equal to

a. 3% b. 40% c. 20% d. 12%


The table below presents data on percentage population covered by drinking water and sanitation facilities

in selected Asian countries.

Population covered by drinking water and sanitation facilities

Percentage coverage

retawgniknirD seitilicafnoitatinaS

nabrU laruR latoT nabrU laruR latoT

aidnI 58 97 18 07 41 92

hsedalgnaB 99 69 79 97 44 84

anihC 79 65 76 47 7 42

natsikaP 28 96 47 77 22 74

senippilihP 29 08 68 88 66 77

aisenodnI 97 45 26 37 04 15

aknaLirS 88 25 75 86 26 36

lapeN 88 06 36 85 21 1

(Source: World Resources 1998-99, p. 251, UNDP, UNEP and World Bank.)

Country A is said to dominate B or A > B if A has higher percentage in total coverage for both drinking water

and sanitation facilities, and, B is said to be dominated by A, or B < A.

A country is said to be on the coverage frontier if no other country dominates it. Similarly, a country is not

on the coverage frontier if it is dominated by at least one other country.

149. Which countries are the countries on the coverage frontier?

a. India and China b. Sri Lanka and Indonesia

c. Philippines and Bangladesh d. Nepal and Pakistan


150. Which of the following statements are true?

A. India > Pakistan and India > Indonesia B. India > China and India > Nepal

C. Sri Lanka > China D. China > Nepal

a. A and C b. B and D c. A, B and C d. B, C and D

151. Using only the data presented under ‘sanitation facilities’ columns, it can be concluded that rural

population in India, as a percentage of its total population is approximately

a. 76 b. 70 c. 73 d. Cannot be determined

152. Again, using only the data presented under ‘sanitation facilities’ columns, sequence China, Indonesia

and Philippines in ascending order of rural population as a percentage of their respective total

population. The correct order is

a. Philippines, Indonesia, China b. Indonesia, China, Philippines

c. Indonesia, Philippines, China d. China, Indonesia, Philippines

153. India is not on the coverage frontier because

A. it is lower than Bangladesh in terms of coverage of drinking water facilities.

B. it is lower than Sri Lanka in terms of coverage of sanitation facilities.

C. it is lower than Pakistan in terms of coverage of sanitation facilities.

D. it is dominated by Indonesia.

a. A and B b. A and C c. D d. None of these

Directions for questions 154 and 155: Answer the questions based on the following information.

These relate to the above table with the additional provison that the gap between the population coverages

of ‘sanitation facilities’ and ‘drinking water facilities’ is a measure of disparity in coverage.

154. The country with the most disparity in coverage of rural sector is

a. India b. Bangladesh c. Nepal d. None of these

155. The country with the least disparity in coverage of urban sector is

a. India b. Pakistan c. Philippines d. None of these

Directions for questions 156 to 165: Each question is followed by two statements I and II.

Mark:

a. if the question can be answered by any one of the statements alone, but cannot be answered by

using the other statement alone.

b. if the question can be answered by using either statement alone.

c. if the question can be answered by using both the statements together, but cannot be answered

by using either statement alone.

d. if the question cannot be answered even by using both the statements together.

156. The average weight of students in a class is 50 kg. What is the number of students in the class?

I. The heaviest and the lightest members of the class weigh 60 kg and 40 kg respectively.

II. Exclusion of the heaviest and the lightest members from the class does not change the average

weight of the students.

157. A small storage tank is spherical in shape. What is the storage volume of the tank?

I. The wall thickness of the tank is 1 cm.

II. When an empty spherical tank is immersed in a large tank filled with water, 20 l of water overflow

from the large tank.

CAT PAPER - 1999

158. Mr X starts walking northwards along the boundary of a field from point A on the boundary, and after

walking for 150 m reaches B, and then walks westwards, again along the boundary, for another

100 m when he reaches C. What is the maximum distance between any pair of points on the

boundary of the field?

I. The field is rectangular in shape.

II. The field is a polygon, with C as one of its vertices and A as the mid-point of a side.

159. A line graph on a graph sheet shows the revenue for each year from 1990 through 1998 by points

and joins the successive points by straight-line segments. The point for revenue of 1990 is labelled

A, that for 1991 as B, and that for 1992 as C. What is the ratio of growth in revenue between

1991-92 and 1990-91?

I. The angle between AB and X-axis when measured with a protractor is 40°, and the angle between

CB and X-axis is 80°.

II. The scale of Y-axis is 1 cm = Rs. 100

160. There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external

point D at a distance d cm from the centre. What are the angles between each tangent and the

X-axis.

I. The coordinates of D are given.

II. The X-axis bisects one of the tangents.

161. Find a pair of real numbers x and y that satisfy the following two equations simultaneously. It is

known that the values of a, b, c, d, e and f are non-zero.

ax + by = c

dx + ey = f

I. a = kd and b = ke, c = kf, k ≠ 0

II. a = b = 1, d = e = 2, f ≠ 2c

162. Three professors A, B and C are separately given three sets of numbers to add. They were expected

to find the answers to 1 + 1, 1 + 1 + 2, and 1 + 1 respectively. Their respective answers were 3, 3 and

2. How many of the professors are mathematicians?

I. A mathematician can never add two numbers correctly, but can always add three numbers

correctly.

II. When a mathematician makes a mistake in a sum, the error is +1 or –1.

163. How many students among A, B, C and D have passed the examination?

I. The following is a true statement: A and B passed the examination.

II. The following is a false statement: At least one among C and D has passed the examination.

164. What is the distance x between two cities A and B in integral number of kilometres?

I. x satisfies the equation 2log x x=

II. x ≤ 10 km

165. Mr Mendel grew 100 flowering plants from black seeds and white seeds, each seed giving rise to

one plant. A plant gives flowers of only one colour. From a black seed comes a plant giving red or

blue flowers. From a white seed comes a plant giving red or white flowers. How many black seeds

were used by Mr Mendel?

I. The number of plants with white flowers was 10.

II. The number of plants with red flowers was 70.

CAT PAPER - 1999

107. For minimum petrol consumption, Zoheb should drive

at 40 kmph, petrol consumption = 160

24 = 6.67 l.


emaGgninepO

ecnalabkcips'reyalP kcips'relaeD

gnisolC

ecnalab

tibeD

)–(

tiderC

)+(

tibeD

)–(

tiderC

)+(

1 0 0 8 61 0 8-

2 8- 0 01 0 01 21

3 21 0 6 6 0 21

4 21 0 8 61 0 4

108. Hence, we see that the maximum gain is Rs. 12

109. Since the maximum negative that Ghosh Babu goesinto is –8, he should begin with at least Rs. 8, so thathe does not have to borrow any money at any point.

110. From the above table it is evident that in four games,Ghosh Babu makes a profit of Rs. 4. Hence, if the finalamount left with Ghosh Babu is Rs. 100, the initialamount that he had would be Rs. 96.

111. (b) ACB is the correct answer choice.as it forms a valid syllogism.

CEKW

SC

TT

CEKW = Companies that employ knowledge workersSC = Software companiesTT = Tara TechThe premises state that all software companiesemploy knowledge workers and Tara Tech is asoftware company. Therefore, Tara Tech employsknowledge workers.(a) ABC is invalid, because if Tara Tech employsknowledge workers, it cannot definitely be concludedthat it is a software company.(c) CDB is invalid, because if only some softwarecompanies employ knowledge workers, Tara Techmay not be among them.(d) ACE introduces a fourth term. ‘Companies thatemploy only knowledge workers’ and, therefore,violates the very definition of a syllogism, which musthave 3 and only 3 terms.

112. (d) BAC is the correct answer choice, as it forms avalid syllogism.

HH

ICM

TC

TC = Instances of traffic congestionICM = Instances of increase in carbon monoxide in theenvironment.HH = Instances that are hazardous to health.The premises state that increase in carbon monoxideis hazardous to health and traffic congestion increasescarbon monoxide in the environment. Therefore, trafficcongestion is hazardous to health.(a) CBA is invalid, because if TC and ICM are bothseparately hazardous to health (HH), no definiterelationship between TC and ICM necessarily follows.(b) BDE is invalid, because the some TC that are notICM need not necessarily be free of any hazard tohealth (HH): they could possibly pollute the environmentwith other noxious gases.

HH

ICMTC

The shaded portion shows those some TC that arenot ICM, but could possibly be hardardous to health(HH).(c) CDE is invalid, because the conclusion E is anegation of one of the premises C. Another checkreveals the TC is the middle term, which appears inboth the premises C and D, and E, therefore, shouldnot appear in the conclusion E, as per the basicdefinition of a syllogism.

113. (a) CEA is the correct answer choice, as it forms avalid syllogism.

TT

S A

Figures S = SweetsTT = Tasty thingsA = Apples

Sweets are a subset of tasty things. Apples are nottasty things. As apples are not a part of the main setof tasty things, they can also not be a part of thesubset of sweets.(b) BDC is invalid, because the set of some A that areS and the set of some A that are not TT may have norelationship with each other (disjoint sets).(c) CBD is invalid, because some A that are S aredefinitely TT, but we have no knowledge of theremaining A, and hence can reach no conclusion aboutthem.(d) EAC is invalid, because if all A are neither S nor TT,we cannot establish a definite relationship between Sand TT.

CAT PAPER - 1999

114. (b) BAE is the correct answer choice, as it forms avalid syllogism.

IT

PT

SB D

PT = Polluted townsSBD = Things that should be destroyedIT = Indian towns or towns in India.The shaded portion are those IT which are polluted(PT) and hence should be destroyed (SBD).The premises state that polluted towns should bedestroyed and that some towns in India are polluted.The ‘some’ in statement E refers to the polluted Indiantowns that should be destroyed.(a) BDE is invalid, because with B and D as premises,the only valid conclusion that follows is C. TownMeghana should be destroyed. ‘Town Meghana’ cannotbe simply replaced by ‘Some town in India,’ as in E.(c) ADE is invalid, because the syllogism has morethan 3 terms. The term SBD does not appear in thepremises A and D, but appears in the conclusion E asa new and fourth term.(d) CDB is invalid, because we can’t talk of all PT in theconclusion B, when we only have information aboutTown Meghana in both the premises C and D. Indeductive reasoning, we cannot proceed from specificcases to general cases. It would, however, be valid toconclude that ‘some polluted towns should bedestroyed.’

115. (a) ACB is the correct answer choice, as it forms avalid syllogism.

P

BC

P = PatriotsC = CriminalsB = BundledasSince patriot and criminal are two distinct sets, whatis patriot, cannot be criminal. Therefore, if Bundeldasis a patriot, Bundeldas cannot be a criminal.(b) ABC is invalid, because if no P is C and B is not C,we cannot be definite that B is not P.

P

B

C

B

Bundledas (B) may be a patriot (P) or not. Nothingdefinite can be concluded.(c) ADE is invalid, on similar lines as explained in thecase of (b).(d) ABE is invalid, because the syllogism has fourterms: patriots, criminals, Bundledas and Bogusdas.

116. (d) ACD is the correct answer choice, as it forms avalid syllogism.

LA

AE

Bl

Bl = BalaramAE = AnteatersLA = Creatures who like antsAnteaters like ants and Balram is an anteater.Therefore, Balram likes ants.(a) DCA is invalid. Just because Balaram likes antsand he is also an anteater, it does not logically followthat all anteaters like ants. It would, however, be validto conclude that ‘some anteaters like ants.’(b) ADC is invalid, because if Balaram like ants, wecannot definitely conclude that Balaram is an anteater,as evident from the Venn diagram.

LA

AE

Bl

B l

(c) ABC is invalid, because it has four terms:Anteaters, creatures who like ants, boys and Balaram.Furthermore, E: ‘Balaram may eat ants’ is a tantologousstatement and can never feature in a valid syllogism.A ‘may’ statement implies ‘may not’ and is always true(tantalogous), and can always stand on its own,without any supporting premises. Hence, such astatement is of no use to a student of logic, who isconcerned with the process of reasoning, arriving ata definite conclusion from definite information given inthe premises.

117. (b) ABE is the correct answer choice, as it forms avalid syllogism.

H

A

P

H = Handsome peopleA = ActorsP = Popular peopleThe shaded portion are some popular people who areactors and hence are handsome people.All actors are handsome and some of those actorsare also popular. Therefore, some who are popularare also handsome.(a) ACD is invalid, as there are four terms: actors,handsome people, Ram and popular actors.Furthermore, just because Ram is handsome does notdefinitely mean that he is an actor, let alone ‘a popular

CAT PAPER - 1999

actor’.(c) and (d) are similarly invalid as option (a), becausethey each have four terms.

118. (a) ABC is the correct answer choice, as it forms avalid syllogism.

TD

M I

BTI

BTI = BTIMI = Modern IndustryTD = Thing that is technology-drivenAll modern industries are technology-driven.BTI is a modern industryTherefore, BTI is technology-driven.(b) ABD is invalid, although it is similar to the correctoption ABC.

TD

M I

BTI

It is invalid simply because the statement D: ‘BTI maybe technology-driven, is a tantalogous statement (thatis, it is always true, regardless of what the premisessay).(c) BCA is invalid. Just because BTI is a modernindustry and it is technology-driven, it does not meanthat all MI are TD. It would, however, be valid to concludethat ‘Some MI are TD’.(d) EBC is invalid, because if BTI is a modern industry,we cannot definitely conclude that it is technology-driven, as evident from the Venn diagram.

M I

TD

BT IBT I

119. (b) ABE is the correct answer choice, as it forms avalid syllogism.

S.P N.B .C .P

BCP

G I

GI = Golmal islandersBCP = Blue-coloured people

SP = Smart peopleNBCP = Not blue-coloured peopleThose smart people who are not blue-coloured people(shaded portion) are definitely not Golmal islanders.(a) BCD is invalid, because there is no connectionbetween some babies that are BCP and the some SPwho are not BCP.

BCPSP

(c) CBD is invalid, because there need not necessarilybe any relationship between the some B that are BCPand the some B that are SP.

BCP SP

B

120. (c) AEB is the correct answer choice, as it forms avalid syllogism.

PG D

M BA

R+S

R + S = Ram and SitaPGD = People in great demandMBA = MBAAs all MBAs are in great demand and Ram and Sitabelong to the set of MBAs, Ram and Sita are also ingreat demand.(a) ABE is invalid because R + S need not be MBAs,just because both are in great demand.(b) ECD makes no sense.(d) EBA is invalid. Just because R + S are MBAs andin great demand does not mean that ‘all MBAs are ingreat demand’. It would, however, be valid to concludethe ‘some MBAs are in great demand’.

121. The main statement clearly states that if the orangutan(O) belongs to the set of not angry (NA), he cannotbelong to the set of frowns (F). Also, O must belong toeither of the two sets.CB states that O is not F and is NA. And DA states thatO is not NA and is F. Therefore, both CB and DA arelogically valid.

122. The main statement clearly states that Ravana (R) iseither a demon (D) or a hero (H). He has to be at leastone of the two, and if he is one, he cannot be theother.DB states that R is not H but is D.And CA states that R is not D but is H.Therefore, both DB and CA are logically valid.

CAT PAPER - 1999

123. The question statement clearly states that wheneverRajeev uses the Internet, he dreams about spiders.However, this does not mean that he dreams aboutspiders only when he uses the Internet. Therefore,using the Internet is only one possible condition forRajeev to dream about spiders. Thus, the Venn diagramfor the question will be:

D .S

U .I

Where,

UI → Uses Internet

DS → Dreams of spiders

Answer choice (a) AD states that Rajeev did not dreamabout spiders, and hence he did not use the Internet.This logically follows the above Venn diagram. If themain set does not occur, the subset will also not occur.Thus, AD is the right option.

124. P = I talk to my professorsQ = I do not need to take a pill for headache.Therefore, both AB(P ⇒ Q) and CD(neg Q ⇒ neg P)are logically consistent, not BA and DC.(d) ‘AB and CD’ is the correct answer choice.

125. (c) ‘A and D’ is the correct answer choice

S LC

Statement A is valid:The shaded portion represents those some sphinxesthat laugh and, therefore, are not cowboys as nocowboys laugh.Statement B is invalid.All G are F.Some G are not S.∴ Some S are not F.

FSG

F = Florescent thingsG = GhostsS = SingersThe valid conclusion is: Some F(shared position) arenot S. (V) and not the converse: Some S are not F. (X)(The some ghosts who are not singers (in shadedportion) are also the ‘some florescent things that arenot singers’)Statement C is invalid:All C are S.All S are H.

∴ Some H are not C.

H

S

C

C = CricketersS = Those who swearH = Those who are hangedThe valid conclusion is:All C are H (ü) and not its negation: Some H are not (C)(x)Statement D is valid.Some CP are P.All CP are W.∴ Some W are P.

W

CP

P

CP = Crazy peopleW = WrestlersP = PianistsThe shaded portion represents those some pianistswho are crazy people and are, therefore, wrestlers.And conversely, they are those some wrestlers whoare pianists.

126. (a) ‘C and D’ is the correct answer choice.Statement A is invalid: The valid conclusion would be‘All W are K’, rather than its converse, ‘All K are W’.

K

G P

W

K = KnightsGP = Good PeopleW = WarriorsStatement B is invalid, because it has four terms:footballers, ministers, tough people and players.Statement C is valid: The ‘some M’ that are P are alsoS. (shaded position).

S

P

M

S = SnacksP = PizzasM = MealsStatement D is valid: The ‘some MD’ that are B are alsoSB. (shaded portion).

CAT PAPER - 1999

SB

B

M D

SB = Sloth bearsB = BarkersMD = Musk deer

127. (b) B only is the correct answer choice.Statement A is invalid, as ‘No WB are PC’ cannot bevalidly concluded. What can, however, be validlyconcluded is that ‘Some PC (which are all D in shadedposition) are not WB’.

PC

W BD

D = DinosaursPC = Prehistoric creaturesWB = Water buffaloesStatement B is valid as evident from the Venn diagram

F

CP

F = Frank creaturesP = PoliticiansC = CrocodilesP is a subset of F.F and C are disjoint sets.As the main set F can never intersect with C, thesubset D will also never intersect or coincide with C.Statement C is invalid: No valid conclusion can followfrom two negative premises, as negatives have theeffect of separating one term from the others.Statement D is invalid, as the ‘Some GI Joes’ who likebananas need not be monkeys.

128. (c) ‘C and B’ is the correct answer choice.Statement A is invalid because it has four terms:a. Earthquakesb. Things that cause havocc. Landslidesd. Things that cause landslidesStatement B is valid as the ‘Some C’ which are GT arealso T (shaded portion).

T

G T

C

T = TransparentGT = Glass thingsC = CuriosAs all glass things (GT) are transparent (T), thosecurios (C) that are GT are definitely T.

Statement C is valid:

B

CO

XY

B = Brittle thingsCO = Clay objectsCO is a subset of B.XY is a subset of CO.Therefore, XY is also a subset of B.Thus, all XY are also brittle.Statement D is invalid.No valid conclusion can follow from two negativepremises, as negatives have the effect of separatingone term from the other.

129. (b) C is the only correct answer choice.Statement A is invalid.MD need not necessarily be among the some actorswho are pretty.Statement B is invalid, as the third segment is not aconclusion logically deduced using both the first andsecond segments. In fact, the conclusion can directlybe deduced from the second segment alone. Anotherway to check for this error is to see whether themiddle term ‘Cops’, that appears in the premises alsoappears in the conclusion. Here, ‘Cops’ appears in allthree segments and option (b) is therefore, not a validsyllogism.Statement C is valid. Those ‘Some men’, who are copsare also brave people (shaded portion).

BP

C

M

BP = Brave peopleC = CopsM = MenC is a subset of BPSome M is C.Therefore, those M that are C, are also BP.Statement D is invalid, MS may still be pretty withoutbeing an actor.

130. (a) ‘A and B’ is the correct answer choice.A and B are both valid: ‘No IIMs are BIMs’ or itsconverse,‘No BIMs are IIMs’ are both equally valid.

II

B IMIIM

II = Institutes in India.IIMs is a subset of II.No II is a BIMAs the mainset II can never intersect with the disjoint

CAT PAPER - 1999

set BIM, the subset IIM will also never intersect orcoincide with BIM.C and D are both invalid: The ‘Some IIMs’ and the ‘SomeBIMs’ need not have any relationship between them,just because they are not in India.

131. (c) Only C is the correct answer choice.Statement A is invalid. We cannot conclude about ‘allYP’, but only about ‘Some YP’ (shaded portion) whoare, incidentally, ‘all CY’.

ST

Y P

C Y I

CYI = Citizens of Yes IslandsST = People who speak only the truthYP = Young peopleStatement B is invalid, because it has four terms:a. Citizens of Yes Islandsb. People who speak only the truthc. Things that are in the Atlanticd. Yes IslandsStatement C is valid. The ‘Some YP’ who are CYI alsoare people who speak only the truth. (shaded portion)

ST

CYI

YP

Statement D is invalid, because the ‘some people’ andthe ‘some CYI’ need not have any relationship betweenthem, just because both speak only the truth.

132. (c) C only is the correct answer choice.Statement A is invalid, as the some fish that areviviparous need not be mammals.

B F

O

Statement B is invalid. We can validly conclude thatthe ‘Some fish (shaded portion)’ that are not oviparousare definitely not birds as well. But, based on this, wecannot conclude that ‘Some fish are birds’, as wehave no knowledge about the ‘remaining fish’.Statement C is valid, as we can validly conclude thatthe ‘Some C’ which are inside the circle O cannot bemammals. But nothing definite can be said about the‘Some C’ which are outside the circle O.

O N .O .

C

Statement D is invalid, because the ‘Some C’, whichare V and the ‘Some C’, which are M, need not haveany relationship between them, as evident from theVenn diagram.

133. (b) B only is the correct answer choice.

W P

S

Statement A is invalid, as no definite relationshipbetween P and W can be established.Note: ‘Many’ is translated as ‘Some’ to convert thestatement in standard form.The ‘Some S (shared portion)’ are not W, but someother S could be W, as shown in the Venn diagramabove.

CG

CB

Statement B is valid, as the ‘Some C (shaded portion)’that do not climb beans stalks cannot be giants.G = GrantsC = ChildrenCB = Creatures which climb beanstalksC is invalid, the ‘Some penguins’ that live in snowdriftsneed not be explorers.D is invalid, as Amar is the tallest among the three, butit is not clear how the heights of Akbar and Anthonyare compared.Note: This is not a ‘Categorical’ syllogism comprisingstatements, as such. All S is P, No S is P, Some S is Pand some S is not P. It is a ‘relational’ syllogismcomprising relational statements that normally featurein analytical reasoning. Be alert: CAT examiner is inthe habit of jumbling up questions to throw you offgear.

134. (d) ‘C and D’ is the correct answer choice.

F

R S

C S

Statement A is invalid: The ‘Some F’ who are RS andthe ‘Some RS’ who can catch snakes need not haveany relationship between them.CS = People who catch snakesRS = Rocket scientistsF = FarmersNote: ‘Many’ or ‘a few’ are both translated as ‘some’to convert the statements in the standard form.Statement B is invalid. Poonam need not be among thesome kangaroos that are made of teak.

BM

EG

Statement C is valid. No matadors can be bulls becausethe former eat grass, while the latter do not.EG: Creatures that eat grassM: Matadors

CAT PAPER - 1999

B: BullsStatement D is valid. The some PB (shaded portion)are in effect the ‘Some skunks’ that drive Cadillacs.

PB

S

DC

DC: Creature that drive CadillacsPB: Polar bearsS: Skunks

135. From the graph, we know the percentage growth insales are:

suoiverP

selas

tnerruC

selasecnereffiD egatnecreP

69-5991 001 052 051 %051

79-6991 052 003 05 %02

89-7991 003 092 01- %33.3–

99-8991 092 086 093 %5.431

It is but obvious from the above table that the maximumpercentage increase relative to previous year occurredin 1995-96.

136. From the graph, we can again calculate the growth inprofits.

suoiverP

tiforp

tnerruC

tiforpecnereffiD egatnecreP

69-5991 5.2 5.4 2 %08

79-6991 5.4 6 5.1 %33.33

89-7991 0.6 5.8 5.2 %66.14

99-8991 5.8 21 5.3 %2.14

The highest percentage growth in net profit relative tothe previous year was achieved in 1995-96.

137.

tiforpteN selasteN oitaR

59-4991 5.2 001 520.0

69-5991 5.4 052 20.0

79-6991 6 003 20.0

89-7991 5.8 092 30.0

99-8991 21 086 810.0

The profitability is maximum for 1997-98.

138. It may be seen that profitability does not follow a fixedpattern as the first three statements try to generalizethe profitability. They are not applicable.

139. Total trade with a region is defined as: The sum ofexports and imports from that region, from the piecharts for 1997-98, we have the following sectorsoccupying maximum area.

yrtnuoC stropxE stropmI edarT

H CEPO 9.7933 2.9739 1.59721

I aisA 6976 9075 50521

GtsaEeporuE

7933 8477 9.54111

C UE 7574 5.3984 5.0569

A ASU 6546 0763 62101

H – OPEC has the maximum trade.

140. From the pie chart, the region having lowest trade isK.1% of imports + 1% of exports∴ Indian exports are 1% of 3397.9 which is roughly340 US $ million.

141.otstropmI

aidnI

stropxE

aidnImorf

ticifededarT

A 11.0763 10.6546 9.5872–

B 59.8302 47.8302 12.0

C 84.3984 60.7574 24.631

D 47.6442 47.8302 804

E 59.8302 47.8302 12.0

F 85.518 73.9101 97.302–

G 10.8477 9.7933 11.0534

H 71.9739 9.7933 72.1895

I 60.9075 8.5976 47.6801–

J 61.1361 59.8961 97.76–

So, we see that region H has highest trade deficit ofapproximately $6,000 million or $6 billion.

142. From the pie chart for 1997-98, we get that USA whichis a region A has the lowest trade deficit.(9% of imports – 19% of total exports)

×−× 33979

100

1940779

100

9

= $– 2785.9 million.

CAT PAPER - 1999

143. From the pie chart, we know that the exports haveincreased from three regions A, G and H as follows.

yrtnuoC 99-8991 89-7991

A ASU 4.5937 6546

GtsaE

naeporuEseirtnuoc

5.8583 9.7933

H CEPO 4.5123 9.7933

Also the exports for 8 months have been given.According to new directions, before question 143,we need to calculate exports for 12 months

21436 12$32,154

8

×= million.

The maximum percentage increase is therefore fromregion A.

144. India’s total trade deficits are as follows.

stropmI stropxE ticifeD

89-7991 97704 97933 0086

99-8991 98124 45123 53001

Total imports for 1998-99 = 8

1228126 ×

= $42,189 millions

Similarly, exports for 1998-99 = 8

1228126 ×

= $32,154 millions

Percentage growth rate = 1006800

680010035×

−

= 47.6%

145. The price changes for each commodity are as follows.

gnidnE gninnigeB ecnereffiD egatnecreP

rahrA 5212 0071 524 52

reppeP 57291 52581 057 4

raguS 5341 0441 5 3.0–

dloG 0283 0524 033 8.7

The highest price change from the graph and the aboveis definitely for Arhar.

146. The price volatility for each individual.

tsehgiHecirp

tsewoLecirp

ecnereffiDegarevA

ecirpVP

rahrA 0032 0051 008 0091 24.0

reppeP 00591 05371 0522 52481 21.0

raguS 0051 0141 09 5541 260.0

dloG 0034 0083 084 0504 21.0

The price volatility for sugar is least, hence answerchoice is (c).Note: Average price can be calculated by highestprice, lowest price, ending and beginning price.

147. Let us assume Mr X invested Rs. 100 in eachcommodity.

esaercniecirPegatnecrep

001.sRnoemocnI

rahrA 52 52

reppeP 4 0.4

raguS 3.0– 3.0–

dloG 8.7– 8.7–

5.12

∴ His income is Rs. 21.5 on Rs. 400.

∴ 21.5100 5.4%

400× = profit

148. As per the table in question 146, the maximum PV isaround 40%.

149. Also Bangladesh > Philippines (97 > 86) for drinkingwater.And Philippines > any other countries for sanitationfacilities.Thus, these three countries are on thecoverage frontier for two facilities.

150. Statement A > Statement B only if statement A hashigher percentage in total coverage for both drinkingwater and sanitation facilities taken independently andnot as a total of the two facilities.Thus, only statement B and statement D areIndia > China(81 > 67 and 29 > 24)India > Nepal(81 > 63 and 29 > 18)Also China > Nepal (67 > 63 and 24 > 18)

CAT PAPER - 1999

151. Let the urban population be x and rural population bey.From the sanitation column, we have0.7x + 0.14y = 0.29(x + y)0.41x = 0.15y

∴ x = y41

15

∴ Percentage of rural population

= 100yx

y×

+

= 100

yy41

15

y×

+

= 10056

41×

= 73.2%

152. In the same way as the previous questions, we canfind percentage of rural population for Philippines,Indonesia and China.

P %05

I %66.66

C %8.97

Thus, P < I < C

153. India is not on coverage frontier because(i) it is below Bangladesh and Philippines for drinkingwater.(ii) for sanitation facilities it is below Philippines,Sri Lanka, Indonesia and Pakistan.


The disparity for the coverage of rural sector is as follows.

rotceslaruR rotcesnabrU

I 56 51

B 25 02

C 94 32

P 74 5

P 02 4

I 22 6

S 5– 02

N 15 03

Note: Disparity = (Percentage denoting drinking facilities

coverage – Percentage denoting sanitation coverage),For example, rural sector of India = 79 – 14= 65%Thus, as it can be seen from the table, in rural sectorthe country with most disparity is India (79 – 14)= 65%.And the country with least disparity in urban sector isPhilippines (92 – 88) = 4%

156. Statement I gives the weight of the heaviest and lightestmembers of the class but no indication as to the numberof students in the class or the total weight of thestudents is there. The second statement is alsoinconclusive, making our answer choice as (d).

157. Statement I gives the thickness of the wall which is ofno use to find the volume of the tank since we do notknow the radius of the sphere.Statement II gives us the answer as the volume ofwater displaced is equal to the volume of the immersedtank (from Archimedes’ principle)So to find the exact storage volume of the tank boththe statements are needed.

158. Statement I by itself does not solve the problem but itdoes tell us about the shape of the field. However, itfails to give information about the points A, B and C asto whether they be at the end of the field, etc. Thisdata is given by the second statement, from which it isknown that

C

A

B100

150

150

The polygon has the length = 150 × 2 = 300 m and thebreadth = 100 m and also that it is a rectangle(from A). Thus, the maximum distance is the diagonallength of the rectangle.

159.

91 9290

R

Q

P A 40°

80°B

C

CAT PAPER - 1999

Ratio of revenues = RQ

QP

Since in a line graph, the years are uniformly spaced

RQ tan80

QP tan40

°⇒ =

°So the ratio can be determined from statement I alone.

Statement II is immaterial because we intend to find theratio and not absolute figures.

160.

C

P

Dd

Q

r

r

r and d are given

From statement I, when co-ordinates of D are given,only one pair of tangents can be drawn onto the givencircle from D. So angle made by x-axis for each canbe found out. Hence statement I is sufficient.

From statement II, all we can interpret is that x-axisbisects one of the tangents. Keeping this in mind, manyfigures are possible.

(i)C

Q

L

D

P

QL = LD

(ii)C

Q

L

D

P

QL = LD

(iii)

D

L

Q

C

P

DL = LQ

(iv)

P

D

L C

Q

DL = LQ

4 more cases are possible when x-axis bisects DP.However, for all the 8 cases, we have 2 sets of slopesfor DP and DQ. Hence angles cannnot be determineduniquely.

161. Statement I when used to solve the sum gives us thesame equation as the second substituted in to the firstequation.kdx + key = kf∴ k(dx + ey) = kfas k ≠ 0.So, it is of no use as we get infinite solutions and nota unique one.Statement II gives us the following equations.x + y = c2x + 2y = f.These are two linear equations in x and y, such that

f

c

2

1

2

1≠=

As2

1

f

c≠ (Given)

Which is a system having a unique solution.

162. Statement II tells us that mathematicians can makemistakes which are always errors of +1 and –1.Also statement I tells us that mathematicians can neveradd 2 numbers correctly but we know he can makemistakes also.Again he can always add 3 numbers correctly.Therefore, as mistakes can be made here too, wecannot decide as to who is a mathematician.

163. From I, we know A and B passed the examination.From II, we know the condition that among C and D atleast one passed (or both passed) is false.Therefore, it is obvious that both C and D have failed.Thus, both statements are necessary to find theanswer.

CAT PAPER - 1999

164. Statement I tells us that A satisfies the equation

xxlog2 =

∴ x2 x =i.e. x = 4, but if x = 16 then also the above relation istrue. Here we need to consider statement II in order toget the unique value of x, i.e. x = 4.

165. Statement I gives us the number of white flowers. Butwe know that a white seed gives both red or whiteflowers. Thus, proving statement II, gives the numberof red flowers. But both black and white seeds givered flowers, again providing no solutions.

FLT – 06 Page 31

Directions for questions 111 to 120: There are ten short arguments given below. Read each of the

passages and answer the question that follows it.

111. In a recent report, the gross enrolment ratios at the primary level, that is, the number of children

enrolled in classes one to five as a proportion of all children aged six to ten, were shown to be very

high for most states; in many cases they were way above 100 per cent! These figures are not worth

anything, since they are based on the official enrolment data compiled from school records. They

might as well stand for ‘gross exaggeration ratios’.

Which one of the following options best supports the claim that the ratios are exaggerated?

a. The definition of gross enrolment ratio does not exclude, in its numerator, children below six

years or above ten years enroled in classes one to five.

b. A school attendance study found that many children enrolled in the school records were not

meeting a minimum attendance requirement of 80 per cent.

c. A study estimated that close to 22 per cent of children enrolled in the class one records were

below six years of age and still to start going to school.

d. Demographic surveys show shifts in the population profile which indicate that the number of

children in the age group six to ten years is declining.

112. Szymanski suggests that the problem of racism in football may be present even today. He begins

by verifying an earlier hypothesis that clubs’ wage bills explain 90 per cent of their performance.

Thus, if players’ salaries were to be only based on their abilities, clubs that spend more should

finish higher. If there is pay discrimination against some group of players — fewer teams bidding for

black players thus lowering the salaries for blacks with the same ability as whites — that neat

relation may no longer hold. He concludes that certain clubs seem to have achieved much less than

what they could have, by not recruiting black players.

Which one of the following findings would best support Szymanski’s conclusion?

a. Certain clubs took advantage of the situation by hiring above-average shares of black players.

b. Clubs hired white players at relatively high wages and did not show proportionately good

performance.

c. During the study period, clubs in towns with a history of discrimination against blacks, under-

performed relative to their wage bills.

d. Clubs in one region, which had higher proportions of black players, had significantly lower wage

bills than their counterparts in another region which had predominantly white players.

Section � III

FLT – 06

113. The pressure on Italy’s 257 jails has been increasing rapidly. These jails are old and overcrowded.

They are supposed to hold up to 43,000 people — 9,000 fewer than now. San Vittore in Milan, which

has 1,800 inmates, is designed for 800. The number of foreigners inside jails has also been increasing.

The minister-in-charge of prisons fears that tensions may snap, and so has recommended to the

government an amnesty policy.

Which one of the following, if true, would have most influenced the recommendation of the minister?

a. Opinion polls have indicated that many Italians favour a general pardon.

b. The opposition may be persuaded to help since amnesties must be approved by a two-thirds

majority in parliament.

c. During a recent visit to a large prison, the Pope, whose pronouncements are taken seriously,

appealed for ‘a gesture of clemency’.

d. Shortly before the recommendation was made, 58 prisons reported disturbances in a period of

two weeks.

114. The offer of the government to make iodised salt available at a low price of one rupee per kilogram is

welcome, especially since the government seems to be so concerned about the ill effects of non-

iodised salt. But it is doubtful whether the offer will actually be implemented. Way back in 1994, the

government, in an earlier effort, had prepared reports outlining three new and simple but experimental

methods for reducing the costs of iodisation to about five paise per kilogram. But these reports have

remained just those — reports on paper.

Which one of the following, if true, most weakens the author’s contention that it is doubtful whether

the offer will be actually implemented?

a. The government proposes to save on costs by using the three methods it has already devised for

iodisation.

b. The chain of fair-price distribution outlets now covers all the districts of the state.

c. Many small-scale and joint-sector units have completed trials to use the three iodisation methods

for regular production.

d. The government which initiated the earlier effort is in place even today and has more information

on the effects of non-iodised salt.

115. About 96 per cent of Scandinavian moths have ears tuned to the ultrasonic pulses that bats, their

predators, emit. But the remaining 4 per cent do not have ears and are deaf. However, they have a

larger wingspan than the hearing moths, and also have higher wing-loadings — the ratio between a

wing’s area and its weight — meaning higher manoeuvrability.

Which one of the following can be best inferred from the above passage?

a. A higher proportion of deaf moths than hearing moths fall prey to bats.

b. Deaf moths may try to avoid bats by frequent changes in their flight direction.

c. Deaf moths are faster than hearing moths, and so are less prone to becoming a bat’s dinner than

hearing moths.

d. The large wingspan enables deaf moths to better receive and sense the pulses of their bat

predators.

FLT – 06 Page 33

116. Argentina’s beef cattle herd has dropped to under 50 million from 57 million ten years ago in 1990.

The animals are worth less, too: prices fell by over a third last year, before recovering slightly. Most

local meat packers and processors are in financial trouble, and recent years have seen a string of

plant closures. The Beef Producers Association has now come up with a massive advertisement

campaign calling upon Argentines to eat more beef — their ‘juicy, healthy, rotund, plate-filling’

steaks.

Which one of the following, if true, would contribute most to a failure of the campaign?

a. There has been a change in consumer preference towards eating leaner meats like chicken and

fish.

b. Prices of imported beef have been increasing, thus making locally grown beef more competitive in

terms of pricing.

c. The inability to cross-breed native cattle with improved varieties has not increased production to

adequate levels.

d. Animal rights pressure groups have come up rapidly, demanding better and humane treatment of

farmyard animals like beef cattle.

117. The problem of traffic congestion in Athens has been testing the ingenuity of politicians and town

planners for years. But the measures adopted to date have not succeeded in decreasing the number

of cars on the road in the city centre. In 1980, an odds and evens number-plate legislation was

introduced, under which odd and even plates were banned in the city centre on alternate days,

thereby expecting to halve the number of cars in the city centre. Then in 1993 it was decreed that all

cars in use in the city centre must be fitted with catalytic converters; a regulation had just then been

introduced, substantially reducing import taxes on cars with catalytic converters, the only condition

being that the buyer of such a ‘clean’ car offered for destruction a car at least 15-year-old.

Which one of the following options, if true, would best support the claim that the measures adopted

to date have not succeeded?

a. In the 1980s, many families purchased second cars with the requisite odd or even number plate.

b. In the mid-1990s, many families found it feasible to become first-time car owners by buying a car

more than 15-year-old and turning it in for a new car with catalytic converters.

c. Post-1993, many families seized the opportunity to sell their more than 15-year-old cars and buy

‘clean’ cars from the open market, even if it meant forgoing the import tax subsidy.

d. All of the above

FLT – 06

118. Although in the limited sense of freedom regarding appointments and internal working, the

independence of the Central Bank is unequivocally ensured, the same cannot be said of its right to

pursue monetary policy without coordination with the Central Government. The role of the Central

Bank has turned out to be subordinate and advisory in nature.

Which one of the following best supports the conclusion drawn in the passage?

a. A decision of the chairman of the Central Bank to increase the bank rate by two percentage

points sent shock-waves in industry, academic and government circles alike.

b. Government has repeatedly resorted to monetisation of the debt despite the reservations of the

Central Bank.

c. The Central Bank does not need the Central Government’s nod for replacing soiled currency

notes.

d. The inability to remove coin shortage was a major shortcoming of this government.

119. The Shveta-chattra or the ‘White Umbrella’ was a symbol of sovereign political authority placed over

the monarch’s head at the time of the coronation. The ruler so inaugurated was regarded not as a

temporal autocrat but as the instrument of protective and sheltering firmament of supreme law. The

white umbrella symbol is of great antiquity and its varied use illustrates the ultimate common basis

of non-theocratic nature of states in the Indian tradition. As such, the umbrella is found, although not

necessarily a white one, over the head of Lord Ram, the Mohammedan sultans and Chatrapati

Shivaji.

Which one of the following best summarises the above passage?

a. The placing of an umbrella over the ruler’s head was a common practice in the Indian subcontinent.

b. The white umbrella represented the instrument of firmament of the supreme law and the non-

theocratic nature of Indian states.

c. The umbrella, not necessarily a white one, was a symbol of sovereign political authority.

d. The varied use of the umbrella symbolised the common basis of the non-theocratic nature of

states in the Indian tradition.

120. The theory of games is suggested to some extent by parlour games such as chess and bridge.

Friedman illustrates two distinct features of these games. First, in a parlour game played for money,

if one wins the other (others) loses (lose). Second, these games are games involving a strategy. In

a game of chess, while choosing what action is to be taken, a player tries to guess how his/her

opponent will react to the various actions he or she might take. In contrast, the card-pastime,

‘patience’ or ‘solitaire’ is played only against chance.

Which one of the following can best be described as a ‘game’?

a. The team of Tenzing Norgay and Edmund Hillary climbing Mt. Everest for the first time in human

history.

b. A national level essay writing competition.

c. A decisive war between the armed forces of India and Pakistan over Kashmir.

d. Oil Exporters’ Union deciding on world oil prices, completely disregarding the countries which

have at most minimal oil production.

FLT – 06 Page 35

Directions for questions 121 to 125: Read each of the five problems given below and choose the best

answer from among the four given choices.

121. Persons X, Y, Z and Q live in red, green, yellow or blue-coloured houses placed in a sequence on a

street. Z lives in a yellow house. The green house is adjacent to the blue house. X does not live

adjacent to Z. The yellow house is in between the green and red houses. The colour of the house, X

lives in is

a. blue b. green

c. red d. Not possible to determine

122. My bag can carry not more than ten books. I must carry at least one book each of management,

mathematics, physics and fiction. Also, for every management book I carry I must carry two or more

fiction books, and for every mathematics book I carry I must carry two or more physics books. I earn

4, 3, 2 and 1 points for each management, mathematics, physics and fiction book, respectively, I

carry in my bag. I want to maximise the points I can earn by carrying the most appropriate combination

of books in my bag. The maximum points that I can earn is

a. 20 b. 21 c. 22 d. 23

123. Five persons with names P, M, U, T and X live separately in any one of the following: a palace, a hut,

a fort, a house or a hotel. Each one likes two different colours from among the following: blue, black,

red, yellow and green. U likes red and blue. T likes black. The person living in a palace does not like

black or blue. P likes blue and red. M likes yellow. X lives in a hotel. M lives in a

a. hut b. palace c. fort d. house

124. There are ten animals — two each of lions, panthers, bison, bears, and deer — in a zoo. The

enclosures in the zoo are named X, Y, Z, P and Q and each enclosure is allotted to one of the

following attendants: Jack, Mohan, Shalini, Suman and Rita. Two animals of different species are

housed in each enclosure. A lion and a deer cannot be together. A panther cannot be with either a

deer or a bison. Suman attends to animals from among bison, deer, bear and panther only. Mohan

attends to a lion and a panther. Jack does not attend to deer, lion or bison. X, Y and Z are allotted to

Mohan, Jack and Rita respectively. X and Q enclosures have one animal of the same species. Z and

P have the same pair of animals. The animals attended by Shalini are

a. bear and bison b. bison and deer c. bear and lion d. bear and panther

125. Eighty kilogram of store material is to be transported to a location 10 km away. Any number of

couriers can be used to transport the material. The material can be packed in any number of units

of 10, 20, or 40 kg. Courier charges are Rs. 10 per hour. Couriers travel at the speed of 10 km/hr if

they are not carrying any load, at 5 km/hr if carrying 10 kg, at 2 km/hr if carrying 20 kg and at

1 km/hr if carrying 40 kg. A courier cannot carry more than 40 kg of load. The minimum cost at which

80 kg of store material can be transported to its destination will be

a. Rs. 180 b. Rs. 160 c. Rs. 140 d. Rs. 120

FLT – 06

Directions for questions 126 to 130: Answer these questions with reference to the table given below.

Information Technology Industry in India

(Figures are in million US dollars)

59-4991 69-5991 79-6991 89-7991 99-8991

erawtfoS

citsemoD 053 094 076 059 0521

stropxE 584 437 3801 0571 0562

erawdraH

citsemoD 095 7301 0501 5021 6201

stropxE 771 53 682 102 4

slarehpireP

citsemoD 841 691 181 922 923

stropxE 6 6 41 91 81

gniniarT 701 341 581 362 203

ecnanetniaM 241 271 281 122 632

dnagnikrowteN

srehto63 37 651 391 732

latoT 1402 6882 7083 1305 2506

126. The total annual exports lies between 35 and 40% to the total annual business of the IT industry, in

a. 1997-98 and 1994-95 b. 1996-97 and 1997-98

c. 1996-97 and 1998-99 d. 1996-97 and 1994-95

127. The highest percentage growth in the total IT business, relative to the previous year was achieved in

a. 1995-96 b. 1996-97

c. 1997-98 d. 1998-99

128. Which one of the following statements is correct?

a. The annual software exports steadily increased but annual hardware exports steadily declined

during 1994-99.

b. The annual peripheral exports steadily increased during 1994-99.

c. The IT business in training during 1994-99 was higher than the total IT business in maintenance

during the same period.


FLT – 06 Page 37

Additional directions for questions 129 and 130:

For any activity, A, year X dominates year Y if the IT business in activity A, in the year X is greater than the

IT business in activity A in the year Y. For any two IT business activities, A and B, year X dominates year

Y if

I. the IT business in activity A, in the year X, is greater than or equal to the IT business in activity A in

the year Y,

II. the IT business in activity B, in the year X, is greater than or equal to the IT business in activity B in

the year Y and

III. there should be strict inequality in the case of at least one activity.

129. For the IT hardware business activity, which one of the following is not true?

a. 1997-98 dominates 1996-97 b. 1997-98 dominates 1995-96

c. 1995-96 dominates 1998-99 d. 1998-99 dominates 1996-97

130. For the two IT business activities, hardware and peripherals, which one of the following is true?

a. 1996-97 dominates 1995-96 b. 1998-99 dominates 1995-96

c. 1997-98 dominates 1998-99 d. None of these

Directions for questions 131 to 140: Each question is followed by two statements, I and II. Answer each

question using the following instructions.

Mark the answer as

a. if the question can be answered by one of the statements alone, but cannot be answered by





d. if the question cannot be answered even by using both statements together.

131. Consider three real numbers, X, Y and Z. Is Z the smallest of these numbers?

I. X is greater than at least one of Y and Z.

II. Y is greater than at least one of X and Z.

132. Let X be a real number. Is the modulus of X necessarily less than 3?

I. X(X + 3) < 0

II. X(X – 3) > 0

133. How many people are watching TV programme P?

I. Number of people watching TV programme Q is 1,000 and number of people watching both the

programmes P and Q, is 100.

II. Number of people watching either P or Q or both is 1,500.

134. ∆PQR has ∠PRQ = 90°. What is the value of PR + RQ?

I. Diameter of the inscribed circle of the ∆PQR is equal to 10 cm.

II. Diameter of the circumscribed circle of the ∆PQR is equal to 18 cm.

FLT – 06

135. Harshad bought shares of a company on a certain day, and sold them the next day. While buying

and selling he had to pay to the broker 1% of the transaction value of the shares as brokerage. What

was the profit earned by him per rupee spent on buying the shares?

I. The sales price per share was 1.05 times that of its purchase price.

II. The number of shares purchased was 100.

136. For any two real numbers:

a ⊕ b = 1 if both a and b are positive or both a and b are negative.

= –1 if one of the two numbers a and b is positive and the other negative.

What is (2 ⊕ 0) ⊕ (–5 ⊕ –6)?

I. a ⊕ b is zero if a is zero

II. a ⊕ b = b ⊕ a

137. There are two straight lines in the x-y plane with equations:

ax + by = c

dx + ey = f

Do the two straight lines intersect?

I. a, b, c, d, e and f are distinct real numbers.

II. c and f are non-zero.

138. ‘O’ is the centre of two concentric circles, AE is a chord of the outer circle and it intersects the inner

circle at points ‘B’ and ‘D’. ‘C’ is a point on the chord in between ‘B’ and ‘D’.

What is the value of AC/CE?

I. BC/CD = 1

II. A third circle intersects the inner circle at ‘B’ and ‘D’ and the point ‘C’ is on the line joining the

centres of the third circle and the inner circle.

139. Ghosh Babu has decided to take a non-stop flight from Mumbai to No-man’s-land in South America,

He is scheduled to leave Mumbai at 5 a.m., IST on December 10, 2000. What is the local time at

No-man’s-land when he reaches there?

I. The average speed of the plane is 700 km/hr.

II. The flight distance is 10,500 km.

140. What are the ages of two individuals, X and Y?

I. The age difference between them is 6 years.

II. The product of their ages is divisible by 6.

FLT – 06 Page 39

Directions for questions 141 to 145: Answer these questions based on the data provided in the table

below.

Factory Sector by Type of Ownership

All figures in the table are in percentage of the total for the corresponding column

rotceS seirotcaF tnemyolpmEdexiF

latipac

ssorG

tuptuo

eulaV

dedda

:cilbuP 7 7.72 2.34 8.52 8.03

tnemnrevoGlartneC 1 5.01 5.71 7.21 1.41

lacolrosetatS

tnemnrevog2.5 2.61 3.42 6.11 9.41

lacolroetatsdnalartneC

tnemnrevog8.0 0.1 4.1 5.1 8.1

:tnioJ 8.1 1.5 8.6 4.8 1.8

etavirpyllohW 3.09 6.46 8.64 8.36 7.85

srehtO 9.0 6.2 2.3 0.2 4.2

latoT 001 001 001 001 001

141. Suppose the average employment level is 60 per factory. The average employment in ‘wholly private’

factories is approximately

a. 43 b. 47 c. 50 d. 54

142. Among the firms in different sectors, value added per employee is highest in

a. Central Government b. Central and State/Local Governments

c. Joint sector d. Wholly private

143. Capital productivity is defined as the gross output value per rupee of fixed capital. The three sectors

with the higher capital productivity, arranged in descending order are

a. Joint, Wholly private, Central and States/Local

b. Wholly private, Joint, Central and States/Local

c. Wholly private, Central and State/Local, Joint

d. Joint, Wholly private, Central

144. A sector is considered ‘pareto efficient’ if its value added per employee and its value added per rupee

of fixed capital is higher than those of all other sectors. Based on the table data, the pareto efficient

sector is

a. Wholly private b. Joint

c. Central and State/Local d. others

145. The total value added in all sectors is estimated at Rs. 1,40,000 crore. Suppose the number of firms

in the joint sector is 2,700. The average value added per factory, in the Central Government is

a. Rs. 141 crore b. Rs. 14.1 crore c. Rs. 131 crore d. Rs. 13.1 crore

FLT – 06

Directions for questions 146 to 149: Answer these questions based on the data presented in the figure

below.

FEI for a country in a year, is the ratio (expressed as a percentage) of its foreign equity inflows to its GDP.

The following figure displays the FEIs for select Asian countries for 1997 and 1998.

1.71

5.96

10.67

2.16

5.825.09

0.72

4.80

9.92

2.50

0

2

4

6

8

10

12

India China Malaysia South Korea Thailand

1997 1998

146. The country with the highest percentage change in FEI in 1998 relative to its FEI in 1997, is

a. India b. China c. Malaysia d. Thailand

147. Based on the data provided, it can be concluded that

a. absolute value of foreign equity inflows in 1998 was higher than that in 1997 for both Thailand and

South Korea.

b. absolute value of foreign equity inflows was higher in 1998 for Thailand and lower for China than

the corresponding values in 1997.

c. absolute value of foreign equity inflows was lower in 1998 for both India and China than the

corresponding values in 1997.

d. None of the above can be inferred

148. It is known that China’s GDP in 1998 was 7% higher than its value in 1997, while India’s GDP grew

by 2% during the same period. The GDP of South Korea, on the other hand, fell by 5%. Which of the

following statements is/are true?

I. Foreign equity inflows to China were higher in 1998 than in 1997.

II. Foreign equity inflows to China were lower in 1998 than in 1997.

III. Foreign equity inflows to India were higher in 1998 than in 1997.

IV. Foreign equity inflows to South Korea decreased in 1998 relative to 1997.

V. Foreign equity inflows to South Korea increased in 1998 relative to 1997.

a. I, III and IV b. II, III and IV c. I, III and V d. II and v

FLT – 06 Page 41

149. China’s foreign equity inflows in 1998 were 10 times that of India. It can be concluded that

a. China’s GDP in 1998 was 40% higher than that of India

b. China’s GDP in 1998 was 70% higher than that of India

c. China’s GDP in 1998 was 50% higher than that of India

d. no inference can be drawn about relative magnitudes of China’s and India’s GDPs

Directions for questions 150 to 153: Answer the questions based on the table below.

The table shows trends in external transactions of Indian corporate sector during the period 1993-94 to

1997-98. In addition, following definitions hold good:

Salesi, Imports

i, and Exports

i respectively denote the sales, imports and exports in year i.

Deficit for year i, Deficiti = Imports

i– Exports

i

Deficit Intensity in year i, DIi = Deficit

i / Sales

i

Growth rate of deficit intensity in year i, GDIi = (DI

i– DI

i – 1 ) / DI

i – 1

Further, note that all imports are classified as either raw material or capital goods.

Trends in External Transactions of Indian Corporate Sector

(All figures in per cent)

raeY 89-7991 79-6991 69-5991 59-4991 49-3991

*ytisnetnitropxE 2.9 2.8 9.7 5.7 3.7

*ytisnetnitropmI 2.41 2.61 5.51 8.31 4.21

tsoclatoT/lairetamwardetropmI

lairetamwarfo2.02 2.91 6.71 3.61 61

ssorG/sdooglatipacdetropmI

stessadexif6.71 8.9 8.11 3.61 5.91

* Ratio of Exports (or Imports) to sales.

150. The highest growth rate in deficit intensity was recorded in

a. 1994-95 b. 1995-96 c. 1996-97 d. 1997-98

151. The value of the highest growth rate in deficit intensity is approximately

a. 8.45% b. 2.15% c. 33.3% d. 23.5%

152. In 1997-98 the total cost of raw materials is estimated as 50% of sales of that year. The turnover of

gross fixed assets, defined as the ratio of sales to gross fixed assets, in 1997-98 is, approximately

a. 3.3 b. 4.3

c. 0.33 d. Not possible to determine

153. Which of the following statements can be inferred to be true from the given data?

a. During the 5-year period between 1993-94 and 1997-98 exports have increased every year.

b. During the 5-year period 1993-94 and 1997-98, imports have decreased every year.

c. Deficit in 1997-98 was lower than that in 1993-94.

d. Deficit intensity has increased every year between 1993-94 and 1996-97.

FLT – 06

Directions for questions 154 to 159: Answer the questions based on the data given below.

The figures below present annual growth rate, expressed as the percentage change relative to the previous

year, in four sectors of the economy of the Republic of Reposia during the 9-year period from 1990 to 1998.

Assume that the index of production for each of the four sectors is set at 100 in 1989. Further, the four

sectors: manufacturing, mining and quarrying, electricity, and chemicals, respectively, constituted 20%,

15%, 10% and 15% of total industrial production in 1989.

Manufacturing

-5

0

5

10

15

1990 1991 1992 1993 1994 1995 1996 1997 1998

Mining and quarrying

-5

0

5

10

1990 1991 1992 1993 1994 1995 1996 1997 1998

Electrical

0

2

4

6

8

10

1990 1991 1992 1993 1994 1995 1996 1997 1998

Chemical

0

5

10

15

1990 1991 1992 1993 1994 1995 1996 1997 1998

FLT – 06 Page 43

154. Which is the sector with the highest growth during the period 1989 to 1998?

a. Manufacturing b. Mining and quarrying

c. Electricity d. Chemical

155. The overall growth rate in 1991 of the four sectors together is approximately

a. 10% b. 1% c. 2.5% d. 1.5%

156. When was the highest level of production in the manufacturing sector achieved during the 9-year

period 1990-98?


157. When was the lowest level of production of the mining and quarrying sector achieved during the

9-year period 1990-98?


158. The percentage increase of production in the four sectors, namely, manufacturing, mining and

quarrying, electricity and chemicals, taken together in 1994, relative to 1989 is approximately

a. 25% b. 20% c. 50% d. 40%

159. It is known that the index of total industrial production in 1994 was 50% more than that in 1989.

Then, the percentage increase in production between 1989 and 1994 in sectors other than the four

listed above is

a. 57.5% b. 87.5% c. 127.5% d. 47.5%


ABC Ltd. produces widgets for which the demand is unlimited and they can sell all of their production. The

graph below describes the monthly variable costs incurred by the company as a function of the quantity

produced. In addition, operating the plant for the first shift results in a fixed monthly cost of Rs. 800. Fixed

monthly costs for second shift operation is estimated at Rs. 1,200. Each shift operation provides capacity

for producing 30 widgets per month.

Variable cost

7000

6000

5000

4000

3000

2000

1000

0

1 6 11 3116 3621 41 5126 46 56

FLT – 06

Note: Average unit cost, AC = Total monthly costs

Monthly productionand marginal cost, MC is the rate of change in total

cost for unit change in quantity produced.

160. Total production in July is 40 units. What is the approximate average unit cost for July?

a. 3,600 b. 90

c. 140 d. 115

161. ABC Ltd. is considering increasing the production level. What is the approximate marginal cost of

increasing production from its July level of 40 units?

a. 110 b. 130

c. 150 d. 160

162. From the data provided it can be inferred that, for production levels in the range of 0 to 60 units,

a. MC is an increasing function of production quantity

b. MC is a decreasing function of production quantity

c. initially MC is a decreasing function of production quantity, attains a minimum and then it is an

increasing function of production quantity


163. Suppose that each widget sells for Rs. 150. What is the profit earned by ABC Ltd. in July?

(Profit is defined as the excess of sales revenue over total cost.)

a. 2,400 b. 1,600

c. 400 d. 0

164. Assume that the unit price is Rs. 150 and profit is defined as the excess of sales revenue over total

costs. What is the monthly production level of ABC Ltd. at which the profit is highest?

a. 30 b. 50 c. 60 d. 40

165. For monthly production level in the range of 0 to 30 units,

a. AC is always higher than MC

b. AC is always lower than MC

c. AC is lower than MC up to a certain level and then is higher than MC.


PAST CAT PAPER – 2002 Explanations Page 1

1 3 2 4 3 4 4 3 5 3 6 1 7 1 8 3 9 3 10 3

11 2 12 4 13 1 14 4 15 1 16 1 17 1 18 4 19 2 20 3

21 3 22 3 23 4 24 1 25 3 26 3 27 2 28 4 29 2 30 2

31 2 32 4 33 4 34 2 35 2 36 2 37 1 38 2 39 1 40 4

41 2 42 2 43 2 44 4 45 3 46 1 47 3 48 2 49 4 50 3

51 3 52 2 53 1 54 2 55 1 56 4 57 4 58 2 59 4 60 4

61 3 62 2 63 4 64 4 65 3 66 2 67 2 68 4 69 3 70 1

71 3 72 2 73 3 74 4 75 4 76 1 77 1 78 4 79 2 80 4

81 4 82 3 83 4 84 3 85 1 86 3 87 1 88 3 89 2 90 2

91 4 92 4 93 4 94 3 95 4 96 2 97 2 98 4 99 3 100 3

101 3 102 2 103 4 104 2 105 4 106 3 107 1 108 3 109 4 110 2

111 3 112 1 113 4 114 3 115 1 116 4 117 3 118 2 119 3 120 2

121 1 122 4 123 1 124 3 125 1 126 3 127 2 128 3 129 4 130 1

131 1 132 4 133 4 134 4 135 2 136 4 137 2 138 2 139 4 140 4

141 4 142 1 143 1 144 2 145 1 146 3 147 4 148 3 149 1 150 3

Scoring table

Section

DI 1 to 50 50

QA 51 to 100 50

EU + RC 101 to 150 50

Total 150

Totalquestions

Totalattempted

Totalcorrect

Totalincorrect

Netscore

Timetaken

Questionnumber

PAST CAT PAPER � 2002

ANSWERS and EXPLANATIONS

PAST CAT PAPER – 2002 ExplanationsPage 2

1. 3 Statement I tells us that(1) Ashish is not an engineer, (2) Ashish got moreoffers than the engineers.Hence, Ashish did not have 0 offers.After this the following table can be achieved.

Profession Names Offers

3 2 1 0 X Profession

CA Ashish × × P × X Engineer

MD Dhanraj P × × × X Engineer

Economist Sameer × P × ×

Engineer × × × P

From statement IV, Dhanraj is not at 0 and 1.

2. 4 Option (3) is ruled out by statement VII.Option (1) is ruled out by statements VII and VIII.From statement IV, Sandeep had Rs. 30 to start andDaljeet Rs. 20.From statement II, option (2) is not possible as Sandeepwas left with Re 1, he spent Rs. 29. But according to(2) he spent Rs. 1.50 more than Daljeet. But Daljeethad only Rs. 20. Hence option (4) is correct.

3. 4 Data insufficient, please check the question.

4. 3 Statements V and VI rule out options (1) and (2). Sincecontestants from Bangalore and Pune did not comefirst, school from Hyderabad can come first. Conventis not in Hyderabad which rules out option (4).

5. 3 The only two combinations possible are:Younger Older

2 43 9

Cubes of natural numbers are 1, 8, 27, 64, ... . Here 64and above is not possible as the age will go above 10.Only (2) and (3) satisfy the case of mother and father.

6. 1 Total seats in the hall 200Seats vacant 20Total waiting 180Ladies 72

Seating capacity of flight2

180 1203

× =

Number of people in flight A = 100For flight B = 180 – 100 = 80

Thus, airhostess for A = 80

420

=

Empty seats in flight B = 120 – 80 = 4040 : 4 = 10 : 1

7. 1N

W E

S

S

M oves @ 20 km ph, t = ½ hr = 30 m inutes

s = 20 × = 10 km∴ 3060

10 km

10 km

20 km

40 km

10 km@ 100 kmpht = 24 m inu tess = 40 km

@ 40 km pht = 30 m inu tes

s = 20 km∴@ 40 km pht = 15 m inu tes

s = 10 km∴

@ 40 km pht = 15 m inu tes

s = 10 km∴

START

IIndSignal

IIIrdSignal IVTH

Signal

Vth SignalFINISH

I Signal

Note: s = Distance covered; v = Velocity (km/hr) t = Time taken; s = v × tThe total distance travelled by the motorist from the startingpoint till last signal is 10 + 10 + 20 + 40 + 10 = 90 km

8. 3N

W E

S

10 km

10 km

20 km

40 km

10 km

S

II

IIIIV

F

40 km

30 km

T

I


Note: According to Pythagoras’ theorem, for a right-angled triangle.B

A C

BC2 = AB2 + AC2

BC = 2 2AB AC+

SF = 2 2ST TF+ = 2 240 30 2500+ = = 50 km

9. 3 For the case when 1st signal were 1 red and 2 greenlights, the surface diagram will be as given below.

N

W E

S

10 km

10 km

20 km

40 km

10 km

S

II

III

IV

F50 km

T

I

40 km

TF = 50 km; ST = 40 kmConsidering the above figure, option (3) is correct,50 km to the east and 40 km to the north.

10. 3 If the car heads towards south from here startingpoint,

N

W E

S

10 km

20 km40 km

10 km

II

III

IV

S

I

40 km

10 km

F

START

FIN ISH

30 km

From the above we can conclude that option (3) iscorrect.

11. 2 Total five lie between 10 E and 40 E.Austria, Bulgaria, Libya, Poland, ZambiaN N N N S

120%

5=

12. 4 Number of cities starting with consonant and in thenorthern hemisphere = 10.Number of countries starting with consonant and inthe east of the meridien = 13.Hence option (4), the differencce is 3.

13. 1 Three countries starting with vowels and in southernhemisphere — Argentina. Australia and Ecuador andtwo countries with capitals beginning with vowels —Canada and Ghana.

14. 4 Let us consider two cases:(a) If 5 min remaining the score was 0 – 2. Then final

score could have been 3 – 3. [Assuming no otherIndian scored]

(b) But if the score before 5 min was 1 – 3, then finalscore could have been 4 – 3.

15. 1 From A, if by adding 12 students, the total number ofstudents is divisible by 8, then by adding 4 students,it will be divisible by 8.


16. 1 From (A), (x + y)1 1

x y

+

= 4 or (x + y)

y x

xy

+

= 4

⇒ (x + y)2 = 4xy

⇒ (x – y)2 = 0

⇒ x = y ... (i)

From (B), (x – 50)2 = (y – 50)2

On solvingx(x – 100) = y(y – 100) ... (ii)This suggests that the values of x and y can either be0 or 100.

17. 1 Statement:A. Let the wholesale price is x.

Thus, listed prices = 1.2xAfter a discount of 10%, new price = 0.9 × 1.2x

= 1.08x1.08 – x = 10$. Thus, we know x can be found.

B. We do not know at what percentage profit, or atwhat amount of profit was the dress actuallysold.

18. 4 A gives 500 as median and B gives 600 as range.A and B together do not give average. Therefore, itcannot be answered from the given statements.

19. 2 From statement A, we know that for all –1 < x < 1,we can determine |x – 2| < 1 is not true.From B, –1 < x < 3, we cannot determine whether|x – 2| < 1 or not. Therefore, statement B alone issufficient.

20. 3 From statement A, we cannot find anything.From B alone we cannot find.From A and B,

300

F R

X 58196

x + 196 + 58 = 300. Thus, x can be found.

21. 3 Jagdish (J), Punit (P), Girish (G)

(A) J = 2

9 [P + G]

P + G + J = 38500Thus, only J can be found.

(B) Similarly, from this only P can be found.Combining we know J, P and G can be found.

22. 3 Emp. numbers 51, 58, 64, 72, 73 satisfy them.Total = 5

23. 4 80% attendance = 80% of 25 = 20 daysEmp. numbers 47, 51, 72, 73, 74, 79, 80.Thus, total = 7

24. 1 Emp. No. Earnings No. of days E/D

E D

(medium) (medium)

2001151 159.64 13.33 11.97

2001158 109.72 9.61 11.41

2001164 735.22 12.07 60.91

2001171 6.10 4.25 -

2001172 117.46 8.50 13.81

2001179 776.19 19.00 40.85

2001180 1262.79 19.00 66.46

From the above we can see that Emp. number 2001180earns the maximum per day salary.

25. 3 If you have practised Vedic mathematics you can easilycompare the fraction in your time. Thus, Emp. numbers51, 58, 64, 71, 72 satisfy the condition.[For emp. 64, you see 12 is not the double of 5. And735 is not even double of 402.

Hence,402 735

5 12> (3)

26. 3 Total revenue of 1999 = 3374

5% of 3374 = 3374 ×5

100 = 168.7

For 1999, revenue for Spain is 55, Rest of LatinAmerica is 115, North Sea is 140, Rest of the world is91.So total four operations of the company accountedfor less than 5% of the total revenue earned in theyear 1999.

27. 2 For man the 200% growth. The value should be morethan three times.

28. 4 Four operations, as given below:(1) North Africa and Middle-East(2) Argentina(3) Rest of Latin America(4) Far Easthave registered yearly increase in income before taxesand charges from 1998 to 2000.

29. 2 Percentage increase in net income before tax andcharges for total world (1998-99)

=1375 248

100248

−× = 454.4%

Spain is making loss.


Percentage increase for North Africa and Middle-East

341 111

111

−× 100 = 207.2%

Percentage increase for Argentina838 94

10094

−= ×

= 791.5%From the table one can directly say that there is nooperation other than Argentina, whose percentageincrease in net income before taxes and charges ishigher than the average (world).

30. 2 Statement 1 is obviously wrong.

(b)54 20

65 52> . Hence, (2) is correct.

(c)500 61

1168 187> . Hence (3) is wrong.

31. 2 Profitability of North Africa and Middle-East in 2000

=356

530= 0.67

Profitability of Spain in 2000 = 225

43= 5.23

Profitability of Rest of Latin America in 2000 = 169

252,

i.e. < 1.

Profitability of Far East in 2000 = 189

311= < 1

32. 4 Except Rest of Latin America and Rest of the World allthe operations are greater than 2.

33. 4 I would rate this question as time-taking because toverify option (4) it takes time. But if you have ruled outoptions (1), (2) and (3), then you can straight awaymark (4).

34. 2 It can be easily observed from the two charts that

Switzerland’s ratio of chart 1 to chart 2 is 20

11 has the

highest price per unit kilogram for its supply. Findingthe ratio of the value and quantity is enough to reachthe solution.

35. 2 Total value of distribution to Turkey is 16% of 5760million Euro.Total quantity of distribution to Turkey is 15% of 1.055million tonnes.So the average price in Euro per kilogram for Turkey is

165760

1005.6

151055

100

× ×

;

36. 2 BC → AC → AAC = 0

37. 1 BD → AE → AAB = 95.2The least cost to reach to AAB is for AE. And that isBD to AE is zero.

38. 2 BB → AB → AAG = 311.1Same as above.

39. 1 First you check the minimum cost for receiving at AAA.This is O for AE. But BB to AE is very high. Next is AC[314.5] BB to AC is 451.1. After AC the others arehigh. Hence, 314.5 + 451.1 = 765.6

40. 4 Number of refineries = 6Number of depots = 7Number of districts = 9Therefore, number of possible ways to send petrolfrom any refinery to any district is 6 × 7 × 9 = 378.

41. 2 If you look for large figures you would find them inboth tables in AE. Add them and we getBE → AE → AAH

42. 2

Position

of

States

(Rank)

96-97 97-98 98-99 99-00 00-01

1) mA mA mA mA mA

2) TN TN TN TN TN

3) GU AP AP AP AP

4) AP GU GU GU UP changed

5) kA UP UP UP GU tw ice

6) UP kA kA kA kA

7) WB WB WB WB WB

}

Year

From above, we can conclude that option (2) is correct.

43. 2 On referring to the above table, we can see that UP isthe state which changed its relative ranking mostnumber of times.

44. 4 We can say directly on observing the graph that thesales tax revenue collections for AP has more thandoubled from 1997 to 2001.


45. 3 Growth rate of tax revenue can be calculated as:(Sales tax revenue of correct year – Sales tax revenueof previous year)

For year 1997-98 7826 7290

7826

− = 0.068

For year 1998-998067 7826

7826

− = 0.030

For year 1999-2000 10284 8067

8067

− = 0.274

For year 2000-01 12034 10284

10284

−= 0.170

46. 1 For this we have to check every option.

For Karnataka, Sales tax revenue of the states

total sales tax

1996-97 ⇒3510

29870 = 0.11

1997-98 ⇒3829

33168 = 0.11

1998-99 ⇒4265

36068 = 0.11

1999-2000 ⇒4839

42348= 0.11

2000-01 ⇒5413

49638= 0.11

So Karnataka is the correct option and no further checkis required.

47. 3 On referring to the table prepared in the solution forquestion (11), we can see that Tamil Nadu has beenmaintaining a constant rank over the years in terms ofits contribution to total tax collections.

48. 2 Only R9

49. 4 Statement (1) is not satisfied by R9.Statement (2) is not satisfied R2 & R3Statement (3) is incorrect as there are five such regionR1, R2, R3, R4 & R11.Statement (4) is correct.

50. 3 All three R9, R10, R11.

51. 3 Total possible arrangements = 10 × 9 × 8Now 3 numbers can be arranged among themselvesin 3! ways = 6 waysGiven condition is satisfied by only 1 out of 6 ways.Hence, the required number of arrangements

=10 9 8

6

× × = 120

52. 2

A

y

30°

3

CDB

4

30°

Let BC = x and AD = y.

As per bisector theorem, BD AB

DC AC= =

4

3

Hence, BD = 4x 3x

; DC7 7

=

In ∆ABD,

22 2 16x

(4) y –49cos30

2 4 y

+° =

× ×

223 16x

2 4 y 16 y –2 49

⇒ × × × = +

22 16x

4 3y 16 y –49

⇒ = + ... (i)

Similarly, from ∆ADC,

22 9x

9 y –49cos30

2 3 y

+° =

× ×

22 9x

3 3y 9 y –49

⇒ = + ... (ii)

Now (i) × 9 – 16 × (ii), we get

2 236 3y – 48 3y 9y – 16y= 12 3y

7⇒ =

53. 1

C

20

B25

A

15

Let the chord = x cm

∴1 1 x

(15 20) 252 2 2

× = × × x 24⇒ = cm

54. 2 f(x) + f(y) = log 1 x 1 y

log1– x 1– y

+ + +

(1 x) (1 y)log

(1– x)(1– y)

+ +=

1 x y xylog

1 xy – x – y

+ + += +

FLT – 07 Page 25

Directions for questions 101 to 104: Answer the questions based on the table given below.

The following table describes garments manufactured based upon the colour and size for each lay. There

are four sizes: M – medium, L – large, XL – extra large and XXL – extra extra large. There are three colours:

yellow, red and white.

Lay

Lay No. M L XL XXL M L XL XXL M L XL XXL

1 14 14 7 0 0 0 0 0 0 0 0 0

2 0 0 0 0 0 0 0 0 42 42 21 0

3 20 20 10 0 18 18 9 0 0 0 0 0

4 20 20 10 0 0 0 0 0 30 30 15 0

5 0 0 0 0 24 24 12 0 30 30 15 0

6 22 22 11 0 24 24 12 0 32 32 16 0

7 0 24 24 12 0 0 0 0 0 0 0 0

8 0 20 20 10 0 2 2 1 0 0 0 0

9 0 20 20 10 0 0 0 0 0 22 22 11

10 0 0 0 0 0 26 26 13 0 20 20 10

11 0 22 22 11 0 26 26 13 0 22 22 11

12 0 0 2 2 0 0 0 0 0 0 0 0

13 0 0 0 0 0 0 0 0 0 0 20 20

14 0 0 0 0 0 0 0 0 0 0 22 22

15 0 0 10 10 0 0 2 2 0 0 22 22

16 0 0 0 0 1 0 0 0 1 0 0 0

17 0 0 0 0 0 5 0 0 0 0 0 0

18 0 0 0 0 0 32 0 0 0 0 0 0

19 0 0 0 0 0 32 0 0 0 0 0 0

20 0 0 0 0 0 5 0 0 0 0 0 0

21 0 0 0 18 0 0 0 0 0 0 0 0

22 0 0 0 0 0 0 0 26 0 0 0 0

23 0 0 0 0 0 0 0 0 0 0 0 22

24 0 0 0 8 0 0 0 1 0 0 0 0

25 0 0 0 8 0 0 0 0 0 0 0 12

26 0 0 0 0 0 0 0 1 0 0 0 14

27 0 0 0 8 0 0 0 2 0 0 0 12

Production 76 162 136 97 67 194 89 59 135 198 195 156

Order 75 162 135 97 67 194 89 59 135 197 195 155

Surplus 1 0 1 0 0 0 0 0 0 1 0 1

Number of Garments

Yellow WhiteRed

101. How many lays are used to produce yellow fabrics?

a. 10 b. 11 c. 12 d. 14

102. How many lays are used to produce XL fabrics?

a. 15 b. 16 c. 17 d. 18

103. How many lays are used to produce XL yellow or XL white fabrics?

a. 8 b. 9 c. 10 d. 15

Section � III

FLT – 07

104. How many varieties of fabrics, which exceed the order, have been produced?

a. 3 b. 4 c. 5 d. 6

Directions for questions 105 to 108: Answer the questions based on the table given below concerning the

busiest 20 international airports in the world.

.oN emaNlanoitanretnI

epyTtropriAedoC noitacoL sregnessaP

1 dleifstraH A LTA ASU,aigroeG,atnaltA 63593977

2 eraH'O-ogacihC A DRO ASU,sionillI,ogacihC 67086527

3 selegnAsoL A XAL ASU,ainrofilaC,selegnAsoL 16567836

4 tropriAworhtaeH E RHL modgniKdetinU,nodnoL 01736226

5 WFD A WFD ASU,saxeT,htroW.tF/sallaD 52100006

6 tropriAadenaH F DNH napaJ,oykoT 21283345

7 tropriAtrufknarF E ARF ynamreG,trufknarF 51385854

8 elluaGedselrahC-yssioR E GDC ecnarF,siraP 34969534

9 ocsicnarFnaS A OFS ASU,ainrofilaC,ocsicnarFnaS 22478304

01 revneD A AID ASU,odaroloC,revneD 13243083

11 lohpihcSmadretsmA E SMA sdnalrehteN,madretsmA 51018763

21 luaP.tS-silopaenniM A PSM ASU,luaP.tS-silopaenniM 13361243

31 natiloporteMtiorteD A WTD ASU,nagihciM,tiorteD 18383043

41 imaiM A AIM ASU,adirolF,imaiM 64299833

51 kraweN A RWE ASU,yesreJweN,kraweN 00041833

61 narraCcM A SAL ASU,adaveN,sageVsaL 58196633

71 robraHykSxineohP A XHP ASU,anozirA,xineohP 35333533

81 opmiK EF LES aeroK,luoeS 47017333

91 hsuBegroeG A HAI ASU,saxeT,notsuoH 33398033

02 ydenneK.FnhoJ A KFJ ASU,kroYweN,kroYweN 00030023

105. How many international airports of type ‘A’ account for more than 40 million passengers?

a. 4 b. 5 c. 6 d. 7

106. What percentage of top ten busiest airports is in the United States of America?

a. 60% b. 80% c. 70% d. 90%

FLT – 07 Page 27

107. Of the five busiest airports, roughly, what percentage of passengers in handled by Heathrow Airport?

a. 30 b. 40 c. 20 d. 50

108. How many international airports not located in the USA handle more than 30 million passengers?

a. 5 b. 6 c. 10 d. 14

Directions for questions 109 to 114: Answer the questions based on the two graphs shown below.

Figure I shows the amount of work distribution, in man-hours, for a software company between offshore and

onsite activities. Figure 2 shows the estimated and actual work effort involved in the different offshore

activities in the same company during the same period. [Note: Onsite refers to work performed at the

customer’s premise and offshore refers to work performed at the developer’s premise.]

0

100

200

300

400

500

Design Coding Testing

Offshore

Onsite

Figure 1

0

100

200

300

400

500


Estimated

Actual

Figure 2

109. Which work requires as many man-hours as that spent in coding?

a. Offshore, design and coding b. Offshore coding

c. Testing d. Offshore, testing and coding

FLT – 07

110. Roughly, what percentage of the total work is carried out onsite?

a. 40% b. 20 %

c. 30 % d. 10 %

111. The total effort in man-hours spent onsite is nearest to which of the following?

a. The sum of the estimated and actual effort for offshore design

b. The estimated man-hours of offshore coding

c. The actual man-hours of offshore testing

d. Half of the man-hours of estimated offshore coding

112. If the total working hours were 100, which of the following tasks will account for approximately 50 hr?

a. Coding b. Design

c. Offshore testing d. Offshore testing plus design

113. If 50% of the offshore work were to be carried out onsite, with the distribution of effort between the

tasks remaining the same, the proportion of testing carried out offshore would be

a. 40% b. 30% c. 50% d. 70%

114. If 50% of the offshore work were to be carried out onsite, with the distribution of effort between the

tasks remaining the same, which of the following is true of all work carried out onsite?

a. The amount of coding done is greater than that of testing

b. The amount of coding done onsite is less than that of design done onsite

c. The amount of design carried out onsite is greater than that of testing

d. The amount of testing carried out offshore is greater than that of total design

Directions for questions 115 to 117: Answer the questions based on the pipeline diagram below.

The following sketch shows the pipelines carrying material from one location to another. Each location has

a demand for material. The demand at Vaishali is 400, at Jyotishmati is 400, at Panchal is 700, and at

Vidisha is 200. Each arrow indicates the direction of material flow through the pipeline. The flow from

Vaishali to Jyotishmati is 300. The quantity of material flow is such that the demands at all these locations

are exactly met. The capacity of each pipeline is 1,000.

Avanti

Vaishali Jyotishmati Panchal

Vid isha

115. The quantity moved from Avanti to Vidisha is

a. 200 b. 800 c. 700 d. 1,000

116. The free capacity available at the Avanti-Vaishali pipeline is

a. 0 b. 100 c. 200 d. 300

FLT – 07 Page 29

117. What is the free capacity available in the Avanti-Vidisha pipeline?

a. 300 b. 200 c. 100 d. 0

Directions for questions 118 to 120: Answer these questions based on the data given below:

There are six companies, 1 through 6. All of these companies use six operations, A through F. The

following graph shows the distribution of efforts put in by each company in these six operations.

17.7

A

18.5

A16.4

A

18.5

A15.1

A

15.6

A

17.6

B

16.7

B16.4

B10.3

B

16.1

B

17.6

B

9.8

C

9.3

C10.9

C 8.2

C

13

C

13.8

C

15.7

D 7.4

D

16.3

D

11.2

D

7.7

D

11.8

D

23.5

E

25.9

E

21.8

E

28.6

E

28.6

E

23.6

E

15.7

F 22.2

F

18.2

F 23.4

F

19.7

F

17.6

F

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 2 3 4 5 6Company

% D

istr

ibu

tio

n o

f E

ffo

rts

118. Suppose effort allocation is inter-changed between operations B and C, then C and D, and then D

and E. If companies are then ranked in ascending order of effort in E, what will be the rank of

company 3?

a. 2 b. 3 c. 4 d. 5

119. A new technology is introduced in company 4 such that the total effort for operations B through F

get evenly distributed among these. What is the change in the percentage of effort in operation E?

a. Reduction of 12.3 b. Increase of 12.3 c. Reduction of 5.6 d. Increase of 5.6

120. Suppose the companies find that they can remove operations B, C and D and redistribute the effort

released equally among the remaining operations. Then which operation will show the maximum

across all companies and all operations?

a. Operation E in company 1 b. Operation E in company 4

c. Operation F in company 5 d. Operation E in company 5

FLT – 07

Directions for questions 121 to 127: Each question is followed by two statements, I and II.

Mark

a. if the question can be answered by one of the statements alone and not by the other.




d. if the question cannot be answered even by using both statements together.

121. What are the values of m and n?

I. n is an even integer, m is an add integer, and m is greater than n.

II. Product of m and n is 30.

122. Is Country X’s GDP higher than country Y’s GDP?

I. GDPs of the countries X and Y have grown over the past 5 years at compounded annual rate of

5% and 6% respectively.

II. Five years ago, GDP of country X was higher than that of country Y.

123. What is the value of X?

I. X and Y are unequal even integers, less than 10, and X

Y is an odd integer.

II. X and Y are even integers, each less than 10, and product of X and Y is 12.

124. On a given day a boat ferried 1,500 passengers across the river in 12 hr. How many round

trips did it make?

I. The boat can carry 200 passengers at any time.

II. It takes 40 min each way and 20 min of waiting time at each terminal.

125. What will be the time for downloading software?

I. Transfer rate is 6 kilobytes per second.

II. The size of the software is 4.5 megabytes.

126. A square is inscribed in a circle. What is the difference between the area of the circle and that of

the square?

I. The diameter of the circle is 225 cm.

II. The side of the square is 25 cm.

127. Two friends, Ram and Gopal, bought apples from a wholesale dealer. How many apples did they

buy?

I. Ram bought one-half the number of apples that Gopal bought.

II. The wholesale dealer had a stock of 500 apples.

FLT – 07 Page 31

Directions for questions 128 to 130: Answer the questions based on the pie charts given below.

Chart 1 shows the distribution of 12 million tonnes of crude oil transported through different modes over a

specific period of time. Chart 2 shows the distribution of the cost of transporting this crude oil. The total

cost was Rs. 30 million.

Chart 1: Volume transported Chart 2: Cost of transportation

128. The cost in rupees per tonne of oil moved by rail and road happens to be roughly

a. Rs. 3 b. Rs. 1.5 c. Rs. 4.5 d. Rs. 8

129. From the charts given, it appears that the cheapest mode of transport is

a. road b. rail c. pipeline d. ship

130. If the costs per tonne of transport by ship, air and road are represented by P, Q and R respectively,

which of the following is true?

a. R > Q > P b. P > R > Q c. P > Q > R d. R > P > Q

Diretions for questions 131 to 134: Answer the questions independently.

131. At a village mela, the following six nautankis (plays) are scheduled as shown in the table below.

.oN iknatuaN noitaruD semiTwohS

1 irtivaSitaS rh1 .m.p2dna.m.a9

2 maluhGakuroJ rh1 .m.a03:11dna.m.a03.01

3 dnaKradnuS nim03 .m.a11dnama01

4 uynamihbAreeV rh1 .m.a11dna.m.a01

5 arehSruaamhseR rh1 .m.p2dnanoon21,.m.a03.9

6 inaRikisnahJ nim03 mp03:1dna.m.a11

You wish to see all the six nautankis. Further, you wish to ensure that you get a lunch break from

12.30 p.m. to 1.30 p.m. Which of the following ways can you do this?

Pipeline

49%

Road

22% Ship

9%

Airfreight

11%

Rail

9%

Pipeline

65%

Rail

12%

Road

6%

Airfreight

7% Ship

10%

FLT – 07

a. Sati Savitri is viewed first; Sundar Kand is viewed third, and Jhansi ki Rani is viewed last

b. Sati Savitri is viewed last; Veer Abhimanyu is viewed third, and Reshma aur Shera is viewed first

c. Sati Savitri is viewed first; Sundar Kand is viewed third, and Joru ka Ghulam is viewed fourth

d. Veer Abhimanyu is viewed third; Reshma aur Shera is viewed fourth, and Jahansi ki Rani is

viewed fifth

132. Mrs Ranga has three children and has difficulty remembering their ages and months of their birth.

The clue below may help her remember.

. The boy, who was born in June, is 7 years old.

. One of the children is 4 years old but it was not Anshuman.

. Vaibhav is older than Suprita.

. One of the children was born in September, but it was not Vaibhav.

. Suprita’s birthday is in April.

. The youngest child is only 2-year-old.

Based on the above clues, which one of the following statements is true?

a. Vaibhav is the oldest, followed by Anshuman who was born in September, and the youngest is

Suprita who was born in April

b. Anshuman is the oldest being born in June, followed by Suprita who is 4-year-old, and the

youngest is Vaibhav who is 2-year-old

c. Vaibhav is the oldest being 7-year-old, followed by Suprita who was born in April, and the youngest

is Anshuman who was born in September

d. Suprita is the oldest who was born in April, followed by Vaibhav who was born in June, and

Anshuman who was born in September

133. The Bannerjees, the Sharmas, and the Pattabhiramans each have a tradition of eating Sunday

lunch as a family. Each family serves a special meal at a certain time of day. Each family has a

particular set of chinaware used for this meal. Use the clues below to answer the following

question.

. The Sharma family eats at noon.

. The family that serves fried brinjal uses blue chinaware.

. The Bannerjee family eats at 2 o’clock.

. The family that serves sambar does not use red chinaware.

. The family that eats at 1 o’clock serves fried brinjal.

. The Pattabhiraman family does not use white chinaware.

. The family that eats last likes makkai-ki-roti.

Which one of the following statements is true?

a. The Bannerjees eat makkai-ki-roti at 2 o’clock, the Sharmas eat fried brinjal at 12 o’clock and the

Pattabhiramans eat sambar from red chinaware

b. The Sharmas eat sambar served in white chinaware, the Pattabhiramans eat fried brinjal at

1 o’clock, and the Bannerjees eat makkai-ki-roti served in blue chinaware

FLT – 07 Page 33

c. The Sharmas eat sambar at noon, the Pattabhiramans eat fried brinjal served in blue chinaware,

and the Bannerjees eat makkai-ki-roti served in red chinaware

d. The Bannerjees eat makkai-ki-roti served in white chinaware, the Sharmas eat fried brinjal at

12 o’clock and the Pattabhiramans eat sambar from red chinaware

134. While Balbir had his back turned, a dog ran into his butcher shop, snatched a piece of meat off the

counter and ran out. Balbir was mad when he realised what had happened. He asked three other

shopkeepers, who had seen the dog, to describe it. The shopkeepers really did not want to help

Balbir. So each of them made a statement which contained one truth and one lie.

. Shopkeeper number 1 said: “The dog had black hair and a long tail.”

. Shopkeeper number 2 said: “The dog had a short tail and wore a collar.”

. Shopkeeper number 3 said: “The dog had white hair and no collar.”

Based on the above statements, which of the following could be a correct description?

a. The dog had white hair, short tail and no collar

b. The dog had white hair, long tail and a collar

c. The dog had black hair, long tail and a collar

d. The dog had black hair, long tail and no collar

Directions for questions 135 and 136: Answer the following questions based on the information given

below.

Elle is three times older than Yogesh. Zaheer is half the age of Wahida. Yogesh is older than Zaheer.

135. Which of the following can be inferred?

a. Yogesh is older than Wahida

b. Elle is older than Wahida

c. Elle may be younger than Wahida

d. None of these

136. Which of the following information will be sufficient to estimate Elle’s age?

a. Zaheer is 10-year-old

b. Both Yogesh and Wahida are older than Zaheer by the same number of years

c. Both (a) and (b)

d. None of these

Directions for questions 137 to 139: Answer the questions based on the passage below.

A group of three or four has to be selected from seven persons. Among the seven are two women: Fiza and

Kavita, and five men: Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group If

Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to

be in the group only if David is also there. David, if selected, would not like Peter in the group. Ram would

like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in

the group.

FLT – 07

137. Which of the following is a feasible group of three?

a. David, Ram and Rahim

b. Peter, Shyam and Rahim

c. Kavita, David and Shyam

d. Fiza, David and Ram

138. Which of the following is a feasible group in four?

a. Ram, Peter, Fiza and Rahim

b. Shyam, Rahim, Kavita and David

c. Shyam, Rahim, Fiza and David

d. Fiza, David, Ram and Peter

139. Which of the following statements is true?

a. Kavita and Ram can be part of a group of four

b. A group of four can have two women

c. A group of four can have all four men

d. None of these

Directions for questions 140 to 146: Answer the questions independently.

140. On her walk through the park, Hamsa collected 50 coloured leaves, all either maple or oak. She

sorted them by category when she got home, and found the following:

The number of red oak leaves with spots is even and positive.

The number of red oak leaves without any spot equals the number of red maple leaves without

spots.

All non-red oak leaves have spots, and there are five times as many of them as there are red spotted

oak leaves.

There are no spotted maple leaves that are not red.

There are exactly 6 red spotted maple leaves.

There are exactly 22 maple leaves that are neither spotted nor red.

How many oak leaves did she collect?

a. 22 b. 17 c. 25 d. 18

141. Eight people carrying food baskets are going for a picnic on motorcycles. Their names are A, B, C,

D, E, F, G, and H. They have 4 motorcycles M1, M2, M3 and M4 among them. They also have 4

food baskets O, P, Q and R of different sizes and shapes and each can be carried only on motorcycles

M1, M2, M3 and M4 respectively. No more than 2 persons can travel on a motorcycle and no more

than one basket can be carried on a motorcycle. There are 2 husband-wife pairs in this group of

8 people and each pair will ride on a motorcycle together. C cannot travel with A or B. E cannot travel

with B or F. G cannot travel with F, or H, or D. The husband-wife pairs must carry baskets O and P.

Q is with A and P is with D. F travels on M1 and E travels on M2 motorcycles. G is with Q, and B

cannot go with R. Who is travelling with H?

a. A b. B c. C d. D

FLT – 07 Page 35

142. In a family gathering there are 2 males who are grandfathers and 4 males who are fathers. In the

same gathering there are 2 females who are grandmothers and 4 females who are mothers. There is

at least one grandson or a granddaughter present in this gathering. There are 2 husband-wife pairs

in this group. These can either be a grandfather and a grandmother, or a father and a mother. The

single grandfather (whose wife is not present) has 2 grandsons and a son present. The single

grandmother (whose husband is not present) has 2 grand daughters and a daughter present. A

grandfather or a grandmother present with their spouses does not have any grandson or granddaughter

present.

What is the minimum number of people present in this gathering?

a. 10 b. 12 c. 14 d. 16

143. I have a total of Rs. 1,000. Item A costs Rs. 110, item B costs Rs. 90, item C costs Rs. 70, item D

costs Rs. 40 and item E costs Rs. 45. For every item D that I purchase, I must also buy two of item

B. For every item A, I must buy one of item C. For every item E, I must also buy two of item D and

one of item B. For every item purchased I earn 1,000 points and for every rupee not spent I earn a

penalty of 1,500 points. My objective is to maximise the points I earn.

What is the number of items that I must purchase to maximise my points?

a. 13 b. 14 c. 15 d. 16

144. Four friends Ashok, Bashir, Chirag and Deepak are out for shopping. Ashok has less money than

three times the amount that Bashir has. Chirag has more money than Bashir. Deepak has an

amount equal to the difference of amounts with Bashir and Chirag. Ashok has three times the

money with Deepak. They each have to buy at least one shirt, or one shawl, or one sweater, or one

jacket that are priced Rs. 200, Rs. 400, Rs. 600, and Rs. 1,000 a piece respectively. Chirag borrows

Rs. 300 from Ashok and buys a jacket. Bashir buys a sweater after borrowing Rs. 100 from Ashok

and is left with no money. Ashok buys three shirts. What is the costliest item that Deepak could buy

with his own money?

a. A shirt b. A shawl c. A sweater d. A jacket

145. In a ‘keep-fit’ gymnasium class there are 15 females enrolled in a weight-loss programme. They all

have been grouped in any one of the five weight-groups W1, W2, W3, W4, or W5. One instructor is

assigned to one weight-group only. Sonali, Shalini, Shubhra and Shahira belong to the same weight-

group. Sonali and Rupa are in one weight-group, Rupali and Renuka are also in one weight-group.

Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight-groups. Somya cannot be with

Ritu, and Tara cannot be with Radha. Komal cannot be with Radha, Somya, or Ritu. Shahira is in

W1 and Somya is in W4 with Ruchika. Sweta and Jyotika cannot be with Rupali, but are in a weight-

group with total membership of four. No weight-group can have more than five or less than one

member. Amita, Babita, Chandrika, Deepika and Elina are instructors of weight-groups with

membership sizes 5, 4, 3, 2 and 1 respectively. Who is the instructor of Radha?

a. Babita b. Elina c. Chandrika d. Deepika

FLT – 07

146. A king has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to

make a cabinet committee. He decides to choose these four such that each selected person

shares a liking with at least one of the other three selected. The selected persons must also hate at

least one of the likings of any of the other three persons selected.

M1 likes fishing and smoking, but hates gambling.

M2 likes smoking and drinking, but hates fishing.

M3 likes gambling, but hates smoking,

M4 likes mountaineering, but hates drinking,

M5 likes drinking, but hates smoking and mountaineering.

M6 likes fishing, but hates smoking and mountaineering.

M7 likes gambling and mountaineering, but hates fishing.

M8 likes smoking and gambling, but hates mountaineering.

Who are the four people selected by the king?

a. M1, M2, M5 and M6 b. M3, M4, M5 and M6

c. M4, M5, M6 and M8 d. M1, M2, M4 and M7


A and B are two sets (e.g. A = Mothers, B = Women). The elements that could belong to both the sets

(e.g. women who are mothers) is given by the set C = A . B. The elements which could belong to either A

or B, or both, is indicated by the set D = BA ∪ . A set that does not contain any elements is known as a

null set represented by ϕ (e.g. if none of the women in the set B is a mother, then C = A .B is a null set, or

C = ϕ ).

Let ‘V’ signify the set of all vertebrates, ‘M’ the set of all mammals, ‘D’ dogs, ‘F’ fish, ‘A’ alsatian and ‘P’,

a dog named Pluto.

147. Given that X = M .D is such that X = D. Which of the following is true?

a. All dogs are mammals b. Some dogs are mammals

c. X = ϕ d. All mammals are dogs

148. If Y = F . (D . V) is not a null set, it implies that

a. all fish are vertebrates b. all dogs are vertebrates

c. some fish are dogs d. None of these

149. If Z = (P . D) ∪ M, then

a. the elements of Z consist of Pluto, the dog, or any other mammal

b. Z implies any dog or mammal

c. Z implies Pluto or any dog that is a mammal

d. Z is a null set

150. If P . A = ϕ and P ∪ A = D, then which of the following is true?

a. Pluto and alsatians are dogs

b. Pluto is an alsatian

c. Pluto is not an alsatian

d. D is a null set

FLT – 07

101. Count only those lays for which any size of yellow

coloured fabric is produced.

They are lay number

1, 3, 4, 6, 7, 8, 9, 11, 12, 15, 21, 24, 25, 27

Hence, 14 is the answer.

102. Count those lays for which extra-extra large fabric is

produced of any colours, i.e. count the lay numbers

for which at least one of XXL from 3 colours is non-

zero.

They are lay number 7, 8, 9, 10, 11, 12, 13, 14, 15, 21,

22, 23, 24, 25, 26, 27 .


103. Again count lay number for which at least one of the

XXL from yellow and white are non-zero.

Lay number 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 23, 24,

25, 26, 27.


104. The varieties for which there is surplus gives the

answer. There are 4 such varieties.

105. Put a decimal after the first two digit in the passengers

column and it wil give the figure in millions.

In that case we have only 5 international airports of

type A having more than 40 million passengers.

They are in serial number 1, 2, 3, 5, 9.

Rest all ‘A’ type is below 40 million.

106. There are only six airports of USA among the top 10

busiest airports. They are in serial number 1, 2, 3, 5,

9, 10.

Hence, %6010010

6=×

107. We have to calculate the percentage of passengers

handled at Heathrow Airport.

Now total number of passengers in the 5 busiest

airport is approximately

(77 + 72 + 63 + 62 + 60) million

= 334 million

At Heathrow it is 62 million.

The approximate percentage is

60100

300× ~ 20%

108. All the international airports handle more than 30 million

passengers. Among these only 6 airports are not

located in USA. Hence, (b) is the answer.

109. Man-hours spent in coding is 420 + 100 = 520.

Now going by options, we see (a) is the only option.

110. Total work is approximately

(100 + 80) + (420 + 100) + (280 + 140) = 1120

On-site work = 80 + 100 + 140 = 320

Percentage of total work carried out on-site is

1001120

320× = 30% approxmately.

111. From figure the total effort in man-hours spent on-site

is 320.

It is nearest to actual man-hours of offshore testing

which is 280 (approximately.)

112. Total man-hours

= (100 + 80) + (420 + 100) + (280 + 140) = 1120.

Total working hours = 100

Total man working = 1120

11.2100

= or 11.

For 50 hr the total man-hours is 50 × 11 = 550 which

is near to coding (420 + 100)

Hence, (a) is the answer

113. Total offshore work = 100 + 420 + 280

= 800 man-hours.

50% of offshore work are carried out on-site.

Distribution of effort are in ratio 180 : 520 : 420

9 : 26 : 21

Effort distributed to testing will be

21400 147

56× = man-hours.

Offshore testing work is 1402

280=

∴ Proportion of testing carried out offshore is

100)147140140(

140×

++ = 30%

114.


Initially 80 100 140

Finally 1302

10080 =+ 310

2

420100 =+ 287

2

294140 =+

115. We see flow from Vaishali to Jyotishmati is 300 where

as demand is 400 so the deficient 100 would be met

by flow from Vidisha. Again the demand of 700 in

Panchal is again to be met by flow from Jyotishmati

which can get it from Vidisha.

Thus, the quantity moved from Avanti to Vidisha is

200 + 100 + 700 = 1000

116. Free capacity at Avanti-Vaishali pipeline is 300, since

capacity of each pipeline is 1000 and demand at

Vidisha is 400 and 300 flows to Jyotishmati.

Thus, free capacity = {1000 – (400 + 300)} = 300

117. Free capactiy in Avanti-Vidisha is zero. Explanation is

similar as in previous answer.

118. On interchanging the effort allocation between

operations B and C, then C and D, and then D and E

we find that B takes the E’s position.

Looking at the effort in B and then ranking in ascending

order we find that the company 3 ranks third.

FLT – 07 Page 13

119. Total effort for operation B through F is 81.5%.

Even distribution will give effort allocation in each

operation = %3.165

5.81=

∴ Change in E = 28.6 – 16.3 = 12.3%

120. Since we are given about company 1, 4, 5 in options

so we will look for changes in these companies only.

Allocation of effort in B, C, D in companies 1 = 43.1

Remaining operations gets %4.143

1.43= each.

Allocation of effort in B, C, D operations of company

4 = 29.7

Remaining operation is allocated extra

29.79.9%

3= each.

Allocation of effort in B, C, D operation of company

5 = 36.8

Remaining operation is allocated 36.8

12.3%3

= each.

We see that operation E in company 5 will then show

the maximum.

121. From II, m, n could be (2, 15) (5, 6), (3, 10) and (1, 30)

but from I, we get m, n as (2, 15).

122. From I nothing can be said since exact figures are not

given.

From II since X > Y (from B) we do not know how

much X is greater than Y, because if it is slightly greater

than it will be less than Y after 5 years whereas if the

difference is very high, then X will be greater than Y

even after 5 years.

123. From I, unequal even integers less than 10 are 2, 4, 6,

8.

X

Y is an odd integer is possible only if x = 6, y = 2

From II, even integers less than 10 are 2, 4, 6, 8.

XY = 12 ⇒ X = 6, Y = 2 or X = 2, Y = 6

Hence, question can be answered using either

statement alone but not from statement B.

124. I gives the capacity of boat and is of no help in finding

out the number of round trips.

From II round trips can be calculated since we know

the total time taken is 12 hr.

125. I gives the rate and II gives the size. It is like I gives the

speed and II the distance and we are to find out time.

So both statements are needed.

126.

O

We know that the diameter of circle will be the diagonal

of the square.

Thus, from any of the two statements, we can find

out the areas of the circle and square.

Hence, (b) is the answer.

127. I gives a general figure of Ram and Gopal.

II does not give any idea of how much apples Ram

and Gopal purchased.

Both statements together also cannot give any result.

128. Cost in rupees of oil moved by rail and road is 18% of

30 million = 5.4 million.

Volume of oil transported by rail and road

= 31% of 12 million tonnes = 3.72 million tonnes.

Cost in rupees per tonnes = 5.4

1.53.72

= approximately.

129. From the chart, we can make out the least among

road, rail, pipeline, ship by looking at the ratio of cost

to volume.

Road = 22

6

Rail = 12

9

Pipeline = 49

65

Ship = 9

10

Obviously road is the lowest and hence the cheapest.

130. Ship, air and road.

Like the previous answer again look at ratio of

22

6,

11

7,

9

10

So22

6

11

7

9

10>>

Hence, P Q R> >

131. Sati-Savitri starts at the earliest.

So we view it first.

(1) Sati-Savitri — 9.00 a.m. to 10.00 a.m.

(2) Veer Abhimanu — 10.00 a.m. to 11.00 a.m.

(3) Jhansi Ki Rani/Sundar Kand — 11.00 a.m. to

11.30 a.m.

(4) Joru Ka Ghulam — 11.30 a.m. to 12.30 p.m.

Now lunch break from 12.30 p.m. to 1.30 p.m.

At 1.30 p.m. he can takes the show of only Jhansi

Ki Rani so it cannot be viewed at 3rd.

FLT – 07

(5) Jhansi Ki Rani — 1.30 p.m. to 2.00 p.m.

(6) Reshma aur Shera 2.00 p.m. to 3.00 p.m.

Hence, option (c) is best.

132. Three children Vaibhav, Suprita and Anshuman.

Vaibhav > Suprita

↓ (Born in April)

One of children is born in September, but it is not

Vaibhav, so it has to be Anshuman.

So Vaibhav is born in June and is 7-year-old. Vaibhav

is 7-year-old and Anshuman is not 4-year-old.

So Suprita is 4-year-old.

Youngest child is 2-year-old and it has to be Anshuman.

Vaibhav > Suprita > Anshuman

(June, 7 years) (April, 4 years) (Sept., 2-year-old)

Hence, (c) is the answer.

133. We can find out the time for lunch of respective families

from the table below:

emiT/ylimaF 00:21 00:1 00:2

amrahS ü

eejrenaB ü

namarihbattaP ü

Fried brinjal → Chinaware

Sambar → White Chinaware

Makkai-ki-roti → Red Chinaware

The family that eats at 1 o’clock serves fried brinjal,

hence Pattabhiraman serves fried brinjal.

The family that eats last like makkai-ki-roti so

Banaerjees like makkai-ki-roti. Sharmas are left with

sambar.

Sharma - 12:00 - Sambar - White

Pattabhiraman - 1:00 - Fried brinjal - Blue

Bannerjees - 2:00 - Makkai-ki-roti - Red

Hence, (c) is the best option.

134. We start making one true and other false.

Case I

T F

Shopkeeper 1: Black hair Long tail

T F

Shopkeeper 2: Short tail Wore a collar

T F

Shopkeeper 3: White hair No collar

Case II

T F

Shop keeper 1: Black hair Long tail

T F

Shop keeper 2: Short tail Wore a collar

T F

Shop keeper 3: White hair No collar

Both the cases are correct, and hence we see only

option (b) is correct.

135. Elle is 3 times older than Yogesh and Zaheer is half

the age of Wahida.

If Wahida is 2x-year-old, then Zaheer is x.

Now Yogesh > Zaheer

⇒ Yogesh > x

Elle is 3 times older than Yogesh.

Which means Elle is older than Wahida as 3x > 2x.

Alternative method:

E = 3y ...(i)

z = w

2, or 2z = w ...(ii)

y > z , implies 2y > 2z implies 2y > w from (ii)

Now, if 2y > w

3y > w, i.e. E > w from (i)

Hence, Elle is older than Wahida.

136. From (a) Zaheer is 10-year-old means Wahida is

20-year-old. From (b) Yogesh and Wahida are older

than Zaheer by same number of years.

This means Yogesh is 20-year-old. Now Elle is 3 times

older than Yogesh.

Elle is 20 × 3 = 60-year-old.

Hence, we see that both (a) and (b) statements are

needed so the answer is (c).

137. Find out from the options.

(a) David, Rama and Rahim

Ram would like to be in the group only if Peter is there,

so it is not feasible.

(b) Peter, Shyam and Rahim

Shyam and Rahim want to be selected together and

none of them have problem or any conditions, hence

feasible.

(c) Since Shyam is there, Rahim has to be but he is

not also Fiza is not there which David insists so not

feasible.

(d) Since Peter is not there and so Ram would not

prefer that group, hence not feasible.

138. Looking at options, we see (c) is best as Shyam and

Rahim is selected and Fiza is there when David is

selected.

In (a) we see Shyam is not there with Rahim.

In (b) Fiza is not there with David.

In (d) Peter and David cannot go together as David

would not like Peter in the group.

139. In Ist option — Kavita is in the group means David is

there and David would not like Peter in the group,

whereas Ram would like to be in the group if Peter is

there so the statement cannot be true.

2nd option — If David is there, then only the group will

have both women Kavita and Fiza, but in that case

we see none of the rest could be the fourth person

as Shyam and Rahim has to be together and Ram

would be if Peter is there and David would not like

Peter in the group, hence statement is false.

3rd option — It is not possible as Ram cannot go with

Shyam and David with Peter.

So none of the above statements are true.

FLT – 07 Page 15

140. Let S = spotted, NS = Non-spotted

kaO elpaM

deR der-noN deR der-noN

S SN S SN S SN S SN

n2 x n01 0 6 x 0 22

There are 50 coloured leaves and is given as red and

non-red.

We make the following table. Let 2n be number of red

oak leaves where n is any natural number.

Now we have 2n + x + 10n + 6 + x + 22 = 50

⇒ 12n + 2x = 22

It is possible for only n = 1, x = 5

We cannot take n > 1

Hence, number of oak leaves are

2 × 1 + 5 + 10 × 1 = 17

141. O, P, Q and R carried on motorcycles M1, M

2, M

3 and M

4

respectively. So

OP Q R

M1

M2

M3

M4

F E A + G C

B D H

Since B cannot be with R so it will go with O that is

only left.

Hence, C and H will go together in M4 with R.

142.G F 1

F1

G S 1 G S 2

G m 1

M 1

G D 1 G D 2

G F 2+G M 2

F2 M 2

Thus, we have 2 grandfathers GF1, GF

2

4 fathers GF1, GF

2, F

1 and F

2

2 grandmothers GM1, GM

2

4 mothers GM1, GM

2, M

1 and M

2

Thus, minimum number will be 12.

143. We have packages as follows:

3 item (D + 2B) = Rs. 40 + Rs.180 = Rs. 220 ... (i)

2 item (A + C) = Rs.180 ... (ii)

4 item (E + 2D + B) = 45 + 50 + 90 = 215 ... (iii)

The combinations of purchase possible are

Case 1: Rs. 220 × 4 = Rs. 880

Points: 12 × 1000 – 120 × 1500 = – 1,68,000

Case 2: Rs. 180 × 5 = Rs. 900

Points: 10 × 1000 – 100 × 1500 = – 1,40,000

Case 3: Rs. 215 × 4 = Rs. 860

Points:16 × 1000 – 140 × 1500 = – 1,94,000

Case 4: 2(220 + 180) + 180 = Rs. 980

Points: 12 × 1000 – 20 × 1500 = – 18,000

Case 5: 2(220 + 215) = Rs. 890

Points : 14 × 1000 – 110 × 1500 = – 1,51,000

Case 6: 2(215 + 180) + 180 = Rs. 970

Points :14 × 1000 – 30 × 1500 = – 31,000

By seeing the above figure, we see that we maximize

the point in last case when purchase is 14 item for

Rs. 970.

144. Bashir < Chirag.

Now Chirag borrows Rs. 300 and Bashir Rs. 100

from Ashok. Ashok buys 3 shirt so he must have at

least Rs. 1,000.

Bashir is left with no money after buying a sweater

and he had to borrow Rs.100 from Ashok means he

had Rs. 500 with him.

Ashok must have less than Rs. 1,500.

Ashok has three times the money with Deepak.

So Deepak cannot have Rs. 300 because Ashok must

have Rs.1,000, again Deepak cannot have Rs. 500

because Ashok should have less than Rs.1,500.

So Deepak has Rs. 400 for which he can purchase

the shawl which is costliest.

145. W1 W4

Rupa Radha Renuka Ruchika Ritu

Sonali Rupali Somya Tara

Shalini Komal Sweta

Shubhra Jyotika

Shahira Deepika

Amita Elina Chandrika Babita

Hence, Elina is instructor of Radha.

FLT – 07

146.

gnihsiF gnikomS gniknirD-maG

gnilb

-tnuoM

-reenia

gni

sekiLM

1

M6

M1

M2

M8

M2

M5

M3

M7

M8

M4

M7

sekilsiDM

2

M7

M3

M5

M6

M4

M1

M5

M6

M8

Now go by options.

(a) M does not hate at least one of the liking of any of

the other 3 persons selected.

(b) None of person shares the liking of at least one of

the other selected.

(c) None of the person shares a liking with at least

one of the other three selected.

(d) M1 shares liking with M

2 and vice versa.

M4 shares liking with M

7 and vice versa.

M1, M

2 dislikes M

7 liking.

M4, M

7 dislikes M

2 liking.

Hence the answer is (d).

147. X = M.D = M ∩ D

X = D

M ∩ D = D

⇒ D ⊂ M

Thus all dogs are mammals.

M

D

148. )VD(FY ∩∩= is not a null set means some F’s are

D’s and sum D’s are V’s .

That means some fish are dogs.

149. M)D.P(Z ∪=

Z = (P ∩ D) ∪ M

P ∩ D means pluto the dog.

P ∩ D ∪ M means pluto the dog or any other mammal.

150. P.A = φ P ∪ A = D

P ∩ A = φ means no alsations are pluto or pluto is not

an alsation where dogs are composed of alsation or

pluto or both.

FLT – 06 Page 9

108.

12 1982

12 165 2

12 13 9

1 – 1

–

–

The answer is 1192.

109. Work with options. If the cylinder has a capacity of

1,200 L, then the conical vessel shall have a capacity

of 700 L. Once 200 L have been taken out from the

same, the remaining volume in each of them shall be

1000 and 500.

Alternative method:

Let the volume of conical tank be x.

Then the volume of cylindrical tank = x + 500

x + 300 = 2(x – 200) ⇒ x = 700

Volume of cylindrical tank = 700 + 500 = 1200.

110. Work with options. Length of wire must be a multiple

of 6 and 8. Number of poles should be one more than

the multiple.

111. If the number of students enrolled for a certain class

do not fit into that age interval, they are in excess and

hence, unrepresentative, thus resulting in bloated

ratios. (a) is wrong because the definition of gross

enrollment ratio itself is flawed. Attendance is not the

focus of our argument. We are also not concerned

with demographic trends, but only with given data.

112. The argument states that ‘clubs that spend more should

finish at a higher ranking’. This is reflected in ‘highly

paid white players returned a low ranking’. (a) focuses

on clubs that recruited black players, a consquence

Szymanski is not immediately concerned with. (c) also

throws no light on the relation ‘clubs that spend more

should finish higher’. Nor does (d).

113. Only (d) connects the recommendation directly to the

cause ‘rising tensions’ in prisons and not to any

marginal political factors. (a), (b) and (c) may have

contributed, but peripherally, to the minister’s decision.

114. (a) and (d) cover the government’s honourable

intentions, which look best on paper. (b) discusses

one feasiblilty factor. (c) is the best choice as it shows

how the project has reached the implementation stage

from the pilot stage.

115. ‘Manoeuvrability’ is linked to ‘flight direction changes’

in (d). (c) just vaguely mentions ‘faster’. (a) makes no

inference, as such. It may or may not be true. There is

insufficient evidence to infer (d), it sounds rather far-

fetched.

116. (b) does not attack the argument, it helps the

Association’s cause. (c) is pointless, if there isn’t

adequate consumption. (d) has little to do with the

core issue in the argument. But (a) if true, would render

the cumulative efforts of the Association fruitless.

117. (a) would only result in more cars per family. (b) and

(c) defeat Athens’ purpose as citizens devise

ingenious methods to maintain status quo both in terms

of number of cars and congestion.

118. The Central Bank can only express ‘reservations’ on

‘monetisation’ to the government. It cannot be the ‘boss’,

it only advises. (c) does not support the conclusion in

any way. (a) and (d) are specific observations, but

they do not contribute to our answer.

119. (d) is a summary for the general words ‘varied use’,

‘common basis’ pertaining to the ‘symbol’ in the

geographical and historical context. (c) does not

present the complete picture. (a) refuses to divulge

the significance of the umbrella. (b) is wrong as the

ruler is regarded as the instrument of firmament of the

supreme law.

120. This answer goes without guessing. There are two

parties in the game, and each has its own strategy

and a guess on the opponent’s move. (a) involves

more of cooperation strategies than game plans. (b) is

competition involving more than two candidates. (d) is

about cartels.

121. Since yellow is between green and red, it should be

house number 2 or 3. Also green is adjacent to blue

house, it should have blue and yellow house on either

side. Hence, the following table can be constructed.

House number 1 2 3 4

Colour Blue Green Yellow Red

Occupant X Z

Since X does not live adjacent to Z, it has to live in blue

house.

122. The ratio of points for carrying books of various

subjects is:

Management : Mathematics : Physics : Fiction

= 4 : 3 : 2 : 1

Since the points are to be maximized, the number of

books that Ramesh should carry in descending order

is management, mathematics, physics and fiction.

The ratio which Ramesh has to maintain is:

Management : Fiction < 1 : 2,

Mathematics : Physics < 1 : 2.

This means that a combination of management and

fiction books in the ratio of 1 : 2 will give 6 points while

a combination of mathematics and physics books in

the ratio of 1 : 2 will give 7 points, hence, Ramesh

should carry the following combination of books to

maximize the points; management 1, mathematics 2,

physics 5 and fiction 2, a total of 22 points.

FLT – 06

123. The following table can be created using the data

given.

snosreP P M U T X

ruoloC

eciohc

eulB

dna

deR

wolleY

deR

dna

eulB

kcalB

nisyatSletoH

tonseoD

niyatsecalaP ecalaP ecalaP

Since X stays in a hotel and P or U or T cannot stay in

a palace, M stays in palace.

124. The attendants of X, Y and Z are to be Mohan, Jack

and Rita. The animals under Mohan’s care is given in

the data. Since Jack does not attend to deer, lion and

bison, the following table can be created using the

data given.

stnadnettA nahoM kcaJ atiR

slaminAdnanoiL

rehtnaP

dnaraeB

rehtnaP

erusolcnE X Y Z

emaN nahoM kcaJ atiR inilahS namuS

slaminA

noiL

dna

rehtnap

raeB

dna

rehtnap

reeD

dna

nosib

noiL

dna

raeb

reeD

dna

nosib

egaC X Y Z Q P

The data for Mohan and Jack can be filled directly.

Similarly, X, Y, Z can be filled directly from data given.

The key after filling in these animals is that Z and P

have the same pair of animals, the only option is deer

and bison.

125. By trial and error, we can make different

combinations and find the cost.

Like 20 kg × 2 + 10 kg × 4, the cost would be

Rs.180. The minimum cost comes in the case of

10 kg × 8, i.e. Rs.160.

Direction for students: The table for questions 126

to 130 in CAT 2001 Bulletin has some misprints and it

should be read like the following.

Information Technology Industry in India

(Figures are in million US dollars)

59-4991 69-5991 79-6991 89-7991 99-8991

erawtfoS

citsemoD 053 094 076 059 0521

stropxE 584 437 3801 0571 0562

erawdraH

citsemoD 095 7301 0501 5021 6201

stropxE 771 53 682 102 4

slarehpireP

citsemoD 841 691 181 922 923

stropxE 6 6 41 91 81

gniniarT 701 341 581 362 203

ecnanetniaM 241 271 281 122 632

gnikrowteN

srehtodna63 37 651 391 732

latoT 1402 6882 7083 1305 2506

126. Total exports

= Software export + Hardware export + Peripherals

export

Hence, total export as a percentage of IT business for

1994-95

%7.321002041

668=×=

For 1995-96 %8.261002886

775=×=

For 1996-97 %361003807

1383=×=

For 1997-98 %391005031

1970=×=

For 1998-99 %441006052

2672=×=

127. Percentage growth for 1995-96 = 41%,

1996-97 = 32%, 1997-98 = 32%, 1998-99 = 20%.

128. (a) and (b) can be easily eliminated from the given

table.

129. Total IT business in hardware (Export + Import) shows

a continuous increase from 1994-95 to 1997-98 and

then declines in 1998-99.

FLT – 06 Page 11

130. In this question there are two activities — hardware

and peripherals, hence for year X to dominate year Y,

at least one activity in year X has to be greater than

that in year Y and the other activity in year X cannot

be in year Y. In (a), (b) and (c) while hardware

dominates in one year, the peripherals dominate in the

other.

131. Statement I implies X > Y, or X > Z, or X > Y and Z

Statement II implies Y > X, or Y > Z, or Y > X and Z.

Combining both statements, we can get Y > X > Z or

X > Y > Z. Hence, Z is the smallest.

132. The first statement implies that X must lie between

0 and – 3. Hence, it gives the answer. But from the

second statement, we have either X > 3 or X < 0. This

does not gives us an information about the modulus

of X.

133. The Venn diagram arrived at from both I and II clearly

indicates that 500 people are watching programme P.

P Q

500 100 900

134. For a given inradius and circumradius, there is only

one possible value of (PR + RQ).

Hence, both the statements are required to answer

the question.

135. Statement I implies that profit is 2.95%, but we want

the profit per rupee spent on buying the shares. The

cost of buying the shares for Harshad is CP + 0.01 CP

= 1.01 CP. The cost of selling is

SP – 0.01 SP = 0.99 SP

The difference of the two is profit, i.e.

0.99 SP – 1.01 CP = 0.99 × 1.05 CP – 1.01 CP

= 0.0295 CP. Hence, profit = 2.95%.

136. We cannot work the questions individually through

I or II. But combining the two statements, we get

(2 ⊕ 0) = (0 ⊕ 2) = 0 and 0 ⊕ (– 5 ⊕ – 6) = 0.

137. Both the statements combined also do not tell us if

they are intersecting or not. The two lines can be

parallel also depending on the values of a, b, d, e.

138. You can see from the following diagram that both

statements individually

BA C D E

imply towards C being the mid-point of BD. The ratio

of AC/CE will be one by using any statement.

139. Here, by combining the two statements, we get the

duration of the flight.

For the arrival time we should have information

regarding the time zone difference of Mumbai and

No-man’s-land.

140. Statement I implies X – Y = 6. .

Statement II implies XY is divisible by 6.

You can see that many values of X and Y can satisfy

statement I and II.

141. If the total number of factories is 100, then the total

number of employees

= 60 × 100 = 6000 of which 64.6% = 3876 work in

wholly private factories. Since the number of wholly

private factories = 90.3, the answer = 3.90

3876 = 43.

Short cut: 45603

2

903.0

6064.0 =×

<×

142. Value added per employee = Value added

Employment

143. Compound productivity = Gross output

Fixed capital.

Hence, compound productivity for various sectors is:

Public sector = 0.6, Central Government = 0.725,

States/Local = 0.47, Central/States/Local = 1.07, Joint

sector = 1.23 and wholly private = 1.36. Hence, the

order should be: Wholly private, Joint, Central/State/

Local, Central Government, Public sector and State/

Local government.

144. Calculate the ratios: Value added/employment and

value added/fixed capital for the sectors mentioned in

the choices. The respective values are:

Wholly private 0.9 and 1.25; Joint sector 1.59 and

1.19; Central/State/Local 1.8, 1.28; others 0.92 and

0.75.

145. The number of factories in joint sector is 1.8% = 2700,

thus the number of factories in Central Government

= 1% of (2700 x 100/1.8) = 1500. Value added by

Central Government = 14.1% of 1,40,000 crore

= 19,740.

Hence, answer = 19740

1500 = Rs. 13.1 crore.

146. Find the difference between FEI in 1998 relative to its

FEI in 1997. Hence, for India it is 0.72 – 1.71 = –0.99.

For China it is 4.8 – 5.96 = – 1.16.

For Malaysia it is 9.92 – 10.67 = –0.75 and for Thailand

it is 5.82 – 5.09 = 0.73.

Change in FEI in 1998 relative to its FEI in 1997.

For India, percentage = 0.99

1.71

−× 100 = –57.89

FLT – 06

For Malaysia, percentage = 0.75

10010.67

−× = –7.02

For Thailand, change is 14.34%.

For China and Korea, changes are – 19.46% and

15.74% respectively.

Hence, we can see that the country with the largest

change in FEI is India.

147. Since the absolute values are not given, it cannot be

calculated.

148. Assume of GDP of India for 1997 to be x.

For 1998, India's FEI = 0.72 102x

0.7344x100

×=

And foreign equity inflows for 1997 = 1.71x

For China, assume GDP as y. Then FEI in 1998

=107y

100× 4.8 = 5.136y. And FEI in 1997 = 5.96y.

For South Korea, let GDP be z.

FEI in 1998 = 95z

100× 2.5 = 2.375z and FEI = 2.16z.

We can see that India and China were lower in 1998

than in 1997, and South Korea is higher in 1998 than

in 1997.

149. Let x be the foreign equity inflow of India. Hence,

China’s foreign equity inflow is 10x.

Now in 1998, FEI in India was 0.72, therefore

x0.72 =

GDP of India

Similarly, FEI in China in 1998 was 4.8, therefore 4.8

=10x

GDP of China

Hence, (GDP of China/GDP of India)

= (10 × 0.72)/4.8 = 1.5.

Thus, China’s GDP is 50% higher than that of India.

150. As from the table, the deficit intensity from 1993-94 to

1997-98 are 5.1, 6.3, 7.6, 8 and 5.

Therefore, highest growth rate is 7.6 – 6.3 = 1.3 which

is in 1994-95.

151. The highest growth rate = %5.231003.6

3.6–6.7=×

152. From the tables given,

Import of raw material = 10.1 × Sales (S) import of

capital goods = 17.6 × Gross fixed assets (GFA)

Given imports = Raw materials + Capital goods

So import = 10.1 S + 17.6 GFA

So imports = 14.2 S

Hence, 14.2 S = 10.1 S + 17.6 GFA

Hence,S 17.6

= = 4.3GFA 4.1

153. Clear from the table.

154. Clear from the given graph.

155. First find out the growth in 1990 of the all four sectors.

So manufacturing 9% of 20 = 1.8. Hence, 20 + 1.8

= 21.8. Similarly, for mining and quarrying it is 15.6.

For electrical, it is 10.85 and for chemical it is 16.1, now

in 1991 there is 1% negative growth in manufacturing.

So 1% of 21.8 becomes 0.218. Thus, 21.8 – 0.218

= 21.582. Similarly, for mining and quarrying it is 15.44.

For electrical it is 11.88 and for chemical it is 16.21.

Now we add the figures for 1991 of all the sectors

which comes to 21.582 + 15.75 + 11.88 + 16.21

= 65.42. Now 65.42 – 64.35 = 1.07 which comes to

approximately 1.5% growth rate.

156. Clear from the graph.

157. In 1990, there is 4% growth. Hence, 4% of 15 = 0.6.

So weightage in 1990 becomes 15.6.

Similarly, in 1991 it becomes 15.44, in 1992 it is 15.6,

in 1993 it is 14.97, in 1994 it is 16.16.

Hence, it can be seen that the lowest level of

production was in 1993.

158. Find out the weightage for all the sectors for 1994.

For manufacturing it is 25.54, for mining and quarrying

it is 16, for electrical it comes out to be 14.5 and for

chemical it is 19.5. The total comes to approximately

77. In 1989, it was 60. Hence, 77 – 60 = 17 which is

approximately 25% increase.

159. Since the index of total industrial production in 1994 is

50% more than in 1989, it becomes 150.

Now total weightage for manufacturing, mining and

quarrying, electrical and chemical in 1994 is

approximately 77. So 150 – 77 = 73.

In 1989, it was 100 – 60 = 40.

So 73 – 40 = 33, which is approximately 87.5%.

160. Cost in shift operation = 800 + 1200 = Rs. 2,000

Variable cost for 40 units = Rs. 3,600

Approximate average unit cost for July

=3600 2000

Rs.14040

+= .

161. The only change for change of production from 40 to

41 is the variable cost which is

Rs. (3730 – 3600) = Rs. 130.

162. The trend for MC is varying and is just the reverse

condition as that stated in C. Take some values and

check.

163. Total sales revenue = Rs. (150 × 40) = Rs. 6,000

Total production cost = Rs. (3600 + 2000) = Rs. 5600.

So profit = Rs. 400.

164. Profit is highest when there is no second shift.

165. (a) and (b) are definitely not true as the case is the

inverse of that mentioned in (c). Take some values

and check.

CAT PAPER – 2005 Page 19MBATest Prep

Sub–Section III-A : Number of questions = 10

Note: Questions 61 to 70 carry one mark each.

Directions for questions 61 to 64: Answer the questions on the basis of the information given below:

A management institute was established on January 1, 2000 with 3, 4, 5, and 6 faculty members in the

Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respec-

tively, to start with. No faculty member retired or joined the institute in the first three months of the year

2000. In the next four years, the institute recruited one faculty member in each of the four areas. All these

new faculty members, who joined the institute subsequently over the years, were 25 years old at the time

of their joining the institute. All of them joined the institute on April 1. During these four years, one of the

faculty members retired at the age of 60. The following diagram gives the area-wise average age (in terms

of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002, and 2003.

49.33

50.2

45

44

49

43

45

52.5

45

44

46 46

45

50.5

51.5

47.8

40

45

50

55

Marketing OB Finance OM

2000

2001

2002

2003

61. From which area did the faculty member retire?

(1) Finance (2) Marketing (3) OB (4) OM

62. Professors Naresh and Devesh, two faculty members in the Marketing area, who have been with the

Institute since its inception, share a birthday, which falls on 20th November. One was born in 1947

and the other one in 1950. On April 1 2005, what was the age of the third faculty member, who has

been in the same area since inception?

(1) 47 (2) 50 (3) 51 (4) 52

63. In which year did the new faculty member join the Finance area?

(1) 2000 (2) 2001 (3) 2002 (4) 2003

Section � III

CAT PAPER – 2005Page 20 MBATest Prep

64. What was the age of the new faculty member, who joined the OM area, as on April 1, 2003?

(1) 25 (2) 26 (3) 27 (4) 28


The table below reports annual statistics related to rice production in select states of India for a particular

year.

Total Area Production Population

(in million

hectares)

(in million

tons)

(in millions)

Himachal Pradesh 6 20 1.2 6

Kerala 4 60 4.8 32

Rajasthan 34 20 6.8 56

Bihar 10 60 12 83

Karnataka 19 50 19 53

Haryana 4 80 19.2 21

West Bengal 9 80 21.6 80

Gujarat 20 60 24 51

Punjab 5 80 24 24

Madhya Pradesh 31 40 24.8 60

Tamilnadu 13 70 27.3 62

Maharashtra 31 50 48 97

Uttar Pradesh 24 70 67.2 166

Andhra Pradesh 28 80 112 76

State % of Area Under

Rice Cultivation

65. Which two states account for the highest productivity of rice (tons produced per hectare of rice

cultivation)?

(1) Haryana and Punjab (2) Punjab and Andhra Pradesh

(3) Andhra Pradesh and Haryana (4) Uttar Pradesh and Haryana

66. How many states have a per capita production of rice (defined as total rice production divided by its

population) greater than Gujarat?

(1) 3 (2) 4 (3) 5 (4) 6

67. An intensive rice producing state is defined as one whose annual rice production per million of

population is at least 400,000 tons. How many states are intensive rice producing states?

(1) 5 (2) 6 (3) 7 (4) 8



The table below reports the gender, designation and age-group of the employees in an organization. It also

provides information on their commitment to projects coming up in the months of January (Jan), February

(Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportu-

nities (BO), Communication Skills (CS), and E-Governance (EG).

Sl.

No.

Name Gender Designation Age group Committed to

projects

during

Interested in

w orkshop

on

1 Anshul M Mgr Y Jan, Mar CS, EG

2 Bushkant M Dir I Feb, Mar BO, EG

3 Charu F Mgr I Jan, Feb BO, CS

4 Dinesh M Exe O Jan, Apr BO, CS, EG

5 Eashwaran N Dir O Feb, Apr BO

6 Fatima F Mgr Y Jan, Mar BO, CS

7 Gayatri F Exe Y Feb, Mar EG

8 Hari M Mgr I Feb, Mar BO, CS, EG

9 Indira F Dir O Feb, Apr BO, EG

10 John M Dir Y Jan, Mar BO

11 Kalindi F Exe I Jan, Apr BO, CS, EG

12 Lavanya F Mgr O Feb, Apr CS, EG

13 Mandeep M Mgr O Mar, Apr BO, EG

14 Nandlal M Dir I Jan, Feb BO, EG

15 Parul F Exe Y Feb, Apr CS, EG

16 Rahul M Mgr Y Mar, Apr CS, EG

17 Sunita F Dir Y Jan, Feb BO, EG

18 Urvashi F Exe I Feb, Mar EG

19 Yamini F Mgr O Mar, Apr CS, EG

20 Zeena F Exe Y Jan, Mar BO, CS, EG

Jan,

M = Male, F = Female; Exe = Executive, Mgr = Manager, Dir = Director;

Y = Young, I = In between, O = Old

For each workshop, exactly four employees are to be sent, of which at least two should be Females and

at least one should be Young. No employee can be sent to a workshop in which he she is not interested in.

An employee cannot attend the workshop on

• Communication Skills, if he/she is committed to internal projects in the month of January.

• Business Opportunities, if he/she is committed to internal projects in the month of February.

• E-governance, if he/she is committed to internal projects in the month of March.

68. Assuming that Parul and Hari are attending the workshop on Communication Skills (CS), then

which of the following employees can possibly attend the CS workshop?

(1) Rahul and Yamini (2) Dinesh and Lavanya

(3) Anshul and Yamini (4) Fatima and Zeena


69. How many Executives (Exe) cannot attend more than one workshop?

(1) 2 (2) 3 (3) 15 (4) 16

70. Which set of employees cannot attend any of the workshops?

(1) Anshul, Charu, Eashwaran and Lavanya

(2) Anshul, Bushkant, Gayatri, and Urvashi

(3) Charu, Urvashi, Bushkant and Mandeep

(4) Anshul, Gayatri, Eashwaran and Mandeep


Sub–Section III-B : Number of questions = 20

Note: Questions 71 to 90 carry two marks each.


In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in

an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds

before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest

seeded player plays the lowest seeded player (seed #32) which is designated match No. 1 of first round;

the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and

so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the

17th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match

No. 16 of first round and is designated match No. 1 of second round. Similarly, the winner of match No. 2

of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second

round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match

No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds

as well.

Seed# Name of Player Seed# Name of Player Seed# Name of Player

1 Maria Sharapova 12 Mary Pierce 23 Silvia Farina Elia

2 Lindsay Davenport 13 Anastasia Myskina 24 Tatiana Golovin

3 Amelie Mauresmo 14 Alicia Molik 25 Shinobu Asagoe

4 Kim Clijsters 15 Nathalie Dechy 26 Francesca Schiavone

5 Svetlana Kuznetsova 16 Elena Bovina 27 Nicole Vaidisova

6 Elena Dementieva 17 Jelena Jankovic 28 Gisela Dulko

7 Justine Henin 18 Ana Ivanovic 29 Flavia Pennetta

8 Serena Williams 19 Vera Zvonareva 30 Anna Chakvetadze

9 Nadia Petrova 20 Elena Likhovtseva 31 Al Sugiyama

10 Venus Williams 21 Daniela Hantuchova 32 Anna-lena Groenefeld

11 Patty Schnyder 22 Dinara Safina

71. If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and

only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay

Davenport in quarter finals, in case Davenport reaches quarter finals?

(1) Justine Henin (2) Nadia Petrova (3) Patty Schnyder (4) Venus Williams


72. If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia

Petrova make it to the semi-finals, then who would play Maria Sharapova in the quarterfinals, in the

event Sharapova reaches quarterfinals?

(1) Dinara Safina (2) Justine Henin (3) Nadia Petrova (4) Patty Schnyder

73. If, in the first round, all even numbered matches (and none of the odd numbered ones) result in

upsets, and there are no upsets in the second round, then who could be the lowest seeded player

facing Maria Sharapova in semi-finals?

(1) Anastasia Myskina (2) Flavia Pennetta (3) Nadia Petrova (4) Svetlana Kuznetsova

74. If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would

definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?

(1) Amelie Mauresmo (2) Elena Dementieva (3) Kim Clijsters (4) Lindsay Davenport


Venkat, a stockbroker, invested a part of his money in the stock of four companies — A, B, C and D. Each

of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and

Steel, in no particular order. At the time of investment, the price of each stock was Rs. 100. Venkat

purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30% and

40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the

value of the stock after one year, expressed as a percentage of the initial value. During the year, two of

these companies announced extraordinarily good results. One of these two companies belonged to the

Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result,

the returns on the stocks of these two companies were higher than the initially expected returns. For the

company belonging to the Cement or the IT industry with extraordinarily good results, the returns were

twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the

returns on announcement of extraordinarily good results were only one and a half times that of the initially

expected returns. For the remaining two companies which did not announce extraordinarily good results,

the returns realized during the year were the same as initially expected.

75. What is the minimum average return Venkat would have earned during the year?

(1) 30% (2) 311/4% (3) 321/2% (4) Cannot be determined

76. If Venkat earned a 35% return on average during the year, then which of these statements would

necessarily be true?

I. Company A belonged either to Auto or to Steel Industry.

II. Company B did not announce extraordinarily good results.

III. Company A announced extraordinarily good results.

IV. Company D did not announce extraordinarily good results.

(1) I and II only (2) II and III only (3) III and IV only (4) II and IV only


77. If Venkat earned a 38.75% return on average during the year, then which of these statement(s)

would necessarily be true?

I. Company C belonged either to Auto or to Steel Industry.

II. Company D belonged either to Auto or to Steel Industry.

III. Company A announced extraordinarily good results.

IV. Company B did not announce extraordinarily good results.

(1) I and II only (2) II and III only (3) I and IV only (4) II and IV only

78. If Company C belonged to the Cement or the IT industry and did announce extraordinarily good

results, then which of these statement(s) would necessarily be true?

I. Venkat earned not more than 36.25% return on average.

II. Venkat earned not less than 33.75% return on average.

III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results.

IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel

Industry.

(1) I and II only (2) II and IV only (3) II and III only (4) III and IV only


The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The

eventual winner is determined through several rounds of voting by members of the IOC with each member

representing a different city. All the four cities in contention are also represented in IOC.

1) In any round of voting, the city receiving the lowest number of votes in that round gets eliminated.

The survivor after the last round of voting gets to host the event.

2) A member is allowed to cast votes for at most two different cities in all rounds of voting combined.

(Hence, a member becomes ineligible to cast a vote in a given round if both the cities (s)he voted for

in earlier rounds are out of contention in that round of voting.)

3) A member is also ineligible to cast a vote in a round if the city (s)he represents is in contention in

that round of voting.

4) As long as the member is eligible, (s)he must vote and vote for only one candidate city in any round

of voting.

The following incomplete table shows the information on cities that received the maximum and

minimum votes in different rounds, the number of votes cast in their favour, and the total votes that

were cast in those rounds.

Round Total

votes

City No. of City No. of 1 London 30 New York 122 83 Paris 32 Beijing 213 75

Maximum votes cast Eliminated


It is also known that:

• All those who voted for London and Paris in round, 1 continued to vote for the same cities in

subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in

round 1, voted for Beijing in round 2 as well.

• Those who voted for New York in round 1, voted either for Beijing or Parish in round 2.

• The difference in votes cast for the two contending cities in the last round was a.

• 50% of those who voted for Beijing in round 1, voted for Paris in round 3.

79. What percentage of members from among those who voted for New York in round 1, voted for Beijing

in round 2?

(1) 33.33 (2) 50 (3) 66.67 (4) 75

80. What is the number of votes cast for Paris in round 1?

(1) 16 (2) 18 (3) 22 (4) 24

81. What percentage of members from among those who voted for Beijing in round 2 and were eligible

to vote in round 3, voted for London?

(1) 33.33 (2) 38.10 (3) 50 (4) 66.67

82. Which of the following statements must be true?

I. IOC member from New York must have voted for Paris in round 2.

II. IOC member from Beijing voted for London in round 3.

(1) Only I (2) Only II (3) Both I and II (4) Neither I nor II

Directions for Questions 83 to 86: Answer the questions on the basis of the information given below:

The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest

Ltd., Aggressive Ltd., Truthful Ltd. And Profitable Ltd. Are disguised in the table as A, B, C and D, in no

particular order.

States Firm A Firm B Firm C Firm DUP 49 82 80 55

Bihar 69 72 70 65MP 72 63 72 65

Further, it is known that:

• In the state of MP, Truthful Ltd. Has the highest market share.

• Aggressive Ltd.’s aggregate revenue differs from Honest Ltd.’s by Rs. 5 million .


83. What can be said regarding the following two statements?

Statement 1: Profitable Ltd. Has the lowest share in MP market.

Statement 2: Honest Ltd.’s total revenue is more than Profitable Ltd.

(1) If Statement 1 is true then Statement 2 is necessarily true.

(2) If Statement 1 is true then Statement 2 is necessarily false.

(3) Both Statement 1 and Statement 2 are true.

(4) Neither Statement 1 nor Statement 2 is true.


Statement 1: Aggressive Ltd.’s lowest revenues are from MP.

Statement 2: Honest Ltd.’s lowest revenues are from Bihar.

(1) If Statement 2 is true then Statement 1 is necessarily false.

(2) If Statement 1 is false then Statement 2 is necessarily true.

(3) If Statement 1 is true then Statement 2 is necessarily true

(4) None of the above.


Statement 1: Honest Ltd. Has the highest share in the UP market.

Statement 2: Aggressive Ltd. Has the highest share in the Bihar market.

(1) Both statements could be true.

(2) At least one of the statements must be true.

(3) At most one of the statements is true.


86. If Profitable Ltd.’s lowest revenue is from UP, then which of the following is true?

(1) Truthful Ltd.’s lowest revenues are from MP.

(2) Truthful Ltd.’s lowest revenues are from Bihar.

(3) Truthful Ltd.’s lowest revenues are from UP.

(4) No definite conclusion is possible.



Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters.

Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood

Relief (FR in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Dis-

tress has to be involved in at least one relief work project.

• A maximum number of volunteers are involved in the FR project. Among them, the number of

volunteers involved in FR project alone is equal to the volunteers having additional involvement in the

ER project.

• The number of volunteers involved in the ER project alone is double the number of volunteers involved

in all the three projects.

• 17 volunteers are involved in the TR project.

• The number of volunteers involved in the TR project alone is one less than the number of volunteers

involved in ER project alone.

• Ten volunteers involved in the TR project are also involved in at least one more project.

87. Based on the information given above, the minimum number of volunteers involved in both FR and TR

projects, but not in the ER project is

(1) 1 (2) 3 (3) 4 (4) 5

88. Which of the following additional information would enable to find the exact number of volunteers

involved in various projects?

(1) Twenty volunteers are involved in FR.

(2) Four volunteers are involved in all the three projects.

(3) Twenty three volunteers are involved in exactly one project.

(4) No need for any additional information.

89. After some time, the volunteers who were involved in all the three projects were asked to withdraw

from one project. As a result, one of the volunteers opted out of the TR project, and one opted out

of the ER project, while the remaining ones involved in all the three projects opted out of the FR

project. Which of the following statements, then, necessarily follows?

(1) The lowest number of volunteers is now in TR project.

(2) More volunteers are now in FR project as compared to ER project.

(3) More volunteers are now in TR project as compared to ER project.


90. After the withdrawal of volunteers, as indicated in Question 89, some new volunteers joined the

NGO. Each one of them was allotted only one project in a manner such that, the number of volun-

teers working in one project alone for each of the three projects became identical. At that point, it

was also found that the number of volunteers involved in FR and ER projects was the same as the

number of volunteers involved in TR and ER projects. Which of the projects now has the highest

number of volunteers?

(1) ER (2) FR (3) TR (4) Cannot be determined


Directions for Questions 26 to 29: Answer the following questions based on the information given below:

A health-drink company’s R&D department is trying to make various diet formulations, which can be used

for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R, and S),

which can be used in different proportions in the formulations. The table below gives the composition of

these ingredients. The cost per unit of each of these ingredients is O: 150, P: 50. Q: 200, R: 500, S: 100.

Composition Ingredient

Carbohydrate% Protein% Fat% Minerals%

O 50 30 10 10

P 80 20 0 0

Q 10 30 50 10

R 5 50 40 5

S 45 50 0 5

26. For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least

30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?

(1) One (2) Two (3) Three (4) Four (5) None

27. Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat

and at least 30% protein? (The diet has to be formed by mixing two ingredients).

(1) P and Q (2) P and S (3) P and R (4) Q and S (5) R and S

28. In what proportion P, Q and S should be mixed to make a diet having at least 60% carbohydrate at

the lowest cost per unit?

(1) 2:1:3 (2) 4:1:2 (3) 2:1:4 (4) 3:1:2 (5) 4:1:1

29. The company is planning to launch a balanced diet required for growth needs of adolescent children.

This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at

least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible?

(1) O and P (2) R and S (3) P and S

(4) Q and R (5) O and S

Section � 1I


Directions for Questions 30 to 33: Each question is followed by two statements, A and B.

Answer each question using the following instructions:

Mark (1) if the question can be answered by using the statement A alone but not by using the statement

B alone.

Mark (2) if the question can be answered by using the statement B alone but not by using the statement

A alone.

Mark (3) if the question can be answered by using either of the statements alone.

Mark (4) if the question can be answered by using both the statements together but not by either of the

statements alone.

Mark (5) if the question cannot be answered on the basis of the two statements.

30. In a particular school, sixty students were athletes. Ten among them were also among the top

academic performers. How many top academic performers were in the school?

A. Sixty per cent of the top academic performers were not athletes.

B. All the top academic performers were not necessarily athletes.

31. Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz

contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared

to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan’s rank was lower than the

median. Who among the five got the highest rank?

A. Atul was the last rank holder.

B. Bala was not among the top two rank holders.

32. Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees

have an engineering background. What is the percentage of male employees with engineering

background?

A. Twenty five per cent of the employees have engineering background.

B. Number of male employees having an engineering background is 20% more than the number of

female employees having an engineering background.

33. ln a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it

win the match?

A. In the second-half Mahindra and Mahindra Club scored four goals.

B. The opponent scored four goals in the match.



The following table shows the break-up of actual costs incurred by a company in last five years (year 2002

to year 2006) to produce a particular product:

Year 2002 Year 2003 Year 2004 Year 2005 Year 2006

Volume of production and sale (units) 1000 900 1100 1200 1200

Costs (Rs.)

Material 50,000 45,100 55,200 59,900 60,000

Labour 20,000 18,000 22,100 24,150 24,000

Consumables 2,000 2,200 1,800 1,600 1,400

Rent of building 1,000 1,000 1,100 1,100 1,200

Rates and taxes 400 400 400 400 400

Repair and maintenance expenses 800 820 780 790 800

Operating cost of machines 30,000 27,000 33,500 36,020 36,000

Selling and marketing expenses 5,750 5,800 5,800 5,750 5,800

The production capacity of the company is 2000 units. The selling price for the year 2006 was

Rs. 125 per unit. Some costs change almost in direct proportion to the change in volume of production,

while others do not follow any obvious pattern of change with respect to the volume of production and hence

are considered fixed. Using the information provided for the year 2006 as the basis for projecting the figures

for the year 2007, answer the following questions:

34. What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in

the year 2007?

(1) 104 (2) 107 (3) 110 (4) 115 (5) 116

35. What is the minimum number of units that the company needs to produce and sell to avoid any

loss?

(1) 313 (2) 350 (3) 384 (4) 747 (5) 928

36. If the company reduces the price by 5%, it can produce and sell as many units as it desires. How

many units the company should produce to maximize its profit?

(1) 1400 (2) 1600 (3) 1800 (4) 1900 (5) 2000

37. Given that the company cannot sell more than 1700 units, and it will have to reduce the price by

Rs.5 for all units, if it wants to sell more than 1400 units, what is the maximum profit, in rupees, that

the company can earn?

(1) 25,400 (2) 24,400 (3) 31,400 (4) 32,900 (5) 32,000



The proportion of male students and the proportion of vegetarian students in a school are given below.

The school has a total of 800 students, 80% of whom are in the Secondary Section and rest are equally

divided between Class 11 and 12.

Male (M) Vegetarian (V)

Class 12 0.6

Class 11 0.55 0.5

Secondary Section 0.55

Total 0.475 0.53

38. What is the percentage of male students in the secondary section?

(1) 40 (2) 45 (3) 50 (4) 55 (5) 60

39. In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the

number of female vegetarians and male non-vegetarians?

(1) less than 8 (2) 10 (3) 12 (4) 14 (5) 16

40. What is the percentage of vegetarian students in Class 12?

(1) 40 (2) 45 (3) 50 (4) 55 (5) 60

41. In the Secondary Section, 50% of the students are vegetarian males. Which of the following

statements is correct?

(1) Except vegetarian males, all other groups have same number of students.

(2) Except non-vegetarian males, all other groups have same number of students.

(3) Except vegetarian females, all other groups have same number of students.

(4) Except non-vegetarian females, all other groups have same number of students.

(5) All of the above groups have the same number of students.


The Table below shows the comparative costs, in US Dollars, of major surgeries in USA and a select few

Asian countries.

Comparative Costs in USA and some Asian countries

(in US Dollar) Procedure

USA India Thailand Singapore Malaysia

Heart Bypasss 130000 10000 11000 18500 9000

Heart Valve Replacement 160000 9000 10000 12500 9000

Angioplasty 57000 11000 13000 13000 11000

Hip Replacement 43000 9000 12000 12000 10000

Hysterectomy 20000 3000 4500 6000 3000

Knee Replacement 40000 8500 10000 13000 8000

Spinal Fusion 62000 5500 7000 9000 6000


The equivalent of one US Dollar in the local currencies is given below:

1 US Dollar equivalent

India 40.928 Rupees

Malaysia 3.51 Ringits

Thailand 32.89 Bahts

Singapore 1.53 S Dollars

A consulting firm found that the quality of the health services were not the same in all the countries above.

A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting

mistakes. The cost of poor quality of surgery is given in the table below:

Procedure Comparative cost of poor quality in USA and some Asian

countries (in US Dollars '000)

USA India Thailand Singapore Malaysia

Heart Bypasss 0 3 3 2 4

Heart Valve Replacement 0 5 4 5 5

Angioplasty 0 5 5 4 6

Hip Replacement 0 7 5 5 8

Hysterectomy 0 5 6 5 4

Knee Replacement 0 9 6 4 4

Spinal Fusion 0 5 6 5 6

42. A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee

replacement. Cost of foreign travel and stay is not a consideration since the government will take

care of it. Which country will result in the cheapest package, taking cost of poor quality into account?

(1) India (2) Thailand (3) Malaysia (4) Singapore (5) USA

43. Taking the cost of poor quality into account, which country/countries will be the most expensive for

knee replacement?

(1) India (2) Thailand (3) Malaysia

(4) Singapore (5) India and Singapore

44. Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a

hysterectomy done in India instead of in her native country, taking into account the cost of poor

quality? (It costs 7500 Bahts for one-way travel between Thailand and India).

(1) 23500 (2) 40500 (3) 57500 (4) 67500 (5) 75000

45. The rupee value increases to Rs.35 for a US Dollar, and all other things including quality, remain the

same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a

Spinal Fusion, taking this change into account?

(1) 700 (2) 2500 (3) 4500 (4) 8000 (5) No difference



A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between

a pair of airports and the corresponding price charged by the company. Travel is permitted only from a

departure airport to an arrival airport. The customers do not travel by a route where they have to stop at

more than two intermediate airports.

Sector

No

Airport of

Departure

Airport of

Arrival

Distance

between the

Airports (km)

Price (Rs.)

1 A B 560 670

2 A C 790 1350

3 A D 850 1250

4 A E 1245 1600

5 A F 1345 1700

6 A G 1350 2450

7 A H 1950 1850

8 B C 1650 2000

9 B H 1750 1900

10 B I 2100 2450

11 B J 2300 2275

12 C D 460 450

13 C F 410 430

14 C G 910 1100

15 D E 540 590

16 D F 625 700

17 D G 640 750

18 D H 950 1250

19 D J 1650 2450

20 E F 1250 1700

21 E G 970 1150

22 E H 850 875

23 F G 900 1050

24 F I 875 950

25 F J 970 1150

26 G I 510 550

27 G J 830 890

28 H I 790 970

29 H J 400 425

30 I J 460 540


46. What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from

A to J?

(1) 2275 (2) 2850 (3) 2890 (4) 2930 (5) 3340

47. The company plans to introduce a direct flight between A and J. The market research results

indicate that all its existing passengers travelling between A and J will use this direct flight if it is

priced 5% below the minimum price that they pay at present. What should the company charge

approximately, in rupees, for this direct flight?

(1) 1991 (2) 2161 (3) 2707 (4) 2745 (5) 2783

48. If the airports C, D and H are closed down owing to security reasons, then what would be the

minimum price, in rupees, to be paid by a passenger travelling from A to J?

(1) 2275 (2) 2615 (3) 2850 (4) 2945 (5) 3190

49. If the prices include a margin of 10% over the total cost that the company incurs, then what is the

minimum cost per kilometer that the company incurs in flying from A to J?

(1) 0.77 (2) 0.88 (3) 0.99 (4) 1.06 (5) 1.08

50. If the prices include a margin of 15% over the total cost that the company incurs, then which among

the following is the distance to be covered in flying from A to J that minimizes the total cost per

kilometer for the company?

(1) 2170 (2) 2180 (3) 2315 (4) 2350 (5) 2390


Directions for Questions 26 to 28: Answer the following questions based on the statements givenbelow:

(i) There are three houses on each side of the road.(ii) These six houses are labeled as P, Q, R, S, T and U.(iii) The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White.(iv) The houses are of different heights.(v) T, the tallest house, is exactly opposite to the Red coloured house.(vi) The shortest house is exactly opposite to the Green coloured house.(vii) U, the Orange coloured house, is located between P and S.(viii) R, the Yellow coloured house, is exactly opposite to P.(ix) Q, the Green coloured house, is exactly opposite to U.(x) P, the White coloured house, is taller than R, but shorter than S and Q.

26. What is the colour of the house diagonally opposite to the Yellow coloured house?(1) White (2) Blue (3) Green(4) Red (5) none of these

27. Which is the second tallest house?(1) P (2) S (3) Q(4) R (5) cannot be determined

28. What is the colour of the tallest house?(1) Red (2) Blue (3) Green(4) Yellow (5) none of these

Section � 1I


Directions for Questions 29 to 31: Answer the following questions based on the information givenbelow:

Telecom operators get revenue from transfer of data and voice. Average revenue received from transfer ofeach unit of data is known as ARDT. In the diagram below, the revenue received form data transfer aspercentage of total revenue received and the ARDT in US Dollars (USD) are given for various countries.

Canada

Ph ilippines ($3 .54% )

Ch ina

M exico

Hong Kong

IsraelThailand

India Braz il

Denm ark

Spain

Austria

Sweden

Po land

G ermanySw itzerland

Singapore Norway

USA

M alays ia

South K orea

UK

Russia

Indonesia ($2,42% )

Ire land

Japan ($13,70% )

Re

ven

ue

fro

mD

ata

Tra

ns

fer

as

a%

of

To

tal

Re

ve

nu

e

10

%2

0%

30

%

$5 $10 $15

ARDT ( in USD)

Legend: ASIA EURO P E AM ER ICAS

29. It was found that the volume of data transfer in India is the same as that of Singapore. Then whichof the following statements is true?(1) Total revenue is the same in both countries.(2) Total revenue in India is about 2 times that of Singapore.(3) Total revenue in India is about 4 times that of Singapore.(4) Total revenue in Singapore is about 2 times that of India.(5) Total revenue in Singapore is about 4 time that of India.


30. It is expected that by 2010, revenue from data transfer as a percentage of total revenue will triplefor India and double for Sweden. Assume that in 2010, the total revenue in India is twice that ofSweden and that the volume of data transfer is the same in both the countries. What is thepercentage increase of ARDT in India if there is no change in ARDT in Sweden?(1) 400% (2) 550% (3) 800%(4) 950% (5) cannot be determined

31. If the total revenue received is the same for the pairs of countries listed in the choicesbelow, choose the pair that has approximately the same volume of data transfer.(1) Philippines and Austria(2) Canada and Poland(3) Germany and USA(4) UK and Spain(5) Denmark and Mexico


For admission to various affiliated colleges, a university conducts a written test with four different sections,each with a maximum of 50 marks. The following table gives the aggregate as well as the sectional cut-offmarks fixed by six different colleges affiliated to the university. A student will get admission only if he/shegets marks greater than or equal to the cut-off marks in each of the sections and his/her aggregate marksare at least equal to the aggregate cut-off marks as specified by the college.

Sectional Cut – off Marks Section A Section B Section C Section D

Aggregate Current Marks

College 1 42 42 42 176 College 2 45 45 175 College 3 46 171 College 4 43 45 178 College 5 45 43 180 College 6 41 44 176

32. Bhama got calls from all colleges. What could be the minimum aggregate marks obtainedby her?(1) 180 (2) 181 (3) 196 (4) 176 (5) 184

33. Charlie got calls from two colleges. What could be the minimum marks obtained by him in asection?(1) 0 (2) 21 (3) 25 (4) 35 (5) 41

34. Aditya did not get a call from even a single college. What could be the maximum aggregatemarks obtained by him?(1) 181 (2) 176 (3) 184 (4) 196 (5) 190


Directions for Questions 35 to 38: Answer the following questions based on the information given below:In a sports event, six teams (A, B, C, D, E and F) are competing against each other Matches are sched-uled in two stages. Each team plays three matches in State – I and two matches in Stage – II. No teamplays against the same team more than once in the event. No ties are permitted in any of the matches. Theobservations after the completion of Stage – I and Stage – II are as given below.

Stage-I:

• Once team won all the three matches.• Two teams lost all the matches.• D lost to A but won against C and F.• E lost to B but won against C and F.• B lost at least one match.• F did not play against the top team of Stage-I.

Stage-II:

• The leader of Stage-I lost the next two matches• Of the two teams at the bottom after Stage-I, one team won both matches, while the other lost both

matches.• Once more team lost both matches in Stage-II.

35. The two teams that defeated the leader of Stage-I are:(1) F & D (2) E & F (3) B & D (4) E & D (5) F & D

36. The only team(s) that won both matches in Stage-II is (are):(1) B (2) E & F (3) A, E & F (4) B, E & F (5) B & F

37. The teams that won exactly two matches in the event are:(1) A, D & F (2) D & E (3) E & F (4) D, E & F (5) D & F

38. The team(s) with the most wins in the event is (are):(1) A (2) A & C (3) F (4) E (5) B & E


Directions for Questions 39 to 42: Answer the following questions based on the information given below:The bar chart below shows the revenue received in million US Dollars (USD), from subscribers to a particularInternet service. The data covers the period 2003 to 2007 for the United States (US) and Europe. The barchart also shows the estimated revenues from subscription to this service for the period 2008 to 2010.

0

100

200

300

400

500

600

700

800

900

1000

03 04 05 06 07 08 09 10

Years

Subscription R

evenue in M

illio

n U

SD

US

Europe

39. The difference between the estimated subscription in Europe in 2008 and what it would have been ifit were computed using the percentage growth rate of 2007 (over 2006), is closest to:(1) 50 (2) 80 (3) 20 (4) 10 (5) 0

40. In 2003, sixty percent of subscribers in Europe were men. Given that women subscribers increaseat the rate of 10 percent annum and men at the rate of 5 percent per annum, what is the approximatepercentage growth of subscribers between 2003 and 2010 in Europe? The subscription prices arevolatile and may change each year.(1) 62 (2) 15 (3) 78 (4) 84 (5) 50

41. Consider the annual percent change in the gap between subscription revenues in the US andEurope. What is the year in which the absolute value of this change is the highest?(1) 03 - 04 (2) 05 - 06 (3) 06 - 07 (4) 08 - 09 (5) 09 - 10

42. While the subscription in Europe has been growing steadily towards that of the US, the growth ratein Europe seems to be declining. Which of the following is closest to the percent change in growthrate of 2007 (over 2006) relative to the growth rate of 2005 (over 2004)?(1) 17 (2) 20 (3) 35 (4) 60 (5) 100



Abdul, Bikram and Chetan are three professional traders who trade in shares of a company XYZ Ltd. Abdulfollows the strategy of buying at the opening of the day at 10 am and selling the whole lot at the close of theday at 3 pm. Bikram follows the strategy of buying at hourly intervals: 10 am, 11am, 12 noon, I pm. And 2pm, and selling the whole lot at the close of the day, Further, he buys an equal number of shares in eachpurchase. Chetan follows a similar pattern as Bikram but his strategy is somewhat different. Chetan’s totalinvestment amount is divided equally among his purchases. The profit or loss made by each investor is thedifference between the sale value at the close of the day less the investment in purchase. The “return” foreach investor is defined as the ratio of the profit or loss to the investment amount expressed as a percent-age.

43. On a day of fluctuating market prices, the share price of XYZ Ltd. ends with a gain, i.e, it is higherat the close of the day compared to the opening value. Which trader got the maximum return on thatday?(1) Bikram(2) Chetan(3) Abdul(4) Bikram or Chetan(5) cannot be determined

44. Which one of the following statements is always true?(1) Abdul will not be one with the minimum return(2) Return for Chetan will be higher than that of Bikram(3) Return for Bikram will be higher than that of Chetan(4) Return for Chetan cannot be higher than that of Abdul(5) none of the above

45. On a “boom” day the share price of XYZ Ltd. keeps rising throughout the day and dpeaks at theclose of the day. Which trader got the minimum return on that day?(1) Bikram (2) Chetan (3) Abdul(4) Abdul or Chetan (5) cannot be determined

One day, two other traders. Dane and Emily joined Abdul, Bikram and Chetan for trading in the shares ofXYZ Ltd. Dane followed a strategy of buying equal numbers of shares at 10 am. 11 am and 12 noon, andselling the same numbers at 1 pm, 2 pm and 3 pm Emily, on the other hand, followed the strategy of buyingshares using all her money at 10 am and selling all of them at 12 noon and again buying the shares for allthe money at 1 pm and again selling all of them at the close of the day at 3 pm. At the close of the day thefollowing was observed.

i. Abdul lost money in the transactions.ii. Both Dane and Emily made profits.iii. There was an increase in share price during the closing hour compared to the price at 2 pm.iv. Share price at 12 noon was lower than the opening price

46. Share price was at its highest at(1) 10 am (2) 11 am (3) 12 noon(4) 1 pm (5) cannot be determined


47. Which of the following is necessarily false?(1) Share price was at its lowest at 2 pm(2) Share price was at its lowest at 11 am(3) Share price at 1 pm was higher than the share price at 2 pm(4) Share price at 1 pm was higher than the share price at 12 noon(5) none of the above


There are 100 employees in an organization across five departments. The following table gives the depart-ment-wise distribution of average age, average basic pay and allowances. The gross pay of an employee isthe sum of his/her basic pay and allowances.

Department Number of Employees

Average Age (Years)

Average Basic Pay (Rs.)

Allowances (% of Basic Pay)

HR 5 45 5000 70 Marketing 30 35 6000 80 Finance 20 30 6500 60 Business

Development 35 42 7500 75

Maintenance 10 35 5500 50

There are limited numbers of employees considered for transfer/promotion across departments Whenevera person is transferred/promoted from a department of lower average age to a department of higher averageage, he/she will get an additional allowance of 10% of basic pay over and above his/her current allowance.There will not be any change in pay structure if a person is transferred/promoted from a department withhigher average age to a department with lower average age.

Questions below are independent of each other.

48. What is the approximate percentage change in the average gross of the HR department due totransfer of a 40-year old person with basic pay of Rs. 8000 from the Marketing department?(1) 9% (2) 11% (3) 13% (4) 15% (5) 17%

49. There was a mutual transfer of an employee between Marketing and Finance departments andtransfer of one employee from Marketing to HR. As a result, the average age of finance departmentincreased by one year and that of Marketing department remained the same. What is the newaverage age of HR department?(1) 30 (2) 35 (3) 40(4) 45 (5) cannot be determined

50. If two employees (each with a basic pay of Rs. 6000) are transferred from Maintenance departmentto HR department and one person (with a basic pay of Rs. 8000) was transferred from Marketingdepartment to HR department, what will be the percentage change in average basic pay of HRdepartment?(1) 10.5% (2) 12.5% (3) 15% (4) 30% (5) 40%



K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a

team from within the members of the department, subject to the following conditions:

1. A team must include exactly one among P, R, and S.

2. A team must include either M or Q, but not both.

3. If a team includes K, then it must also include L, and vice versa.

4. If a team includes one among S, U, and W, then it must also include the other two.

5. L and N cannot be members of the same team.

6. L and U cannot be members of the same team.

The size of a team is defined as the number of members in the team.

1. Who cannot be a member of a team of size 3?

(1) L (2) M (3) N (4) P (5) Q

2. Who can be a member of a team of size 5?

(1) K (2) L (3) M (4) P (5) R

3. What would be the size of the largest possible team?

(1) 8 (2) 7 (3) 6 (4) 5 (5) Cannot be determined

4. What could be the size of a team that includes K?

(1) 2 or 3 (2) 2 or 4 (3) 3 or 4 (4) Only 2 (5) Only 4

5. In how many ways a team can be constituted so that the team includes N?

(1) 2 (2) 3 (3) 4 (4) 5 (5) 6

Section � 1


Directions for questions 6 to 10: Answer questions on the basis of the information given below:

In a Class X Board examination, ten papers are distributed over five Groups - PCB, Mathematics, Social

Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a

student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in

the papers within the Group. The final score is the simple average of the Group Scores. The data for the top

ten students are presented below. (Dipan's score in English Paper II has been intentionally removed in the

table.)

PCB Group Social

Science Group

Vernacular Group

English Group Name of the student

Phy. Chem. Bio.

Mathematics Group

Hist. Geo. Paper I Paper II Paper I Paper II

FinalScore

Ayesha (G) 98 96 97 98 95 93 94 96 96 98 96.2

Ram (B) 97 99 95 97 95 96 94 94 96 98 96.1

Dipan (B) 98 98 98 95 96 95 96 94 96 ?? 96.0

Sagnik (B) 97 98 99 96 96 98 94 97 92 94 95.9

Sanjiv (B) 95 96 97 98 97 96 92 93 95 96 95.7

Shreya (G) 96 89 85 100 97 98 94 95 96 95 95.5

Joseph (B) 90 94 98 100 94 97 90 92 94 95 95

Agni (B) 96 99 96 99 95 96 82 93 92 93 94.3

Pritam (B) 98 98 95 98 83 95 90 93 94 94 93.9

Tirna (G) 96 98 97 99 85 94 92 91 87 96 93.7

Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.

6. How much did Dipan get in English Paper II?

(1) 94 (2) 96.5 (3) 97 (4) 98 (5) 99

7. Among the top ten students, how many boys scored at least 95 in at least one paper from each of

the groups?

(1) 1 (2) 2 (3) 3 (4) 4 (5) 5

8. Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group,

then their standing in decreasing order of final score would be:

(1) Pritam, Joseph, Tirna, Agni (2) Joseph, Tirna, Agni, Pritam

(3) Pritam, Agni, Tirna, Joseph (4) Joseph, Tirna, Pritam, Agni

(5) Pritam, Tirna, Agni, Joseph


9. Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize.

Among those who are eligible, the student obtaining the highest Group Score in Social Science

Group is awarded this prize. The prize was awarded to:

(1) Shreya (2) Ram

(3) Ayesha (4) Dipan

(5) No one from the top ten

10. Each of the ten students was allowed to improve his/her score in exactly one paper of choice with

the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she

chose to improve. After that, the topper among the ten students was:

(1) Ram (2) Agni (3) Pritam (4) Ayesha (5) Dipan


Mathematicians are assigned a number called Erdös number (named after the famous mathematician,

Paul Erdös). Only Paul Erdös himself has an Erdös number of zero. Any mathematician who has written

a research paper with Erdös has an Erdös number of 1. For other mathematicians, the calculation of his/

her Erdös number is illustrated below:

Suppose that a mathematician X has co-authored papers with several other mathematicians. From among

them, mathematician Y has the smallest Erdös number. Let the Erdös number of Y be y. Then X has an

Erdös number of y+1 . Hence any mathematician with no co-authorship chain connected to Erdös has an

Erdös number of infinity.

In a seven day long mini-conference organized in memory of Paul Erdös, a close group of eight mathema-

ticians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the

conference, A was the only participant who had an infinite Erdös number. Nobody had an Erdös number

less than that of F.

1 On the third day of the conference F co-authored a paper jointly with A and C. This reduced the

average Erdös number of the group of eight mathematicians to 3. The Erdös numbers of B, D, E, G

and H remained unchanged with the writing of this paper. Further, no other co-authorship among any

three members would have reduced the average Erdös number of the group of eight to as low as 3.

2 At the end of the third day, five members of this group had identical Erdös numbers while the other

three had Erdös numbers distinct from each other.

3 On the fifth day, E co-authored a paper with F which reduced the group's average Erdös number by

0.5. The Erdös numbers of the remaining six were unchanged with the writing of this paper.

4 No other paper was written during the conference.

11. How many participants in the conference did not change their Erdös number during the conference?



12. The person having the largest Erdös number at the end of the conference must have had Erdös

number (at that time):

(1) 5 (2) 7 (3) 9 (4) 14 (5) 15

13. How many participants had the same Erdös number at the beginning of the conference?


14. The Erdös number of C at the end of the conference was:

(1) 1 (2) 2 (3) 3 (4) 4 (5) 5

15. The Erdös number of E at the beginning of the conference was:

(1) 2 (2) 5 (3) 6 (4) 7 (5) 8


Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading

days. At the beginning of the first day, the MCS share was priced at Rs 100, while at the end of the fifth day

it was priced at Rs 110. At the end of each day, the MCS share price either went up by Rs 10, or else, it

came down by Rs 10. Both Chetan and Michael took buying and selling decisions at the end of each

trading day. The beginning price of MCS share on a given day was the same as the ending price of the

previous day. Chetan and Michael started with the same number of shares and amount of cash, and had

enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading

days.

1 Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other

hand, each day if the price went down, he bought 10 shares at the closing price.

2 If on any day, the closing price was above Rs 110, then Michael sold 10 shares of MCS, while if it

was below Rs 90, he bought 10 shares, all at the closing price.

16. If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once

during the five days, what was the price of MCS at the end of day 3?

(1) Rs 90 (2) Rs 100 (3) Rs 110 (4) Rs 120 (5) Rs 130

17. If Chetan ended up with Rs 1300 more cash than Michael at the end of day 5, what was the price of

MCS share at the end of day 4?

(1) Rs 90 (2) Rs 100 (3) Rs 110

(4) Rs 120 (5) Not uniquely determinable

18. If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the

share at the end of day 3?

(1) Rs 90 (2) Rs 100 (3) Rs 110 (4) Rs 120 (5) Rs 130


19. If Michael ended up with Rs 100 less cash than Chetan at the end of day 5, what was the difference

in the number of shares possessed by Michael and Chetan (at the end of day 5)?

(1) Michael had 10 less shares than Chetan.

(2) Michael had 10 more shares than Chetan.

(3) Chetan had 10 more shares than Michael,

(4) Chetan had 20 more shares than Michael.

(5) Both had the same number of shares.

20. What could have been the maximum possible increase in combined cash balance of Chetan and

Michael at the end of the fifth day?

(1) Rs 3700 (2) Rs 4000 (3) Rs 4700 (4) Rs 5000 (5) Rs 6000


A significant amount of traffic flows from point S to point T in the one-way street network shown below.

Points A, B, C, and D are junctions in the network, and the arrows mark the direction of traffic flow. The fuel

cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the

street.

A

BS C T

D

9 5

2 3 2

7 1 6

2

Motorists travelling from point S to point T would obviously take the route for which the total cost of

travelling is the minimum. If two or more routes have the same least travel cost, then motorists are indiffer-

ent between them. Hence, the traffic gets evenly distributed among all the least cost routes.

The government can control the flow of traffic only by levying appropriate toll at each junction. For example,

if a motorist takes the route S-A-T (using junction A alone), then the total cost of travel would be Rs 14 (i.e.,

Rs 9 + Rs 5) plus the toll charged at junction A.

21. If the government wants to ensure that no traffic flows on the street from D to T, while equal amount

of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions

A, B, C, and D respectively to achieve this goal is:

(1) 1,5,3,3 (2) 1,4,4,3 (3) 1,5,4,2 (4) 0,5,2,3 (5) 0,5,2,2


22. If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel

costs and toll combined) regardless of the route they choose and the street from B to C is under

repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and

D respectively to achieve this goal is:

(1) 2,5,3,2 (2) 0,5,3, 1 (3) 1,5,3,2 (4) 2,3,5,1 (5) 1,3,5,1

23. If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to

A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C,

and D respectively to achieve this goal is:

(1) 0,5,4,1 (2) 0,5,2,2 (3) 1,5,3,3 (4) 1,5,3,2 (5) 0,4,3,2

24. If the government wants to ensure that all routes from S to T get the same amount of traffic, then a

feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal

is:

(1) 0,5,2,2 (2) 0,5,4,1 (3) 1,5,3,3 (4) 1,5,3,2 (5)1,5,4,2

25. The government wants to devise a toll policy such that the total cost to the commuters per trip is

minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes

through junction B. The cost incurred by the commuter travelling from point S to point T under this

policy will be:

(1) Rs. 7 (2) Rs. 9 (3) Rs. 10 (4) Rs. 13 (5) Rs. 14

CAT PAPER – 2004 Explanations Page 1MBATest Prep

Scoring table

Section

DI 1 to 38 38

Quant 39 to 73 35

EU + RC 74 to 123 50

Total 123

Total

questions

Total

attempted

Total

correct

Total

wrong

Net

Score

Time

TakenQuestion

number

1 1 2 4 3 2 4 3 5 3 6 4 7 4 8 1 9 1 10 3

11 1 12 2 13 2 14 3 15 4 16 1 17 4 18 1 19 2 20 4

21 1 22 1 23 1 24 2 25 3 26 4 27 3 28 1 29 2 30 2

31 4 32 3 33 3 34 4 35 4 36 2 37 4 38 4 39 3 40 2

41 1 42 2 43 1 44 2 45 1 46 1 47 3 48 4 49 4 50 2

51 3 52 4 53 2 54 2 55 3 56 4 57 4 58 3 59 4 60 3

61 3 62 2 63 3 64 2 65 1 66 2 67 2 68 4 69 4 70 1

71 3 72 3 73 1 74 2 75 1 76 4 77 3 78 2 79 4 80 3

81 1 82 4 83 1 84 3 85 2 86 1 87 3 88 3 89 4 90 2

91 4 92 2 93 1 94 2 95 4 96 1 97 2 98 1 99 3 100 3

101 1 102 1 103 2 104 4 105 2 106 1 107 1 108 3 109 4 110 4

111 3 112 3 113 3 114 3 115 2 116 3 117 2 118 2 119 3 120 1

121 3 122 2 123 4

CAT PAPER � 2004


SUP-0001/09

CAT PAPER – 2004 ExplanationsPage 2 MBATest Prep

1. 1 GPA of Preeti = 3.2

i.e.F D X D Y

3.25

+ + + +=

0 + 2 + x + 2 + y = 16

x + y = 12

So only combination possible is A, A.

So Preeti obtained A grade in statistics.

2. 4 Tara received same grade in 3 courses. We already

know that Tara has got B grade in one of the subject

and GPA is 2.4. So in 3 courses in which he scored

same grade is B.

So Tara has received the same grade as Manab.

3. 2 GPA of Gowri is 3.8

i.e. 3 + 3 + 6 + x + 4 = 3.8 × 5

16 + x = 18

x = 2

So in strategy, Gowri's grade is C.

Rahul's grade in strategy = (4.2 × 5) – 15 = 6, i.e., A.

Fazal's grade in strategy = (2.4 × 5) – 8 = 4, i.e., B.

Hence, Gowri's grade will be higher than that of Hari.

4. 3 As Fazal GPA = 2.4

So D + F + B + P + D = 2.4 × 5

2 + 0 + 4 + P + 2 = 12

P = 4

So his grade in strategy is B.

So Grade of Utkarsh in marketing is also B.

So for Utkarsh, x + B + F + C + A = 3 × 5

x + 4 + 0 + 3 + 6 = 15

x = 2

So grade of Utkarsh in finance = D.

5. 3 Average income of Ahuja

=700 1700 1800 4200

3 3

+ +=

Average income of Bose

=800 1600 2300 4700

3 3

+ +=

Average income of Coomar

=300 1100 1900 3300

3 3

+ +=

Average income of Dubey

=1200 2800 4000

2 2

+=

It's clear that lowest average income is of Coomar. (It

is clear visually as well)

6. 4 From the figure draw a line parallel to the expenditure

axis and midway between observations of each

family's values.

7. 4 From figure the Ist member of Dubey family is on the

line indicating income = expenditure.

The 2nd member is just above the line.

8. 1 Look at the leftmost member of Ahuja family.

Solution for questions 9 to 12:

Comparing Table 1 and 2, university 4 corresponds to UK and

university 6 corresponds to USA (after as day 3 values are

concerned and university 8 corresponds to India and university

3 to Netherlands now Indian or Netherlands can take university

1 or university 5. Now university 2 and 7 belongs to either UK

or Canada (only one)

UNIVERSITY DAY COUNTRY

1 2 3

University 1 1 0 0 India / Netherlands

University 2 2 0 0 UK / Canada

University 3 0 1 0 Netherlands

University 4 0 0 2 UK

University 5 1 0 0 India/Netherlands

University 6 1 0 1 USA

University 7 2 0 0 UK/Canada

University 8 0 2 0 India

9. 1 10. 3 11. 1 12. 2

13. 2 In 1999, total number of Naya mixer-grinder = 124

Number of Naya mixer-grinder disposed = 20% of 30

= 6

Number of mixtures bought

124 = [50 + 24] 50

14. 3 Number of Naya mixer-grinder disposed in 1999 ⇒ 6

Number of Naya mixer-grinder disposed in 2000 ⇒ 10

Total disposed by end of 2000 = 16

15. 4 Initial number of Purana mixer-grinder not available,

hence cannot be determined.

16. 1 20 Purana mixer-grinder were purchased in 1999.

17. 4 Thailand and Japan (Maximum difference of 4 ranks

(5 – 1) = 4)

18. 1 China (Maximum difference between 2 parameter is

2)

19. 2 Japan (Maximum difference of 4)

20. 4 Japan and Malaysia (Inferring from question 17)

21. 1 Statement A: 20% of Z > 25% of S

Z 5

S 4> Cannot say.

Statement B: 13% of S > 10% of Z

⇒ 39% of S > 30% of Z. So 40% of S must be greater

than 33% of Z.

Hence statement B is sufficient to answer.


22. 1 Assume A, B, C, D get score 10, 8, 6, 4 reap.

A B C D

10 8 6 4

Statement A:

With the conditions A will give vote to B

With the conditions B will give vote to A

With the conditions C will give vote to A

Even if D gives to A/B/C - 2 situation arises.

Either A will win or there will a tie when D gives vote to

B.

Even then A will win.

So we are getting the answer.

Statement B: Can conclude anything.

Answer (1) first statement.

23. 1 Statement A: Cannot say anything.

Statement B: Because amongst the Top 5 3 are boys,

2 are girls. And Rashmi is third among the girls and

Kumar is 6th.

We can conclude.

Answer (1) statement II is sufficient.

24. 2 Statement A: We can find, there are 12 Tails and 9

Heads.

After tosses he will reach at blue point. So statement

A is sufficient.

Statement B: 3 more Tails greater than Heads. So he

will reach at blue point after tosses.

So statement B is also sufficient.

25. 3 Statement A: 2 kg potato cost + 1 kg gourd cost < 1 kg

potato cost + 1 kg gourd cost

⇒ 1 kg potato cost < 1 kg gourd cost.

So statement A is not sufficient.

Statement B: 1 kg potato cost + 2 kg onion cost = 1 kg

onion cost + 2 kg gourd cost 1 kg potato cost + 1 kg

onion cost = 2 kg gourd cost.

So statement B is also not sufficient.

Combining both statements we get

1 kg potato cost < 1 kg gourd cost …(i)

1 kg potato cost + 1 kg onion cost

= 2 kg gourd cost …(ii)

So the onion is costliest.

26. 4 Statement A: 13 currency notes will give diff. Values.

Statement B: Multiple of 10 and by many.

Even if you combine the statement, we can have

various values.

Answer is (4).

Solution for questions 27 to 30: Go through the following

table.

Pakistan South Africa Australia

K 28 51 < 48

R < 22 49 55

S < 22 75 50

V 130 < 49 < 48

Y 40 < 49 87

Top 3 batsman 198 175 192

India Total 220 250 240

27. 3 28. 1 29. 2 30. 2

Solutions for questions 31 to 34: For solving these

questions make a table like this:

Africa America Australasia Europe

L 0 1 1 1 3

H 1 1 6

P 2 1 6

R 1 1 6

4 8 5 4

21

(i) As the labour expert is half of each of the other, so the

only possible combination isL – 3HPR 6 each

(ii) Statement (d): If the number of Australasia expert is 1

less, i.e. total export are 20 American be twice as

each of other. The only combined possible is Americas

8.

Australasia 4 + 1 = 5

Europe 4

Africa 4

Now, we need to workout the various options possible

in the blank cells.


L 0 1 1 1 3

H 2 2 1 1 6

P 1 2 2 1 6

R 1 3 1 1 6

4 8 5 4

21



L 0 1 1 1 3

H 1 3 1 1 6

P 1 2 2 1 6

R 2 2 1 1 6

4 8 5 4

21


L 0 1 1 1 3

H 1 3 1 1 6

P 2 1 2 1 6

R 1 3 1 1 6

4 8 5 4

21

31. 4 32. 3 33. 3 34. 4

Solution for question 35 and 36: After 2nd round, team

goals for and goals against table can be drawn:

Team Round 1 and Round 2 combinations

Goals for → Goals

against

Goals for → Goals

against

Germany 2 → 1 1 → 0

Argentina 1 → 0 1 → 0

4 → 0 1 → 2 Not

possible Spain

5 → 1 0 → 1 Possible

Pakistan 2 → 0 0 → 1

1 → 2 0 → 4 Not

possible New

Zealand 0 → 1 1 → 5 Possible

South

Africa

1 → 2 0 → 2

35. 4 36. 2

Solutions for question 37 and 38: From the statements

from (a), (b), (c) given in the problem four teams (Spain, Ar-

gentina, Germany, Pakistan) appear to win their matches in the

fifth round. However, there are only three matches per round

and hence only three teams can win their matches in any

round. Hence, the data set appears to be inconsistent.

37. 4 38. 4

39. 3 The boats will be colliding after a time which is given

by;

20 4t hours 80 minutes

5 10 3= = =

+ .

After this time of 80 minutes, boat (1) has covered

5 2080 kms kms

60 3× = ,

whereas boat (2) has covered

1080 kms

60× =

40kms.

3

After 79 minutes, distance covered by the first boat =

d1 =

20 5– kms

3 60

After 79 minutes, distance covered by the second

boat = d2 =

40 10– kms

3 60

So the separation between the two boats

= 20 – ( )1 2d d+ = 1

kms4

Alternative method:

Relative speed of two boats = 5 + 10 = 15 km/hr

i.e. in 60 min they cover (together) = 15 km

∴ in 1 min they will cover (together) =15 1

km60 4

40. 2

2

x/2

x

In original rectangle ratio = x

2

In Smaller rectangle ratio = 2

x

2

Givenx 2

x 2 2x2

2

= ⇒ =

Area of smaller rectangle = x

2 x 2 2 sq. units2

× = =


35. 2 DC is the mandatory pair, which makes 3 and 4

incorrect. E is the opening statement. A concludes the

argument by substantiating the argument in EBCD.

Therefore, the analogy from the previous argument is

being extended in ‘A’ (keyword – “similarly”)

36. 4 From the options, it can be ascertained that ‘B’ is the

opening statement. Also, B explains “greater interest…

than”, hence ‘C’ is the natural antecedent to ‘B’, wherein

“a similar neglect” has been talked, about. Hence (4) is

the correct option.

37. 2 After reading statement B the first question that comes

to mind is what does ‘it’ stand for. The question is

answered by statement (E) which should be the logical

antecedent. This makes EB a mandatory pair and that

is present only in option (2).

38. 2 Option (2) talks about a ‘near’ friend. There is nothing

like a near friend. It should have been ‘close’ friend

39. 1 It should have been “I have my hands full”.

40. 3 It should have been “I can’t bear her being angry”.

41. 2 Answer choice (4), says that the danger being talked

about is ‘imminent’, which is not necessarily the case

as per the author in the passage, whereas the fact

that everyone is complacent about it, is being talked

about throughout the passage, which makes option

(2) correct.

42. 3 Options (1) and (4) are incorrect because these

choices are too narrow . Choice (3) is mentioned

directly in the passage in the last 3 paragraphs.

43. 1 This is the correct option as choice (2) is too narrow.

Choice (3) is a universal truth which may not be the

case. There could be a problem between 1 and 4 but

4 is ruled out because this option is one of the reasons

supporting the author’s argument but is not his key

argument as such. Moreover, the author does not say

that the crisis is imminent.

44. 4 In the 2nd paragraph, the author is being sarcastic

about the fact that the new production and refining

capacity will effortlessly bring demand and supply

back to balance. (line 2 onwards “the accepted …just

like that”) and he quotes Tommy Cooper to emphasize

his sarcasm. It must be remembered that we have to

consider the author’s point of view, not Tommy

Cooper’s. Therefore option (4) is correct

45. 4 Option (1) and (3) are contrary to what Derrida says

in the passage which makes them incorrect. There

can be a confusion between 2 and 4. Option (2) could

have been an inference if the statement had been

“Language limits our interpretations of reality”. But the

word ‘construction’ is incorrect. Therefore only option

(4) according to the passage, is correct.

46. 3 According to the passage, Derrida is against

logocentrism and choices (1), (2) and (4) are pro

logocentrism which leaves option (3) which is differ-

ent from logocentrism.

47. 1 This is a fact based question. In paragraph 2, refers

to line 5 “Rather, they exist … position”. Option (1)

directly follows from this line.

48. 1 Answer choice (4) is contrary to what is being said.

Answer choice (3) is irrelevant. There can be a

confusion between 1 and 2 but it must be noted that it

is not the meaning of the text which is based on binary

opposites but the interpretation. This leaves us only

with answer choice (1).

49. 1 Option (1) is a logical corollary to the passage. The

paragraph is silent about the audience of sodoku,

therefore (2) and (3) cannot be answers. Option (4)

is of extreme nature and thus ruled out.

50. 2 Option (1) is extreme. (3) is not talked about in the

passage 4th is not true according to the passage,

making (2) correct.

51. 3 Option (2) talks about humility which is not talked about

in the passage, option (3) is an extension of the

concept of being a minnow.

52. 1 The passage talks about hubris of civilization and

humility is a direct consequence thus … ‘humble’ is

correct. (2), (3) and (4) are not talked about in the

passage.

53. 2 The second sentence does not use the article. It should

be ‘As a/the project progresses” in sentence C there

should be the indefinite article ‘a’ before single-minded

which leaves us with option (2) as the correct answer.

54. 3 Sentence B should have “making them break apart”.

Sentence C should have “many offending chemicals”.

55. 2 B should be “rarely has …”

C should begin with ‘The’.

56. 1 Option B should be “since the Enlightenment.

Option C should be “in the 1820’s”

57. 3 Resurrecting i.e. bring back to practice is the best

choice. (1), (2) and (4) are negative options.

58. 3 Sputtering is a light popping sound of a flame which is

dying out. The ideas conveyed are dim and grim so

‘shining’, bright and effulgent are out.

59. 4 Such a scene should be distressing to a sensitive

traveler. Irritating and disgusting are negative options.

1 can be clearly ruled out.

60. 4 The one word reply conveys that it is terse. As it has

no element of humour we can easily rule out – “witty”.

Questions 61 to 64:

Note 61-64:

In any department in any given year; the average ages range

from 45 – 55 year.


(1) When a 25 year old joins; the avg. dips by around 5 to

6 yrs.

(2) When some 60 yrs old retires the avg. ages dips lesser

than in (1).

Marketing Total Age

2000 49.33 × 3 = 148

2001 44 × 4 = 176 here one faculty joined, age 25.

2002 45 × 4 = 180

2003 46 × 4 = 184

OB Total Age

2000 50.5 × 4 = 202

2001 51.5 × 4 = 200

2002 52.5 × 4 = 210

2003 47.8 × 5 = 239 One faculty joined, age 25.

Finance Total Age

2000 50.2 × 5 = 251

2001 49 × 4 = 196 Year 2001 one faculty retired age 60.

2002 45 × 5 = 225 One faculty joined age 25.

2003 46 × 5 = 230

OM Total Age

2000 45 × 6 = 270

2001 43 × 7 = 301 One faculty joined age 25.

2002 44 × 7 = 308

2003 45 × 7 = 315

61. 1 Clear from the data

62. 4 From the data of 2000: Let that person be X, on April 1,

2000 (age of Naresh) + (age of Devesh) + (age of X)

= 49.33 × 3 = 148 yr.

Now ages of Naresh/Devesh on 1 Apr. - 2000 ≡

52y 4m 10d

49y 4m 10d

+ + + + + _________________

(101y + 8m + 20d)

⇒ the age of X on 1-Apr-2000 is 47y + 3m + 10d

⇒ the X’s age on 1st April 2005 is ≡ (52y + 3m + 10d)

63. 3 Read the notes in the beginning, the average age dips

twice (from 2000–2001) & from (2001–2002). The dip

is more when a 25 yr old joins and lesser when

somebody retires.

64. 4 New faculty joined in 2001, on 1 April, 2001 his age

was 25 yrs. So on April 1, 2003, his age is 28 years.

65. 1 State Productivity (Tons per hectare)

Haryana19.2

63.2

=

Punjab24

64

=

Andhra Pradesh112

522.4

=

Uttar Pradesh67.2

416.8

=

Hence, Haryana and Punjab have the highest

productivity.

66. 2 Gujarat →24

51 = 0.47

Only per capita production of rice for Haryana, Punjab,

Maharashtra and Andhra Pradesh are greater than

0.47.

67. 4 As seen from the table

Haryana, Gujarat, Punjab, MP, Tamil Nadu, Maharashtra,

UP and AP are intensive rice producing states.

68. 1 Rahul and Yamini.

69. 2 Gayatri, Urvashi and Zeena, cannot attend atleast

more than one workshop.

70. 2 Anshul, Bushkant, Gayatri and Urvashi cannot attend

any of the workshops.

71. 4 1 16

2 15

3 14

4 13

5 12

6 11

7 10

8 9

We will have to draw two tables in the Question number

71. Winners after round two would be 1, 2, 3, 4, 5, 11,

10, 9 for 8 rounds respectively. As Lindsay is number

two she will play Venus Williams in quarter final.

72. 3 Elena is at number 6, Serena is at number 8

If they loose then table would be

1 9

2 7

3 11

4 5

Maria is number 1 she will play

Number 9, i.e. Nadia Petrova

73. 1 1 32

2 31

3 30

4 29

5 28

6 27

7 26

8 25

9 24

10 23

11 22

12 21

13 20

14 19

15 18

16 17


Matches in bold letters had upsets.

Then from the table would be winners are:

1, 31, 29, 5, 27, 7, 25, 9, 23, 11, 21, 13, 19, 15, 17

So for next round table is

1 17

31 15

3 19

29 13

5 21

27 11

7 23

25 9

No upset in second round hence table in next round is

1 9

15 7

3 11

13 5

We are given Maria is in semi-final. As we are not sure

what is the result of other games. Table is drawn as

below:

Table in next round could be:–

1 5/13

7/15 3/11

Hence Anastasia will play with Maria Sharapova.

74. 31 8

2 7

3 6

4 5

In this case Kim Clijster will either not reach semi final

or she will play Maria in semi final.

Hence she cannot play Maria in final.

75. 1 The minimum return will be gained if the extraordinary

performing stocks (double & 1.5 growth) are the ones

whose expected returns are lowest (i.e. 10% & 20%).

Taking the minimum value of the expected returns as

10. We have to see which of the two values of 10 and

20 multiplied by 2 and 1.5 and vice versa yields the

minimum value.

Hence comparing the minimum value between

20 × 2 + 10 × 1.5 and 20 × 1.5 + 10 × 2, the 2nd one is

minimum. Hence the minimum average return is

20 1.5 10 2 30 4030%

4

× + × + +=

76. 2 If the average return is 35%, then the total return is

35 × 4 = 140.

The only possible arrangement of 140 being

40 × 1.5 + 30 + 20 × 2 + 10.

A = 20 × 2 (Cement or IT)

B = 10

C = 30

D = 40 (1.5) (Steel or Auto)

From the data given in the question we see that A has

to be Cement or IT.

D is Steel or Auto.

Hence statements (II) and (III) are correct.

77. 3 Total return is 38.75 × 4 = 155

The possible arrangement is

20 + 10 + 30 × 1.5 + 40 × 2

Hence

A = 20, B = 10, C = 30 (Steel or Auto)

D = 40 (Cement or IT)

Hence, statements (I) and (IV) are correct.

Hence (3).

78. 2 Given C … Cement or IT industry

C’s Return is 30 × 2 = 60%

Among the other values we see that the possible

arrangements can be

10 × 1.5 + 20 + 40, 10 + 20 × 1.5 + 40, 40 + 20 + 40 ×

1.5

The average returns will be in each case

10 × 1.5 + 20 + 40 + 60

4 (33.75%),

10 + 20 × 1.5 + 40 + 60

4 (35%),

40 + 20 + 40 × 1.5 + 60

4 (45%).

Considering 33.75% as the valid value, then B be-

longs to the Auto industry.

Hence (II) and (IV) are correct.

Hence (2)

Questions 79 to 82:

L = London, Paris = P, New York= NY, Beijing = B

In round III, one of the two cities, either London or Paris will get

38 votes and the other 37. Further:

1) The persons representing London, Paris, Beijing and

New York can not vote as long as their own cities are

in contention. In round I, New York gets eliminated and

hence the representative from NY becomes eligible

for voting in the II round hence increasing the total

votes by 1. This means the total votes in the first

round must be 83 – 1 = 82.

2) After round II, the representative from Beijing votes in

the III round. This should have increased the number

of total votes by 1 and the total votes must have

become 83 + 1 = 84.

We are given that the total votes in round III are 75

only. We conclude that 84 – 75 = 9 people who voted

in round I and II have become ineligible for voting in

round III.


3) 9 people who have voted in round I and II become

ineligible for voting in round III. The reason of their

ineligibility is that till round I and II, they have already

voted for two different cities which are not available

for contention in round III. All of these 9 voters are

those who voted for NY in round I and then voted for

Beijing in round II.

4) Beijing’s vote in round II is 21. This includes 9 votes

from people who voted for NY in the first round. So 21

– 9 = 12 people voted for Beijing in both round I and II.

5) We are given that 75% of the people who voted for

Beijing in round I, voted again for Beijing in round II as

well. So, 16 people must have voted for Beijing in

round I.

6) In round I we have:

82 = L + P + B + NY

Or

82 = 30 + P + 16 + 12

Giving P = 24

7) In round II we have:

83 = L + 32 + 21, giving L = 30

8) NY had 12 votes in round I. 9 of these votes went to

B(see point 2 , again). The rest 3 went to P.

9) 16 votes for B in round I. 12 of them still vote for B. The

rest 4 voted for either L or P. As L has the same

number of votes in both the rounds I and II. This means

in round II, these 4 votes must have gone to Paris only.

10) The representative from NY did not vote in round I. But

has voted in round II. As L has the same people voting

for it (30 votes in both the rounds I and II) and we

know the exact break up of B in II. This NY-represen-

tative vote must go to Paris only. Further, in order to

avoid ineligibility, this NY rep must vote for Paris only in

round III also.

11) Paris (in round II) break up is:

32 = 24 ( from round I, who voted for Paris )

+ 4 ( out of the 16, who voted for Beijing in round I)

+ 3( out of 12, who voted for NY in round I )

+ 1 (NY -Rep)

12) Beijing gets eliminated in round II. So the rep of Beijing

can vote in round III.

13) 12 People (out of 21) who voted for Beijing in round II

are still eligible for vote in round III.

14) 50% of people who voted for Beijing in I ( i.e. 8 People)

voted for Paris in round III. These 8 People include 4 of

those who voted for Paris in round II also. Therefore

4(out of 12 who voted for Beijing in round II and are

still eligible for vote in round III ) people have voted for

Paris in round III.

15 ) This implies that the rest 8(out of 12 who voted for

Beijing in round II and are still eligible for vote in round

III ) can vote for London only. This makes London’s

vote = 30+ 8 or 38 in round III. Which implies that Paris

got 37 votes.

16) The Beijing Rep who is eligible to vote in round III must

have voted for Paris only.

The following table sums up the Vote Pattern:

RoundTotal

VotesLondon (L) Paris(P) Beijing (B)

New

York

(NY)

I 82 30 24 16 12

II 83 3032 = ( 24 + 4 + 3

+ 1 of NY-rep)21 (12 + 9) X

III 75 38 = (30 + 8)37= (32 + 4 + 1

of B-rep )X X

(The Data Shown in Bold was already provided in the prob-

lem. The other data is deduced from the solution.)

79. 4 Required percentage = 9

10012

× = 75%

80. 4 As seen from the table. Paris got 24 votes.

81. 4 Required percentage = 8

10012

× = 66.67%

82. 1 Based on the table IOC members from New York must

have voted for Paris in round (2).

Questions 83 to 86: The given information can be shown

below:

States Firm A Firm B Firm C Firm D

UP 49 82 80 55

Bihar 69 72 70 65

MP 72 63 72 65

Total 190 217 222 185

83. 2 As Truthful Ltd. has highest market share hence

Truthful Ltd. can be A or C.

From neutral statement either B and C are aggressive

and honest or A and D are aggressive and honest.

According to statement 1 of question 83, B is profitable,

then A and D are aggressive and honest.

Then honest total revenue cannot be more than that of

profitable, hence statement 2 is false.

84. 3 According to statement 1 aggressive is (B). Then

Honest Ltd. has to be C (as given in neutral statement).

Then statement 2 is also true have Honest Ltd’s. lowest

revenue is from Bihar.

Hence answer (3).

85. 3 B is honest according to Statement 1

Atmost only one statement can be true as both give

Aggressive and Honest as firm B.

Firm B cannot have two names.

86. 3 Profitable can be either A or D. Then aggressive and

honest has to be B and C. Hence truthful is A or D.

And for both A and D lowest revenue is from UP.

Hence choice (3).


Questions 87 to 90:

• 17 in TR

FR ER

TR (17 )

• 10 in TR also in at least one more ⇒ 7 in TR alone

FR ER

TR (17)

7

• TR alone = one less than ER alone ⇒ ER alone = 8

• ER alone = double of all 3 ⇒ In all three = 8

42

=

FR ER

TR (17)

7

8

x y4

• FR alone = (FR and ER)

FR ER

TR (17)

7

8

x y4

p q

⇒ p = q + 4 ...(1)

Total = 37

[7 + 8 + p + (x + y + q) + 4]

= 37 [p + q = 12]

⇒ p – a = 4 ⇒ p = 8 and q = 4

FR ER

TR (17)

7

8

x y4

8 4(16 + x)

(16 + y)

Now, total number of FR is maximum

⇒ 8 + 4 + 4 + x > 8 + 4 + 4 + y

⇒ x > y and x + y = 6

as n(TR) = 17 = x + y + 4 + 7

⇒ x = {4, 5, 6}

y = {0, 1, 2}

87. 3 Both FR and TR but not ER

= x

Minimum x = 4

88. 1 Option (2) and option (3) are superfluous. They are

not required.

Option (1), if given, would tell us the value of x = 4 and

hence y = 2.

89. 2 Out of 4 who are in all three projects, 2 move out of FR

and one-one move out of ER and TR.

FR (14 + x) ER (15 + y)

TR (16)

7

8

x + 1 y+ 2

Null

8 5 (= 1 + 4 )

Minimum in FR = 14 + x = 14 + 4 = 18

Maximum in ER = 15 + y = 15 + 2 = 17

{ }{ }

As

x 4, 5, 6

y 0,1, 2

= =

Hence, option (2).

90. 4 FR and ER = 5

ER and TR = y + 2

⇒ 5 = y + 2

⇒ y = 3;

which is not a possible value as y is 0, 1, or 2 only.

⇒ option (4)

Inconsistent data.


1 1 2 3 3 4 4 5 5 5 6 3 7 1 8 1 9 4 10 5

11 4 12 2 13 2 14 2 15 3 16 3 17 2 18 1 19 5 20 4

21 5 22 2,3 23 1,4 24 4 25 3 26 5 27 1 28 2 29 3 30 4

31 2 32 1 33 4 34 5 35 3 36 3 37 2 38 5 39 1 40 4

41 3 42 1 43 4 44 2 45 4 46 3 47 5 48 4 49 2 50 1

51 1 52 2 53 1 54 2 55 5 56 2 57 2 58 4 59 2 60 4

61 2 62 4 63 1 64 4 65 4 66 3 67 2 68 5 69 1 70 5

71 5 72 5 73 2 74 5 75 3

CAT PAPER � 2006


LRDI 1 to 25 25

EU + RC 26 to 50 25

QA 51 to 75 25

Total 75

Total

questions

Total

attempted

Total

correctTotal

wrong

Net

Score

Time

Taken

Question

number

SUP-0003/09



From statement one, team would include exactly one among P,

R, S

⇒ P (or) R (or) S.

From statement two, team would include either M, or Q

⇒ M but not Q

(or) Q but not M

From statement three, if a team includes K, it will include L or

vice versa.

⇒ K, L always accompany each other.

From statement four, if one of S, U, W is included, then the

other two also have to be included.

⇒ S, U, W are always together.

From statement five, L and N cannot be included together

⇒ L, N are never together.

From statement six, L and U cannot be included together.

⇒ L, U are never together.

1. 1 From statements one and two;

one of P, R, S and

one of M, Q are to be selected. We require one more

member.

But from statement three; (K, L) are always together.

Hence 'L' cannot be included in a team of 3 members.

2. 3 Again, from statement one;

one of P, R, S has to be selected.

To make a team of '5'

'S' will be chosen (which leaves out P and R)

⇒ If 'S' is chosen 'U' and ‘W’ have to be chosen

(statement four)

⇒ If 'U' is chosen 'L' cannot be chosen (statement

five)

⇒ K cannot be chosen (statement three)

And from statement two; one of M (or) Q has to be

chosen.

3. 4 From statements one and two

Two members are to be selected.

Of the remaining seven;

To maximize the size of the team.

We would chose S,

⇒ U and W are included in the team (statement four)

We cannot include K (or) L because we would then

have to leave out N and U (from statements five and

six)

4. 5 If 'K' is included 'L' has to be included (statement three)

If 'L' is chosen neither N nor U can be chosen

(statements five and six)

⇒ S, W are also not included because S, U, W have to

be always together. (Statement four)

Hence one of P (or) R would be selected (statement

one) and one of M (or) Q would be selected statement

(two)

(K, L) and two of the above five have to be included.

5. 5 If a team includes N, it cannot include 'L'.

And therefore not even 'K' (from statement five and

three)

According to statement one

One of P (or) R (or) S has to be included.

According to statement two

One of M (or) Q has to be selected.

So the following cases are possible

P Q N,

R Q N

P M N,

R M N

If 'S' is selected

S U W M N

S U W Q N

are the only possible cases.

Hence in all 4 + 2 = 6 ways can be constituted.


6. 3 Let Dipan get x marks in paper II

Dipan's average in PCB group = 98

Maths group = 95

S.S. group = 95.5

Vernacular group = 95

English group = +

96 x

2

Sum of all = 96 × 5

So 95.5 + 96 × 3 + +x

482

= 96 × 5

⇒ = × − −x

96 2 95.5 482

( )= − = × =x 2 96.5 48 2 48.5 97

So, answer is (3)

7. 1 The only boy getting 95 in atleast one of the subjects

of the group among all the groups is Dipan.

So answer is option (1).


8. 1 A group score of 100 in Social Science would have

Increased the scores as follows:

Score Increase

Group Score

Final Score Increase

Final group Score

Pritam 22 11 =

112.2

5

96.1

Joseph 9 4.5 =

4.5.9

5

95.9

Tirna 21 10.5 =

10.52.1

5

95.8

Agni 9 4.5 =

4.5.9

5

95.4

So, the order is Pritam > Joseph > Trina > Agni.

Option (1).

9. 4 The student having atleast 95 in every group is Dipan,

so the answer is Dipan, option (4).

10. 5 Let us increase the score in one of the subjects of the

following candidates

Least Scores Contribution in net Score

Final Score

Ram 94 in group of 2 3 in 5 groups

96.1 + .6 = 96.7

Agni 82 in group of 2 9 in 5 groups

94.3 + 1.8 = 96.1

Pritam 83 in group of 2 8.5 in 5 groups

93.9 + 1.7 = 95.6

Ayesha 93 in group of 2 3.5 in 5 groups

96.2 + .7 = 96.9

Dipan 95 in group of 1 5 in 5 groups

96 + 1 = 97.0

So, Dipan will end with a highest total.

So the answer is option (5).


As only Paul Erdös was having an Erdös number of zero so

the minimum Erdös number among A, B, C, D, E, F, G, H should

be 1 or greater than one. At the end of the third day F co-

authored a paper with A and C. F had the minimum Erdös

number among the 8 people. So if F's Erdös number is y, then

A and C's Erdös number should change to (y + 1) after third

day. As A and C decreased the average by maximum possible

extent, it means C had the second-height Erdös number among

all eight, as A had an Erdös number of infinity. Suppose Erdös

numbers of A, B, C, D, E, F, G, H are y + 1, b, y + 1, c, d, e, y,

g, h respectively at the end of third day.

∴ (y + 1 + b + y + 1 + c + d + e + y + g + h) = 24 = (3 × 8)

3y + 2 + b + c + d + g + h = 24

When E co-authored with F, the average Erdös number reduced

again, it means, E's Erdös number was not the same with A &

C initially. As at the end of third day, 5 people had same Erdös

number, they should be A, C and any 3 out of B, D, G, H.

Suppose those 3 people are B, D, G. Then

(3y + 2 + y + 1 + y + 1 + h) = 24

6y + h + e = 19 …(i)

On the fifth day E co-authored a paper with F and hence Erdös

number of E changed to (y + 1). Also the average decreased

by 0.5 that means the total decreased by

Hence, e - (y + 1) = 4

⇒ e – y = 5

Putting the value of e in equation (i), we get

6y + h + (5 + y) = 19

7y + h = 14

Only possible value of y = 1 as h cannot be zero.

So after 3rd round Erdös number of A, C, E, F were 2, 2, 2, 1

respectively.

11. 4 Only A, C, E changed their Erdös number, rest 5 did not

change their Erdös number.

12. 2 At the end of conference 6 people including E were

having an Erdös number of 2 and F was having 1 as

Erdös number. So 8th person was having an Erdös

number of [20 – (2 × 6 + 1)] = 7

13. 2 As at the end of 3rd round 5 people were having

same Erdös number. A and C changed their Erdös

number after coauthoring with F. So, the other 3 would

have same Erdös number in the beginning.

14. 2 2

15. 3 After co-authoring with F, E was having Erdös number

of 2, which was 4 less than initial Erdös number of E.

So answer is 2 + 4 = 6.



16. 3 Day

1Day 2

Day 3

Day 4

Day 5

Startprice

100 90 100 110 120

End price 90 100 110 120 110

In the above table Chetan sold shares on Day 2, Day 3

and Day 4 whereas Michael sold shares on Day 4

only.

Therefore at the end of day 3 the price of Share is Rs.

110.

17. 2 Day

1Day 2

Day 3

Day 4

Day 5

Startprice

100 90 100 110 100

End price 90 100 110 100 100

Let initial amount with Chetan and Michael is y.

Total Money with Chetan = y - 900 + 1000 + 1100 +

1200 - 1100 = y + 1300

Total money with Michael = y

Therefore Chetan ended up with Rs.1300 more cash

than Michael.

Therefore at the end of day 4 the price of Share is

Rs. 100.

18. 1 Day

1Day 2

Day 3

Day 4

Day 5

Startprice

100 90 80 90 100

End price 90 80 90 100 110

Assume initial number of share with Chetan and Michael

is x. In the above table Chetan buy 10 share each on

day 1, day 2 and sold 10 share on day 3, day 4 and

day 5.

∴ Total shares with Chetan is x - 10.

In the above table Michael buy shares only on day 2.

∴ Total shares with Michael is x + 10.

∴ Michael had 20 shares more then Chetan.

Therefore at the end of day 3 the price of share is Rs.

90.

19. 5 Day

1Day 2

Day 3

Day 4

Day 5

Startprice

100 90 100 110 120

End price 90 80 110 120 110

Let initial amount with Chetan and Michael is Y.

Total money with Chetan = Y - 900 + 1000 + 1100 +

1200 - 1100 = Y + 1300

Total money with Michael = Y + 1200

Therefore difference between Chetan and Michael is

Rs. 100 and Number of shares with Michael and Chetan

is same.

20. 4 Day

1Day 2

Day 3

Day 4

Day 5

Startprice

100 110 120 130 120

End price 110 120 130 120 110

Let initial amount with Chetan and Michael is Y.

Chetan sold shares on Day 1, Day 2, Day 3 whereas

buys shares on Day 4 and Day 5.

Total Money with Chetan is = Y + 110 × 10 + 120 × 10

+ 130 × 10 - 120 × 10 - 110 × 10 = Y + 1300

Total money with Michael = Y + 1200

Total money with Michael = Y + 120 × 10 + 130 × 10 +

120 × 10 = Y + 3700

Total money with Michael & Chetan = 2Y + 5000.

Therefore maximum possible increase is 5000.


In this set the fuel cost for each of the path is given. In addition

there are four toll collection junctions.

21. 5 No traffic flows on the street from D to T

Now we have fuel cost on different paths as

SAT 9 + 5 = Rs. 14 + toll at junction A

SBAT 2 + 2 + 5 = Rs. 9 + toll at junction B and D

SBCT 2 3 + 2 = Rs. 7 + toll at junction B and C

SDCT 7 + 1 + 2 = Rs. 10 + toll at junction D and C

Now checking the options we find that toll at junction

A is 0 or 1.

When toll is 0, fuel cost on SAT = 14 + 0 = Rs. 14

When toll is 1, fuel cost on SAT = 14 + 1 = Rs. 15

The fuel cost on all the paths should be equal.

Option, (1), (2), (3) can be ruled out as in all these

options toll at C and D adds up to more than Rs. 5. As

fuel cost on SDCT is Rs. 10 without toll, so with toll it

cannot exceed Rs. 15 (i.e. toll of path SAT).

Option (4) is ruled out as in this option SAT comes out

to be Rs. 14 and SDCT sums up to 15.

Correct answer is option (5).


22. 2 & 3

Available routes are

SAT → Rs. 14

SBAT → Rs. 9

SDCT → Rs. 10

SDT → Rs. 13

Now fuel cost of SAT - fuel of SDT = 14 – 13 = Rs. 1.

Hence toll at junction D should be 1 more than the toll at

A. So option (1), (4) and (5) are ruled out.

Now fuel cost of SAT - fuel cost of SBAT = 14 – 9 =

Rs. 5. So toll at junction B should be Rs. 5. So answer

could be either (2) or option (3).

23. 1 & 4

Note: Both the options (1) and (4) are correct.

Available paths considering no toll are

SAT → Rs. 14

SBCT → Rs. 7

SBAT → Rs. 9

SDCT → Rs. 10

SDT → Rs. 13

Fuel cost on path SAT - fuel cost on SDT = 14 - 13 =

Rs. 1, toll at junction D should be 1 more than the toll at

junction A.

So option (2), (3) and (5) are ruled out.

Checking options (1) and (4).

When A = 0, paths SAT, SBAT and SDT are equally

likely to be taken by a motorist.

When A = 1, toll at B and C should be equal to Rs. 5

and Rs. 3 respectively.

24. 4 Available routes are

SAT → Rs. 14

SBAT → Rs. 9

SBCT → Rs. 7

SDCT → Rs. 10

SDT → Rs. 13

Fuel cost on path SAT - fuel cost on path SDT = 14 - 13

= Rs. 1.

So the toll at junction D should be 1 more than toll at

junction A. So option 1 and 3 are ruled out.

Fuel cost on path SAT - fuel cost on path SBCT = 14 -

7 = Rs. 7.

So sum of toll at junction B and C should be 7 more

than the toll at A. Hence only option (4) matches.

25. 3 We have to find a path on which minimum cost is

incurred and such that total traffic through B does not

exceed 70%

So, option (5) is ruled out because we can send al

traffic through SDCT or SDT and meet all conditions.

Option (1) is also ruled out as in that case all traffic will

be passed through SBCT [not possible as traffic at B

can't be more than 70%]

Option (2) is also ruled out as it is possible only when

toll at junction C is 2. In that case also all traffic will

pass through B.

Option (3) can be the answer, when toll at junction B

is 4 and toll at junction C is 0. Then SDCT will have toll

equal to Rs. 10.

As Rs. 10 is lesser than Rs. 13 so option (4) is also

ruled out.

Answer is option (3).

26. 5 The paragraph stresses on the relationships between

the factories, dealers and the consumers. Every entity

has certain short-term expectations from each other.

This makes these relationships strenuous. This strain

leads to feelings of mistrust and lack of commitment.

So the longer this continues, the more the chances of

everyone succumbing to this vicious trap and they

would soon realize that they have sacrificed long-

term stability and gain for short-term benefits. Hence

Option (5). Option (4) is too specific to industry (at the

cost of the other players – dealers and customers),

option (2) suffers from the same short-comings

together with throwing the technical (unexplained)

jargon ‘supply chain’ to us. Option (1) takes into account

only 2 players and repeats what is stated in the

passage about “dealers adjusting prices and making

deals” in the term ‘Deal making’; option (3) seems close

but can be eliminated as the word ‘adversary’ is too

strong. The passage implies that everyone tries to

maximize his benefits, not that they ‘oppose’ one

another.

27. 1 The passage heads towards describing the functions

that bad / good maps (and therefore theories) serve.

Just as a ‘Bad theory’ does not help us understand a

problem, a ‘good theory’ is invaluable to us, though it

may be simplified. ‘Simplified’ here implies that less

valuable information is left out. According to this logic,

option (2), (3), (4), get eliminated. Option (5) is close

but more negative in tone than required. The word

‘limitation’ here indicates a short coming whereas the

passage implies that it is a simplification as it would

not be of practical use otherwise.

28. 2 Going with the direction of the passage, the last line is

stating ‘now all players “profess” to seek only peace’.

Profess means to mask or to pretend. Thus option (2)

which talks about the veil being lifted is the most logical

statement that completes the passage. More so this

also follows from the source of the text.

29. 3 The answer is very direct. With every statement of

his, the author seeks to show how foolish those people

are who call his advice ‘rules’. After his first statement

he has posed the rhetorical question “Call that a rule?”

The same should follow after his second “scarcely a

rule!”



Using the given expressions —

1 1

22 2

2 23 3

2 2 34 4

3 2 2 35 5

3 3 2 46 6

a p b q

a pq b q

a p q b pq

a p q b pq

a p q b p q

a p q b p q

= =

= =

= =

= =

= =

= =

and so on

24. 1 ( )n n n n

–1 12 2 2 2

n na b n is even p q p q+

+ = +

( ) ( )n–1

2q pq p q= +

25. 4 ( )n 1 n 1 n 1 n 1

2 2 2 2n na b n is odd p q p q

+ − − +

+ = +

( )( )n–1

2p q pq= +

Substituting1 2

p and q3 3

= =

n 1

2n n

2a b

9

− + =

Substituting n = 7, n na b 0.01+ >

Substituting n = 9, n na b 0.01+ <

Hence smallest value of n is 9

26. 1 As the diet should contain 10% minerals and only twoingredient contains 10% minerals i.e. O and Q.Hence only by mixing O and Q a diet with 10% mineralscan be formed.Hence, there is only one way.

27. 4 The required diet can be formed by mixing P and S orQ and S only but the lowest cost per unit can beachieved by Q and S only.

28. 5 To make a diet with atleast 60% carbohydrates wecan use option (2) or (5) only but the lowest cost perunit can be achieved when P, Q and S are mixed in theratio 4 : 1 : 1.

29. 5 As the ingredients are fixed in equal amounts, so wecan take the average of the constituent percentage ofthe elements used.Only option O and S satisfies all the conditions.

30. 1 From statement A, it is clear that 40% of top academicperformers are athletes and that is equal to 10. Sototal number of academic performers can be calculated.Statement B does not provide any relevant information.So the answer is (1).

31. 4 Statement A and B alone are not sufficient but if bothare combined, then we can form the followingsequence:

1 2 3 4 5

D E B C A

So the answer is (4).

32. 3 Statement A alone is sufficient because 10% of thefemale employees have engineering background, 70%of the employees are females, so 7% of the employeesare female and having engineering background. Hence,18% of the employees are male and havingengineering background. From statement B, we knowthe number of male employees having engineeringbackground. So, the percentage of male employeeshaving engineering background can be calculated. So,the answer is (3)

33. 5 Statement A alone is not sufficient because it is notgiving any information about the opponent. StatementB alone also not sufficient because it is not giving anyinformation regarding the performance of Mahindra &Mahindra in the second half. Even if both thestatements are used we will have two cases.

M & M 0 1

Opponent 3 4

So in one case match is drawn and in another case itis won by Mahindra & Mahindra.Hence the answer is (5)


Looking at the values in the table one can easily conclude thatthe costs which are directly proportional to the change involume of proportion are ‘Material’, ‘Labour’ and ‘Operatingcost of machines’. Rest of the costs are all fixed costs. If ‘x’ isthe number of units produced in 2007 then the total cost ofproduction would beC = 9600 (Fixed cost) + 100x (Variable cost)Variable cost = 100x because as the number of units for 2006is 1200 and variable cost for that is 120000 i.e. 100 times thenumber of units.

34. 2 Total cost = 9600 + 100 × 1400 = 149600

Cost per unit = ( )149600107 approx.

1400=


35. 3 To avoid any loss the total selling price should beequal to the total cost price. If ‘x’ units are producedand selling price of each unit is 125 Rs.Therefore, 125x = 9600 + 100x25x = 9600

x 384⇒ =Hence, 384 units should be produced.

36. 5 Same as in question number 36 profit would bemaximum if the number of units are maximum i.e. 2000

37. 1 If the company sells a maximum of 1400 units, theselling price is fixed at Rs. 125 per unit. If more than1400 units are sold, the selling price is reduced toRs. 120 per unit. The company cannot sell more than1700 units.To earn maximum profit at a unit selling price ofRs. 125, the company must sell 1400 units. Themaximum profit earned, denoted by P0, is calculatedas below:

Profit = (Selling Price) – (Cost Price)P0 = 125 × 1400 – (9600 + 100 × 1400) = Rs. 25400

Now if the company sells an x number of units(x > 1400) then the profit earned will be:Px = 120 × x – (9600 + 100 × x) = 20 × x – 9600

The minimum value of x for which Px will be more thanP0 must satisfy the following inequality:

20 × x – 9600 > 25400

⇒ x > 1750

As only a maximum of 1700 units can be sold, Px willnever be more than P0. Hence the maximum profit thatcan be earned is Rs. 25400 only.Hence (1) is correct.


From the given information the following table can be formed:

M F V NV Total

Class 12 48 32 32 48 80

Class 11 44 36 40 40 80

Secondary Section

288 352 352 288 640

Total 380 420 424 800

38. 2 From the above tablePercentage of male students in the secondary section

=288

100 45%640

× =

39. 5 From the above tableMale vegetarians = 8Female vegetarians = 24So, their difference is 16.

40. 1 Percentage of vegetarian students in Class 12 =

32100 40%

80× =

41. From the main table

M F V Male Veg

Female Veg

Total

Class 12 48 32 32 80 Class 11 44 36 40 80 Secondary Section

288 352 352 320 320 640

Total 380 420 424 800

This question is wrong because the number of Malevegetarian cannot be greater than 288.

42. 3 For Malaysia, total cost= (11,000 + 6,000) + (10,000 + 8,000) + (10,000 +8,000)= US$ 47,000 (minimum)Hence, the answer is Malaysia

43. 1 In India, total cost in US$ = 8,500 + 9,000 = 17,500which is maximumHence, the answer is India.

44. 4 In India, total cost in US$ = 3000 + 5000 + 1500

32.89

(transportation cost)= 8456.06In Thailand, total cost in US$ = 4500 + 6000 = 10,500Difference in amount is 10,500 – 8456.06 = US$ 2044

≈ 67,500 Bahts

45. 2 In India, total cost for spirial fusion in US$ =

5500 40.9286431.5

35

×=

In Singapore, total cost for spirial fusion in US$ = 9000

Difference (in US$) is 9000 – 6431.5 = 2568.5 2500≈

46. 4 For the shortest route we have to consider the pathA-C-F-J.Following table compiles the distance and thecorresponding price.

Path Distance Price

A-C 790 1350 C-F 410 430 F-J 970 1150 Total 2170 2930

Hence the price for travelling by the shortest route isRs. 2930.


47. 2 For the lowest price we have to consider the pathA-H-J.Following table compiles the distance and thecorresponding price.

Path Distance Price

A-H 1950 1850 H-J 400 425 Total 2350 2275

If the company charges 5% below the minimum priceof Rs. 2275 then it should charge 0.95 × 2275= Rs. 2161

48. 3 If airports C, D and H are closed, then the passengermust follow the path A-F-J for minimum price.Following table compiles the distance and thecorresponding price.

Path Distance Price

A-F 1345 1700 F-J 970 1150 Total 2315 2850

So the corresponding minimum price paid by apassenger is Rs. 2850.

49. 2 For minimum cost per km, we have to consider thepath A-H-JFrom solution of question 47, we know the distanceof path A-H-J is 2350 km and the price is Rs. 2275.The price include a margin of 10%.So, the minimum cost per km =

10 12275 0.88

11 2350× × =

50. 4 For minimum cost per km, again we have to considerthe path A-H-J as illustrated in the solution of question49.The distance of path A-H-J is 2350 km.

51. 5 ‘Reciprocal roles determine normative human behaviourin society’.This is the main idea of the passage that is carriedthroughout. Note that ‘role of biology’ is negated and‘reciprocal roles’ are affirmed in paragraph 1 and 2.

52. 2 ‘We would not have been offended by the fatherplaying his role ‘tongue in cheek’’.All the other options would have been false if biologicallinkages would have structured human society.

53. 4 The last para where the author mentions the examplesof a waitress and clergyman, and driver refers to thealignment of self with the rules being performed andsociety preventing manifestation of the true self.

54. 1 C and EIn (A) ‘to’ is redundant.In (B) ‘hands on about Israel’.In (D) a Shaliach, a sort of recruiter to Minneapolis.

55. 5 B onlyIn (A) ‘into’ should be used in place of ‘in’In (C) the article is missing before the word ‘slump’In (D) the singular form ‘stimulus’ should be used inplace of ‘stimuli’In (E) ‘effect’ should be used in place of ‘affect’

56. 3 B and DIn (A) ‘said’ should be used instead of ‘told’In (C) ‘handed down to’ should be used in place of‘handed to’In (E) a subject is required after ‘hence’

57. 2 ‘The difference between two artistic interpretations’Refer the last three lines of the 1st para where theauthor talks about the gap between the two artisticinterpretations within the depth of the creative powerand doesn’t mention width.

58. 1 ‘Define the place of the poet in his culture’.The lines starting with “But suddenly I understood…..”define the position of the poet in his culture.

59. 4 Refer to the 5th line of the 2nd para. Here the term"adventures of experience" refers to the poet & artistswho over vitalize and enrich the past for us.

60. 5 “The personification of a whole organization is a textualdevice …” is the choice which continues the theme inthe last two lines of the paragraph in the best possibleway. The latter half of the paragraph is talking aboutpersonification of whole organizations and this is thechoice which completes the paragraph satisfactorily.The choice justifies why whole organizations arepersonified even though they cannot speak ascharacters.

61. 1 ‘Yet despite these technical developments…… …careabout’.In the first line of the paragraph the author speaksabout the magical allure still retained by photographs.Then he goes on to describe the negative effects oftechnological advancements on the same. Thus, inline with the first idea (1) describes how photographsare still holding out against these negative effects.

62. 2 ‘No inventory would ever include those, ofcourse’.Thepara starts with listing out ‘the inventory’. The optionwhich says ‘what she lacked………..naturalshrewdness’ is beyond the scope of the argument. Allthe options can be easily eliminated. ‘Those’ in theoption ‘No inventory would ever include those,ofcourse’, refers to human intuition and intelligence ofMma Ramotswe.

CAT PAPER – 2003(Re-Test) Explanations Page 23

101. 1 Is a sitter, its just simple addition and subtraction, FRG

+ CZE = 43.01 and US Total = 42.83

Hence difference in time = 43.01 – 42.83 = 0.18

102. 2 The first two rankers of final score are 8905 and

8897. The third ranker is carrying a score of 8880. So

he needs to score 8881 to get a bronze, whereas his

sum is 582 + 3003 = 3585.

Least score required = 8881 – 3585 = 5296

103. 2 Based on score 2 – Michael Smith is 9th which means

that if we exclude Daley Thompson there are 9 people

below him. Based on High-Jump alone Michael would

be 3rd last and on Pole Vault he would be 9th again.

Which means that Michael needs to ensure that he is

ahead of the same two guys in the Long Jump to keep

the same position.

104. 2 Here you need to compare the ratio as which of the

following is the highest 189

561,

209

587 and rest of the

option have equal value.

Now you can see that 209

587 is greater than

189

561.

105. 1 Population of the Chaidesh is lowest for lowest per

capita availability of Tea wrt production, i.e. for 1995.

106. 1 From 96 to 99 in each year the production has increased

but the area has decreased. Therefore, the production

in unit per area is highest in 1999.

107. 3 Cement Limestone Power Wages

93 94 100 20 25 15

02 03 104 21 27 15.8

−

−

So percentage profit = 104 (21 27 15.8)

100104

− + +×

40.2100 38.65%

104= × =

108. 2

Steel Power Wages Iron Ore

93 94 100 30 10 25

02 03 105.5 32.4 10.53 26.5

−

−

So percentage profit

= 105.5 (32.4 10.53 26.5)

100105.5

− + +×

= 34.18%

109. 1 You only need to see the the particular row in the table

for the given options and for Power it experienced

continuous rise.

110. 4 Again for timber and wages experienced declined

only once for the given period.


The table consists of sorting the different nations according to

the birth rate and death rate. The only thing to remember is that

if two countries have same rank (3), then next country will get

(5) rank. So

rank of Philippines is 33,

rank of Spain is 17,

rank of Taiwan is 28.

In-between total 9 countries.

In consolidated list 37th country is Venezuela.

In last question, we have to check last country of South America

(42, 11) and last country of Africa (50, 28). In-between there

are 8 countries of Asia.

111. 2

112. 1

113. 4

114. 1

115. 3 March rainfall is lower than September rainfall in every

location. Just check the bar graph.

116. 2 Peak rainfall occurs in April. Just check the bar graph.

For questions 117 to 119: Based on observation only.

117. 3 4 and 2

118. 4 5

119. 4 Egg and onion.

120. 4 According to statement (1), A which has the third

highest profitability has the lowest operating income

in 2002-03.

According to statement (2), company D has the highest

combined operating income and has the lowest

operating profit.

According to statement (3), only company B has higher

operating income in 2001-02 than 2002-03, and has

higher profitability in 2002-03 than 2001-02.

According to statement (4), the companies having

profitability between 10-20% are A, C, E but C has

operating income equal to 200 crore.

So the answer is 4.

121. 3 Operating profit of companies is:

A = 15

B = 7.75

C = 30

D = 3

E = 35

F = 20

So the answer is E.

CAT PAPER – 2003(Re-Test) ExplanationsPage 24

122. 1 The companies excluded are B and D. As both of them

have –ve profitability, the answer is –ve. So the

answer is (1).

123. 4 Companies exceeding profitability of 10% are C and E.

So the average is ( )30 35

32.52

+= .


Increase of HP is from 884 to 970, i.e. 86

Increase of Kerala is from 1004 to 1058, i.e. 54

Increase of Punjab is from 832 to 874, i.e. 42

Increase of Assam is 919 to 932, i.e. 13

Increase of J & K is 882 to 900, i.e. 18

124. 2 HP and Kerala are highest.

125. 3 Goa (1091 to 960)

Tamil Nadu (1044 to 986)

Bihar (1061 to 921)

Orissa ( 1037 to 972)

Bihar just by inspection

126. 3 Females outnumbering males means that the sex ratio

is more than 1000.

So option (3), i.e. the number remains unchanged for

4 years.


Congress – Thursday BJP – Friday

SP – Thursday BSP – Friday

CPM – Friday

127. 1 Congress procession can only be allowed on

Thursday.

128. 4 According to the given table, statement (4) is not true.

129. 4 From statement A, both Aakash and Biplab have the

same scores. But we cannot find the man of match.

From statement B only, we cannot find the man of the

match.

Combining both statements we can find the man of the

match i.e. Aakash.

130. 3 From statement A, their ranks will be A - 4, B -1, C - 2,

D - 3.

From statement B, also their ranks will be A - 4, B -1,

C - 2, D - 3.

131. 1 From statement A, the number of members are 20.

So Each member will pay Rs. 30.

From statement B, we cannot find the each payable

amount.

132. 1 F + n = 4 (k + n) … (i)

M + n = 3 (k + n) …(ii)

From the above equations

F – M = (k + n)

From A

F – M = 10 ⇒ k + n = 10

F + n = 40

M + n = 30

⇒ F + M + 2n = 70

Hence, from A alone, we can get the answer.


If a person copies from one source, he must have the same

blank answers as the source and exactly one wrong answer

more than the source (as the copier has introduced one wrong

answer on his own). If the person copies from two sources,

the distinct wrong answers from the two sources would be

left blank by the copier and the same wrong answers in the

two sources would be copied as it is.

133. 2 A and D have only one source since they have only

one wrong answer each.

C may have copied from only one source i.e. I and

hence only B has two sources

134. 3 I did it before C since 27 is the wrong choice for I,

similarly A,D,E made keys before C. Hence 4 people

made their keys before C.

135. 4 Both G and H can’t be sources to any of F,B or I and

hence (4) is the correct option.

136. 3 F introduced wrong answer to question 14. because

nobody else has done question 14 wrong.

137. 4 A, D and G have one distinct wrong answer and no

blank answers. So, they must have the same source.

E and H also have a common wrong answer and no

blanks.

Hence, both groups had identical sources.

138. 3 VCD = 70% Microwave = 75% ACS = 80% Washing

M/c = 85%

Least percentage of employees having both VCD and

Microwave = 70 + 75 – 100 = 45%

Least percentage having all 3 – VCD, Microwave,

ACS = 45 + 80 – 100 = 25%

Least percentage having all 4 = 25% + 85% – 100%

= 10%

CAT PAPER – 2003(Re-Test) Explanations Page 25


4 Families

The key to cracking this question is to follow the simple

fundamentals in Analytical Reasoning of going 1 line at a time

and making a simple table

Arrival Order Husband Wife Kids

1 Joya 2

2 Shanthi 0

3 Sridevi

4 Sunil 1

Sentence 1 – Family with 2 kids before no kids

Sentence 2 – Shanthi with no kids came before Sridevi

Sentence 3 – Sunil and wife came last with only kid

Sentence 4 – Anil and Joya not husband and wife

Sentence 5 – Anil and Raj are fathers – hence cannot

be the family with no kids

Sentence 6 – Sridevi and Anita cannot be the persons

with no kid

Sentence 7 – Anil and Joya not husband and wife

Sentence 8 – Joya before Shanti and Anita was already

present.

Using the above info – Anil and Raj cannot be married

to Shanthi as Shanthi has no kids! Hence, Sunil has to

be married to Sridevi (not with Joya already stated)

and Raman with Shanthi.

Arrival Order Husband Wife Kids

1 Anil Anita 1

2 Raj Joya 2

3 Raman Shanthi 0

4 Sunil Sridevi 1

139. 1

140. 2

141. 3

142. 2


7 Faculty

JC came in first and the next 2 people were SS and SM. When

he left, DG left with him. JP and VR stayed behind.

Entry Exit Met

JC à SS à SM JC& DG JP&VR

JP&VR together JC& one more person

SS left immediately after SM

PK only met JP & DG

The key to this question is that when JP & VR entered apart

from JC there was ONLY 1 other person. This could not have

been SS or SM as they came and left together. Hence, this

would have to be DG.

Hence, DG came 4th, before JP and is the answer to both 143

and 144.

Now for Qs 145 we need to see how many people did VR

meet. Both SS and SM had already left and JC and DG were

sitting. He entered with JP eliminating 2 and 5 from our answer

choices. Since, PK did not meet VR – the answer is 3 and not

4.

143. 2

144. 3

145. 2

146. 4


D A F

Entrance Corridor

C E B

147. 3 If E faces the corridor, person to his left is C.


148. 4 According to figure, E faces A’s office.


149. 1 According to figure, F’s neighbour is A.


150. 2 According to figure, B’s room is last on the right.


CAT PAPER – 2003 (Re-Test)Page 66

Directions for questions 101 to 103: Answer the questions on the basis of the following information.

In a Decathlon, the events are 100 m, 400 m, 100 m hurdles, 1,500 m, High jump, Pole vault, Long jump,

Discus, Shot put and Javelin. The performance in the first four of these events is consolidated into

Score-1, the next three into Score-2, and the last three into Score-3. Each such consolidation is obtained

by giving appropriate positive weights to individual events. The final score is simply the total of these three

scores. The athletes with the highest, second highest and the third highest final scores receive the gold,

silver, and the bronze medals respectively. The table below gives the scores and performance of 19 top

athletes in this event.

Name CountryFinal

ScoreScore-1 Score-2 Score-3 100m

High

jump

Pole-

vault

Eduard Hämäläinen BLS 8802 491 5322 2989 10.74 2.08 4.8

Michael Smith CAN 8855 174 5274 3407 11.23 1.97 4.9

Tomas Dvorak

Uwe Freimuth DDR 8799 441 5491 3124 11.06 1.97 4.8

Torsten Voss DDR 8880 521 5234 2868 10.69 2.1 5.1

Erki Nool EST 8768 408 5553 2808 10.71 1.99 5.4

Christian Plaziat FRA 8775 563 5430 2781 10.72 2.1 5

Jürgen Hingsen FRG 8792 451 5223 3033 10.95 2 4.9

Siegfried Wentz FRG 8856 470 5250 3137 10.85 2.05 4.8

Guido Kratschmer FRG 8861 575 5308 3064 10.58 2 4.6

Daley Thompson GBR 582 3003 10.55 2.11 4.6

Frank Busemann GER 8905 568 5392 2945 10.6 2.04 4.8

Alexandr Apaichev SOV 8803 492 5370 3115 10.92 1.95 4.8

Grigory Degtyarov SOV 8823 339 5196 3114 11.05 2.08 4.9

Robert Zmelik TCH 8832 494 5455 2883 10.78 2.06 5.1

Dave Johnson USA 8811 366 5370 3114 10.78 2.1 5

Steve Fritz USA 8827 427 5163 3119 10.75 2.04 5

Bruce Jenner USA 8846 483 5280 3200 10.94 2.03 4.8

Dan O’Brien USA 8897 408 5331 3120 10.36 2.09 4.8

CZE 8796 499 5169 3128 10.63 1.91 4.7

101. The athletes from FRG and USA decided to run a 4 × 100 m relay race for their respective countries

with the country having three athletes borrowing the athlete from CZE. Assume that all the athletes

ran their stretch of the relay race at the same speed as in Decathlon event. How much more time did

the FRG relay team take as compared to the USA team?

1. 0.18 2. 0.28 3. 0.78 4. 0.00

102. What is the least that Daley Thompson must get in Score-2 that ensures him a bronze medal?

1. 5309 2. 5296 3. 5271 4. 5270

103. At least how many competitors (excluding Daley Thompson) must Michael Smith have out-jumped

in the long jump event?

1. One 2. Two 3. Three 4. Four

Section � 1II

CAT PAPER – 2003 (Re-Test) Page 67

Directions for questions 104 to 106: Answer the questions on the basis of the following charts.

Per Capita Availability of Tea (gm) in Chaidesh

487 464510 544 566

0

100

200

300

400

500

600

1995 1996 1997 1998 1999

Year

(Note: Availability is defined as production less export.)

Production and export of Tea (Chaidesh)

660

645

587

561

421

220

215

209

189

207

0 100 200 300 400 500 600 700

1999

1998

1997

1996

1995

Production (million Kg) Export (million Kg)

104. In which year during the period 1996-1999 was Chaidesh’s export of tea, as a proportion of tea

produced, the highest?

1. 1996 2. 1997 3. 1998 4. 1999

105. In which of the following years was the population of Chaidesh the lowest?

1. 1995 2. 1996 3. 1997 4. 1999

106. The area under tea cultivation continuously decreased in all four years from 1996 to 1999, by 10%,

7%, 4%, and 1%, respectively. In which year was tea productivity (production per unit of area) the

highest?

1. 1999 2. 1998 3. 1997 4. 1996



The following is the wholesale price index (WPI) of a select list of items with the base year of 1993-94.

In other words, all the item prices are made 100 in that year (1993-94). Prices in all other years for an item

are measured with respect to its price in the base year. For instance, the price of cement went up by 1%

in 1994-95 as compared to 1993-94. Similarly, the price of power went up by 3% in 1996-97 as compared

to 1993-94.

1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-2000 2000-01 2001-02 2002-03

All items 100 102.0 102.5 104.0 103.0 105.0 106.0 108.0 107.0 106.0

Cement 100 101.0 100.5 103.0 102.5 103.5 103.1 103.8 103.7 104.0

Limestone 100 102.0 102.5 102.75 102.25 103.0 104.0 105.0 104.5 105.0

Power 100 101.5 102.5 103.0 103.5 104.0 106.0 107.0 107.5 108.0

Steel 100 101.5 101.0 103.5 104.0 104.25 105.0 105.5 106.0 105.5

Timber 100 100.5 101.5 102.0 102.5 102.0 103.0 103.5 104.0 104.5

Wages 100 101.5 103.0 103.5 104.0 104.25 104.0 104.75 104.9 105.3

107. Let us suppose that one bag of cement (50 kg) consumes 100 kg of limestone and 10 units of

power. The only other cost item in producing cement is in the form of wages. During 1993-94,

limestone, power and wages contributed, respectively, 20%, 25% and 15% to the cement price per

bag. The average operating profit (per cent of price per cement bag) earned by a cement manufacturer

during 2002-03 is closest to

1. 40% 2. 39.5% 3. 38.5% 4. 37.5%

108. Steel manufacturing requires the use of iron ore, power and manpower. The cost of iron ore has

followed the All Items index. During 1993-94 power accounted for 30% of the selling price of steel,

iron ore for 25%, and wages for 10% of the selling price of steel. Assuming the cost and price data

for cement as given in the previous question, the operating profit (per cent of selling price) of an

average steel manufacturer in 2002-03

1. is more than that of a cement manufacturer

2. is less than that of a cement manufacturer

3. is the same as that of a cement manufacturer

4. Cannot be determined

109. Which item experienced continuous price rise during the ten-year period?

1. Power 2. Cement 3. Wages 4. Limestone

110. Which item(s) experienced only one decline in price during the ten-year period?

1. Steel and limestone 2. Steel and timber

3. Timber 4. Timber and wages


Directions for questions 111 to 114: Answer the questions on the basis of the following table.

Below is a table that lists countries region-wise. Each region-wise list is sorted, first by birth rate and then

alphabetically by name of country. We now wish to merge the region-wise list into one consolidated list

and provide overall rankings to each country based first on birth rate and then on death rate. Thus, if some

countries have the same birth rate, then the country with a lower death rate will be ranked higher. Further,

countries having identical birth and death rates will get the same rank. For example, if two countries are

tied for the third position, then both will be given rank 3, while the next country (in the ordered list) will be

ranked 5.

Rank CountryBirth

Rate

Death

RateRegion

1 South Africa 36 12 Africa

2 Egypt 39 13 Africa

3 Cameroon 42 22 Africa

4 Mozambique 45 18 Africa

5 Zaire 45 18 Africa

6 Ghana 46 14 Africa

7 Angola 47 23 Africa

8 Madagascar 47 22 Africa

9 Morocco 47 16 Africa

10 Tanzania 47 17 Africa

11 Ethiopia 48 23 Africa

12 Ivory coast 48 23 Africa

13 Rhodesia 48 14 Africa

14 Uganda 48 17 Africa

15 Nigeria 49 22 Africa

16 Saudi Arabia 49 19 Africa

17 Sudan 49 17 Africa

18 Algeria 50 16 Africa

19 Kenya 50 14 Africa

20 Upper Volta 50 28 Africa

Rank CountryBirth

Rate

Death

RateRegion

1 Germany (FRG) 10 12 Europe

2 Austria 12 13 Europe

3 Belgium 12 12 Europe

4 Germany (DRG) 12 14 Europe

5 Sweden 12 11 Europe

6 Switzerland 12 9 Europe

7 U.K. 12 12 Europe

8 Netherlands 13 8 Europe

9 France 14 11 Europe

10 Italy 14 10 Europe

11 Greece 16 9 Europe

12 Bulgaria 17 10 Europe

13 Hungary 18 12 Europe

14 Spain 18 8 Europe

15 USSR 18 9 Europe

16 Yugoslavia 18 8 Europe

17 Czech. Rep. 19 11 Europe

18 Portugal 19 10 Europe

19 Romania 19 10 Europe

20 Poland 20 9 Europe


Rank CountryBirth

Rate

Death

RateRegion

1 Japan 16 6 Asia

2 Korea (ROK) 26 6 Asia

3 Sri Lanka 26 9 Asia

4 Taiwan 26 5 Asia

5 Malaysia 30 6 Asia

6 China 31 11 Asia

7 Thailand 34 10 Asia

8 Turkey 34 12 Asia

9 India 36 15 Asia

10 Burma 38 15 Asia

11 Iran 42 12 Asia

12 Vietnam 42 17 Asia

13 Korea

(DPRK)43 12 Asia

14 Pakistan 44 14 Asia

15 Nepal 46 20 Asia

16 Bangladesh 47 19 Asia

17 Syria 47 14 Asia

18 Iraq 48 14 Asia

19 Afghanistan 52 30 Asia

Rank CountryBirth

Rate

Death

RateRegion

1 U.S.A. 15 9 N. America

2 Canada 16 7 N. America

3 Cuba 20 6 N. America

4 Mexico 40 7 N. America

1 Australia 16 8 Pacific

2 Philippines 34 10 Pacific

3 Indonesia 38 16 Pacific

1 Argentina 22 10 S. America

2 Chile 22 7 S. America

3 Colombia 34 10 S. America

4 Brazil 36 10 S. America

5 Venezuela 36 6 S. America

6 Guatemala 40 14 S. America

7 Peru 40 13 S. America

8 Ecuador 42 11 S. America

111. In the consolidated list, what would be the overall rank of the Philippines?

1. 32 2. 33 3. 34 4. 35

112. In the consolidated list, how many countries would rank below Spain and above Taiwan?

1. 9 2. 8 3. 7 4. 6

113. In the consolidated list, which country ranks 37th?

1. South Africa 2. Brazil 3. Turkey 4. Venezuela

114. In the consolidated list, how many countries in Asia will rank lower than every country in South

America, but higher than at least one country in Africa?

1. 8 2. 7 3. 6 4. 5


Directions for questions 115 and 116: Answer the questions on the basis of the data presented in the

figure below.

Rainfall at Selected Locations in Certain Months

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7

Locations

Ra

infa

ll (

in c

m.)

March April September November

115. Which of the following statements is correct?

1. November rainfall exceeds 100 cm in each location

2. September rainfall exceeds 50 cm in each location

3. March rainfall is lower than September rainfall in each location

4. None of these

116. Locations 6 and 7 differ from all the rest because only in these two locations,

1. April rainfall exceeds March rainfall

2. Peak rainfall occurs in April

3. November rainfall is lower than March rainfall

4. April rainfall is less than 200 cm


Directions for questions 117 to 119: Answer the questions on the basis of the data presented in the

figure below.

Mid-year Prices of Essential Commodities

0

10

20

30

40

50

60

70

80

1996 1997 1998 1999 2000 2001 2002

Year

Pri

ce

s (

Rs

.)

Rice (kg) Dal (kg) Edible oil (kg)

Egg (dozen) Chillies (kg) Onioin (kg)

117. During 1996-2002, the number of commodities that exhibited a net overall increase and net overall

decrease, respectively, were

1. 3 and 3 2. 2 and 4 3. 4 and 2 4. 5 and 1

118. The number of commodities that experienced a price decline for two or more consecutive years is

1. 2 2. 3 3. 4 4. 5

119. For which commodities did a price increase immediately follow a price decline only once in this

period?

1. Rice, edible oil and dal 2. Egg and dal

3. Onion only 4. Egg and onion


Directions for questions 120 to 123: Answer the questions on the basis of the following charts.

The profitability of a company is defined as the ratio of its operating profit to its operating income, typically

expressed in percentage. The following two charts show the operating income as well as the profitability of

six companies in the financial years (F.Ys.) 2001-02 and 2002-03.

Operating Income

0

50

100

150

200

250

300

A B C D E F

Company

Op

era

tin

g I

nc

om

e (

cro

res

)

Fy 01-02 Fy 02-03

Profitability

-5%

0%

5%

10%

15%

20%

25%

A B C D E FCompany

Fy 01-02 Fy 02-03

The operating profits of four of these companies are plotted against their respective operating income

figures for the F.Y. 2002-03, in the third chart given below.

40

35

30

25

20

15

10

5

0

100 150 200 250 300

Operating Pro fit vs Operating Incom e

Operating Income

Op

era

tin

g P

rofi

t

120. Which of the following statements is NOT true?

1. The company with the third lowest profitability in F.Y. 2001-02 has the lowest operating

income in F.Y. 2002-03

2. The company with the highest operating income in the two financial years combined has the

lowest operating profit in F.Y. 2002-03

3. Companies with a higher operating income in F.Y. 2001-02 than in F.Y. 2002-03 have higher

profitability in F.Y 2002-03 than in F.Y. 2001-02

4. Comanies with profitability between 10% and 20% in F.Y. 2001-02 also have operating incomes

between 150 crore and 200 crore in F.Y. 2002-03


121. Which company recorded the highest operating profit in F.Y. 2002-03?

1. A 2. C 3. E 4. F

122. What is the approximate average operating profit, in F.Y 2001-02, of the two companies excluded

from the third chart?

1. –7.5 crore 2. 3.5 crore 3. 25 crore 4. Cannot be determined

123. The average operating profit in F.Y. 2002-03 of companies with profitability exceeding 10% in F.Y.

2002-03, is approximately

1. 17.5 crore 2. 25 crore 3. 27.5 crore 4. 32.5 crore

Directions for questions 124 to 126: Answer the questions on the basis of the table given below:

Sex Ratio (Number of females per 1,000 males) of Selected States in India : 1901-2001

1901 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001

AP 985 992 993 987 980 986 981 977 975 972 978

Assam 919 915 896 874 875 868 869 896 910 923 932

Bihar 1061 1051 1020 995 1002 1000 1005 957 948 907 921

Goa 1091 1108 1120 1088 1084 1128 1066 981 975 967 960

Gujarat 954 946 944 945 941 952 940 934 942 934 921

Haryana 867 835 844 844 869 871 868 867 870 865 861

HP 884 889 890 897 890 912 938 958 973 976 970

J&K 882 876 870 865 869 873 878 878 892 896 900

Karnataka 983 981 969 965 960 966 959 957 963 960 964

Kerala 1004 1008 1011 1022 1027 1028 1022 1016 1032 1036 1058

MP 972 967 949 947 946 945 932 920 921 912 920

Maharashtra 978 966 950 947 949 941 936 930 937 934 922

Orissa 1037 1056 1086 1067 1053 1022 1001 988 981 971 972

Punjab 832 780 799 815 836 844 854 865 879 882 874

Rajasthan 905 908 896 907 906 921 908 911 919 910 922

TN 1044 1042 1029 1027 1012 1007 992 978 977 974 986

UP 938 916 908 903 907 998 907 876 882 876 898

WB 945 925 905 890 852 865 878 891 911 917 934

India 972 964 955 950 945 946 941 930 934 927 933

124. The two states which achieved the largest increases in sex ratio over the period

1901-2001 are

1. Punjab and HP 2. HP and Kerala 3. Assam and J & K 4. Kerala and J & K

125. Among the states which have a sex ratio exceeding 1000 in 1901, the sharpest decline over the

period 1901-2001 was registered in the state of

1. Goa 2. TN 3. Bihar 4. Orissa


126. Each of the following statements pertains to the number of states with females outnumbering

males in a given census year. Which of these statements is NOT correct?

1. This number never exceeded 5 in any census year.

2. This number registered its sharpest decline in 1971.

3. The number of consecutive censuses in which this number remained unchanged never

exceeded 3.

4. Prior to the 1971 census, this number was never less than 4.

Directions for questions 127 and 128: Answer the questions on the basis of the following information.

Shown below is the layout of major streets in a city.

A

B

C

D

E

Two days (Thursday and Friday) are left for campaigning before a major election, and the city

administration has received requests from five political parties for taking out their processions along the

following routes.

Congress: A-C-D-E BJP: A-B-D-E SP: A-B-C-E

BSP: B-C-E CPM: A-C-D

Street B-D cannot be used for a political procession on Thursday due to a religious procession. The district

administration has a policy of not allowing more than one procession to pass along the same street on the

same day. However, the administration must allow all parties to take out their procession during these two

days.

127. Congress procession can be allowed

1. only on Thursday 2. only on Friday

3. on either day 4. only if the religious procession is cancelled

128. Which of the following is NOT true?

1. Congress and SP can take out their processions on the same day.

2. The CPM procession cannot be allowed on Thursday.

3. The BJP procession can only take place on Friday.

4. Congress and BSP can take out their processions on the same day.


Directions for questions 129 to 132: Each question is followed by two statements, A and B. Answer

each question using the following instructions:

Choose 1 if the question can be answered by using statement A alone but not by using B alone.

Choose 2 if the question can be answered by using statement B alone but not by using A alone.

Choose 3 if the question can be answered by using either statement alone and

Choose 4 if the question can be answered using both the statements together but not by either statement

alone.

129. In a cricket match, the ‘Man of the Match’ award is given to the player scoring the highest number

of runs. In case of a tie, the player (out of those locked in the tie) who has taken the higher number

of catches is chosen. Even thereafter if there is a tie, the player (out of those locked in the tie) who

has dropped fewer catches is selected. Aakash, Biplab, and Chirag who were contenders for the

award dropped at least one catch each. Biplab dropped two catches more than Aakash did, scored

50, and took two catches. Chirag got two chances to catch and dropped both. Who was the ‘Man of

the Match’?

A. Chirag made 15 runs less than both Aakash and Bipla2.

B. The catches dropped less by Biplab are 1 more than the catches taken by Aakash.

130. Four friends — A, B, C and D got the top four ranks in a competitive examination, but A did not get

the first, B did not get the second, C did not get the third, and D did not get the fourth rank.

Who secured which rank?

A. Neither A nor D were among the first 2.

B. Neither B nor C was third or fourth.

131. The members of a local club contributed equally to pay Rs. 600 towards a donation. How much did

each one pay?

A. If there had been five fewer members, each one would have paid an additional Rs. 10.

B. There were at least 20 members in the club, and each one paid not more than Rs. 30.

132. A family has only one kid. The father says, “After ‘n’ years, my age will be 4 times the age of my

kid.” The mother says, “After ‘n’ years, my age will be 3 times that of my kid.” What will be the

combined ages of the parents after ‘n’ years?

A. The age difference between the parents is 10 years.

B. After ‘n’ years the kid is going to be twice as old as she is now.



Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people.

The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H and I in

this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the

mastermind obtains the correct answer-key. All the others create their answer-key in the following manner.

They obtain the answer-key from one or two people who already possess the same. These people are

called his/her ‘sources’. If the person has two sources, then he/she compares the answer-keys obtained

from both sources. If the key to a question from both sources is identical, it is copied, otherwise it is left

blank. If the person has only one source, he/she copies the source’s answers into his/her copy. Finally,

each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her

answer key.

The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more

of them introducing wrong answers to the same question. The investigative agency has a copy of the

correct answer key and has tabulated the following data. These data represent question numbers.

Name Wrong Answer(s) Blank Answer(s)

A 46 —

B 96 46, 90, 25

C 27, 56 17, 46, 90

D 17 —

E 46, 90 —

F 14, 46 92, 90

G 25 —

H 46, 92 —

I 27 17, 46, 90

133. Which one among the following must have two sources?

1. A 2. B 3. C 4. D

134. How may people (excluding the mastermind) needed to make answer-keys before C could make his

answer-key?

1. 2 2. 3 3. 4 4. 5

135. Both G and H were sources to

1. F 2. B 3. I 4. None of the nine


1. C introduced the wrong answer to question 27.

2. E introduced the wrong answer to question 46.

3. F introduced the wrong answer to question 14.

4. H introduced the wrong answer to question 46.


137. Which of the following two groups of people had identical sources?

I. A, D and G II. E and H

1. Only I 2. Only II 3. Neither I nor II 4. Both I and II

Directions for question 138: Answer the question on the basis of the following information.

138. Seventy percent of the employees in a multinational corporation have VCD players, 75% have

microwave ovens, 80% have ACS and 85 have washing machines. At least what percentage of

employees has all four gadgets?



Four families decided to attend the marriage ceremony of one of their colleagues. One family has no kids,

while the others have at least one kid each. Each family with kids has at least one kid attending the

marriage. Given below is some information about the families, and who reached when to attend the

marriage.

The family with two kids came just before the family with no kids.

Shanthi who does not have any kids reached just before Sridevi’s family.

Sunil and his wife reached last with their only kid.

Anil is not the husband of Joya.

Anil and Raj are fathers.

Sridevi’s and Anita’s daughters go to the same school.

Joya came before Shanthi and met Anita when she reached the venue

Raman stays the farthest from the venue.

Raj said his son could not come because of his exams.

139. Who among the following arrived third?

1. Shanthi 2. Sridevi 3. Anita 4. Joya

140. Name the correct pair of husband and wife.

1. Raj and Shanthi 2. Sunil and Sridevi 3. Anil and Sridevi 4. Raj and Anita

141. Of the following pairs, whose daughters go to the same school?

1. Anil and Raman 2. Sunil and Raman 3. Sunil and Anil 4. Raj and Anil

142. Whose family is known to have more than one kid for certain?

1. Raman’s 2. Raj’s 3. Anil’s 4. Sunil’s



Seven faculty members at a management institute frequent a lounge for strong coffee and stimulating

conversation. On being asked about their visit to the lounge last Friday we got the following responses.

JC: I came in first, and the next two persons to enter were SS and SM. When I left the lounge, JP and

VR were present in the lounge. DG left with me.

JP: When I entered the lounge with VR, JC was sitting there. There was someone else, but I cannot

remember who it was.

SM: I went to the lounge for a short while, and met JC, SS and DG in the lounge that day.

SS: I left immediately after SM left.

DG: I met JC, SS, SM, JP and VR during my first visit to the lounge, I went back to my office with JC.

When I went to the lounge the second time, JP and VR were there.

PK: I had some urgent work, so I did not sit in the lounge that day, but just collected my coffee and left.

JP and DG were the only people in the lounge while I was there.

VR: No comments.

143. Based on the responses, which of the two, JP or DG, entered the lounge first?

1. JP 2. DG

3. Both entered together 4. Cannot be determined

144 . Who was sitting with JC when JP entered the lounge?

1. SS 2. SM 3. DG 4. PK

145. How many of the seven members did VR meet on Friday in the lounge?

1. 2 2. 3 3. 4 4. 5

146. Who were the last two faculty members to leave the lounge?

1. JC and DG 2. PK and DG 3. JP and PK 4. JP and DG



CorridorEntrance

The plan above shows an office block for six officers — A, B, C, D, E and F. Both B and C occupy offices

to the right of the corridor (as one enters the office block) and A occupies an office to the left of the corridor.

E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices

of C and D face each other. E does not have a corner office. F’s office is further down the corridor than A’s,

but on the same side.

147. If E sits in his office and faces the corridor, whose office is to his left?

1. A 2. B 3. C 4. D

148. Whose office faces A’s office?

1. B 2. C 3. D 4. E

149. Who is/are F’s neighbour(s)?

1. A only 2. A and D 3. C only 4. B and C

150. D was heard telling someone to go further down the corridor to the last office on the right. To whose

room was he trying to direct that person?

1. A 2. B 3. C 4. F


Sub-Section I – A: Number of Questions = 26

Note: Questions 1 to 26 carry one mark each.

Directions for questions 1 to 4: Answer the questions on the basis of the information given below.

The Dean's office recently scanned student results into the central computer system. When their character

reading software cannot read something, it leaves the space blank. The scanner output reads as follows:

Name Finance Marketing Statistics Strategy Operations GPA

Aparna B F 1.4

Bikas D D F F

Chandra D A F F 2.4

Deepak A B D D 3.2

Fazal D F B D 2.4

Gowri C C A B 3.8

Hari B A D 2.8

Ismet B A

Jagdeep A A B C 3.8

Kunal F A F F 1.8

Leena B A B F 3.2

Manab A B B

Nisha A D B A F 3.6

Osman C B B A 4.6

Preeti F D D 3.2

Rahul A C A F 4.2

Sameer C F B

Tara B 2.4

Utkarsh F C A 3

Vipul A C C F 2.4

In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2, and 0 grade points respectively. The GradePoint Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example

Nisha's GPA is (6 + 2 + 4 + 6 + 0) / 5 = 3.6. Some additional facts are also known about the students'

grades. These are

(a) Vipul obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.

(b) Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.

(c) Tara received the same grade in exactly three courses.

1. What grade did Preeti obtain in Statistics?

(1) A (2) B (3) C (4) D

Section � 1


2. In operations, Tara could have received the same grade as

(1) Ismet (2) Hari (3) Jagdeep (4) Manab

3. In Strategy, Gowri's grade point was higher than that obtained by

(1) Fazal (2) Hari (3) Nisha (4) Rahul

4. What grade did Utkarsh obtain in Finance?

(1) B (2) C (3) D (4) F


The data points in the figure below represent monthly income and expenditure data of individual members

of the Ahuja family ( ), the Bose family ( ), the Coomar family ( ), and the Dubey family ( ). For

these questions, savings is defined as

1000

2000

3000

01000 2000 3000 Expenditure

Inc

om

e

L ine indicating Income = Expend itu re

Savings = Incom e – Expenditure

5. Which family has the lowest average income?

(1) Ahuja (2) Bose (3) Coomar (4) Dubey


6. Which family has the highest average expenditure?


7. Which family has the lowest average savings?


8. The highest amount of savings accrues to a member of which family?



Prof. Singh has been tracking the number of visitors to his homepage. His service provider has provided

him with the following data on the country of origin of the visitors and the university they belong to:

COUNTRY 1 2 3

Canada 2 0 0

Netherlands 1 1 0

India 1 2 0

UK 2 0 2

USA 1 0 1

Number of visitors

DAYUNIVERSITY 1 2 3

University 1 1 0 0

University 2 2 0 0

University 3 0 1 0

University 4 0 0 2

University 5 1 0 0

University 6 1 0 1

University 7 2 0 0

University 8 0 2 0

DAY

Number of visitors

9. To which country does University 5 belong?

(1) India or Netherlands but not USA (2) India or USA but not Netherlands

(3) Netherlands or USA but not India (4) India or USA but not UK

10. University 1 can belong to

(1) UK (2) Canada

(3) Netherlands (4) USA

11. Which among the listed countries can possibly host three of the eight listed universities?

(1) None (2) Only UK

(3) Only India (4) Both India and UK

12. Visitors from how many universities from UK visited Prof. Singh's homepage in the three days?

(1) 1 (2) 2

(3) 3 (4) 4



Purana and Naya are two brands of kitchen mixer-grinders available in the local market. Purana is an old

brand that was introduced in 1990, while Naya was introduced in 1997. For both these brands, 20% of the

mixer-grinders bought in a particular year are disposed off as junk exactly two years later. It is known that

10 Purana mixer-grinders were disposed off in 1997. The following figures show the number of Purana and

Naya mixer-grinders in operation from 1995 to 2000, as at the end of the year.

120

162

182

222236 236

0 0

30

80

124134

0

50

100

150

200

250

1995 1996 1997 1998 1999 2000

Purana Naya

13. How many Naya mixer-grinders were purchased in 1999?

(1) 44 (2) 50

(3) 55 (4) 64

14. How many Naya mixer-grinders were disposed off by the end of 2000?

(1) 10 (2) 16

(3) 22 (4) Cannot be determined from the data

15. How many Purana mixer-grinders were disposed off in 2000?

(1) 0 (2) 5


16. How many Purana mixer-grinders were purchased in 1999?

(1) 20 (2) 23




A study was conduced to ascertain the relative importance that employees in five different countries

assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisive-

ness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two

countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. Thefollowing table indicates the rank order of the five traits for each country.

Rank India China Japan Malaysia Thailand

1 C N D V V

2 P C N D C

3 N P C P N

4 V D V C P

5 D V P N D

Country

17. Which of the following pairs of countries are most dissimilar?

(1) China and Japan (2) India and China

(3) Malaysia and Japan (4) Thailand and Japan

18. Which of the following countries is least dissimilar to India?

(1) China (2) Japan (3) Malaysia (4) Thailand

19. Which amongst the following countries is most dissimilar to India?

(1) China (2) Japan (3) Malaysia (4) Thailand

20. Three of the following four pairs of countries have identical levels of dissimilarity. Which pair is the

odd one out?

(1) Malaysia and China (2) China and Thailand

(3) Thailand and Japan (4) Japan and Malaysia

Directions for questions 21 to 26: Each question is followed by two statements, A and B. Answer each

question using the following instructions.

Choose (1) if the question can be answered by using one of the statements alone but not by using the

other statement alone.

Choose (2) if the question can be answered by using either of the statements alone.

Choose (3) if the question can be answered by using both statements together but not by either state-

ment alone.

Choose (4) if the question cannot be answered on the basis of the two statements.

21. Zakib spends 30% of his income on his children's education, 20% on recreation and 10% on

healthcare. The corresponding percentage for Supriyo are 40%, 25%, and 13%. Who spends more

on children's education?

A. Zakib spends more on recreation than Supriyo.

B. Supriyo spends more on healthcare than Zakib.


22. Four candidates for an award obtain distinct scores in a test. Each of the four casts a vote to

choose the winner of the award. The candidate who gets the largest number of votes wins the

award. In case of a tie in the voting process, the candidate with the highest score wins the award.

Who wins the award?

A. The candidates with top three scores each vote for the top score amongst the other three.

B. The candidate with the lowest score votes for the player with the second highest score.

23. In a class of 30 students, Rashmi secured the third rank among the girls, while her brother Kumar

studying in the same class secured the sixth rank in the whole class. Between the two, who had a

better overall rank?

A. Kumar was among the top 25% of the boys merit list in the class in which 60% were boys.

B. There were three boys among the top five rank holders, and three girls among the top ten

rank holders.

24. Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a blue mark. He tosses

a coin. If it comes up heads, he moves one step to the right; otherwise he moves one step to the left.

He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does

he stop?

A. He stops after 21 coin tosses.

B. He obtains three more tails than heads.

25. Ravi spent less than Rs. 75 to buy one kilogram each of potato, onion, and gourd. Which one of the

three vegetables bought was the costliest?

A. 2 kgs potato and 1 kg gourd cost less than 1 kg potato and 2 kg gourd.

B. 1 kg potato and 2 kgs onion together cost the same as 1 kg onion and 2 kgs gourd.

26. Nandini paid for an article using currency notes of denominations Re. 1, Rs. 2, Rs. 5, and Rs. 10

using at least one note of each denomination. The total number of five and ten rupee notes used was

one more than the total number of one and two rupee notes used. What was the price of the article?

A. Nandini used a total of 13 currency notes.

B. The price of the article was a multiple of Rs. 10.


Sub-Section I-B: Number of Questions = 12

Note: Questions 27 to 38 carry two marks each.


Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament

where the same set of players played for India and all the major batsmen got out. John summarized the

batting performance through three diagrams, one for each game. In each diagram, the three outer triangles

communicate the number of runs scored by the three top scores from India, where K, R, S, V, and Y

represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram

denotes the percentage of the total score that was scored by the top three Indian scorers in that game. No

two players score the same number of runs in the same game. John also calculated two batting indices for

each player based on his scores in the tournaments; the R-index of a batsman is the difference between

his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are

arranged in a non-increasing order.

Pakistan South A frica Australia

90%

Y(40)

K(28)V(130)

70%

K(51)

R(49)S(75)

80%

R(55)

S(50)Y(87)

27. For how many Indian players is it possible to calculate the exact M-index?

(1) 0 (2) 1 (3) 2 (4) More than 2

28. Among the players mentioned, who can have the lowest R-index from the tournament?

(1) Only Kaif, Rahul or Yuvraj (2) Only Kaif or Rahul

(3) Only Kaif or Yuvraj (4) Only Kaif

29. How many players among those listed definitely scored less than Yuvraj in the tournament?

(1) 0 (2) 1 (3) 2 (4) More than 2

30. Which of the players had the best M-index from the tournament?

(1) Rahul (2) Saurav (3) Virender (4) Yuvraj



Twenty one participants from four continents (Africa, America, Australasia, and Europe) attended a United

Nations conference. Each participant was an expert in one of four fields, labour, health, population studies,

and refugee relocation. The following five facts about the participants are given.

(a) The number of labour experts in the camp was exactly half the number of experts in each of the

other three categories.

(b) Africa did not send any labour expert. Otherwise, every continent, including Africa, sent at least one

expert for each category.

(c) None of the continents sent more than three experts in any category.

(d) If there had been one less Australasian expert, then the Americas would have had twice as many

experts as each of the other continents.

(e) Mike and Alfanso are leading experts of population studies who attended the conference. They are

from Australasia.

31. Which of the following combinations is NOT possible?

(1) 2 experts in population studies from the Americas and 2 health experts from Africa attended the

conference.

(2) 2 experts in population studies from the Americas and 1 health expert from Africa attended the

conference.

(3) 3 experts in refugee relocation from the Americas and 1 health expert from Africa attended the

conference.

(4) Africa and America each had 1 expert in population studies attending the conference.

32. If Ramos is the lone American expert in population studies, which of the following is NOT true about

the numbers of experts in the conference from the four continents?

(1) There is one expert in health from Africa.

(2) There is one expert in refugee relocation from Africa.

(3) There are two experts in health from the Americas.

(4) There are three experts in refugee relocation from the Americas.

33. Alex, an American expert in refugee relocation, was the first keynote speaker in the conference.

What can be inferred about the number of American experts in refugee relocation in the conference,

excluding Alex?

i. At least one

ii. At most two

(1) Only i and not ii (2) Only ii and not i (3) Both i and ii (4) Neither i nor ii

34. Which of the following numbers cannot be determined from the information given?

(1) Number of labour experts from the Americas.

(2) Number of health experts from Europe.

(3) Number of health experts from Australasia.

(4) Number of experts in refugee relocation from Africa.



The year was 2006. All six teams in Pool A of World Cup hockey, play each other exactly once. Each win

earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the

highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goal For

- Goals Against) qualifies.

In the opening match, Spain lost to Germany. After the second round (after each team played two matches),

the pool table looked as shown below.

Pool A

Teams Games

Played

Won Drawn Lost Goals

For

Goals

Against

Points

Germany 2 2 0 0 3 1 6

Argentina 2 2 0 0 2 0 6

Spain 2 1 0 1 5 2 3

Pakistan 2 1 0 1 2 1 3

New

Zealand

2 0 0 2 1 6 0

South

Africa

2 0 0 2 1 4 0

In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South

Africa. All the third round matches were drawn. The following are some results from the fourth and fifth

round matches

(a) Spain won both the fourth and fifth round matches.

(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.

(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.

35. Which one of the following statements is true about matches played in the first two rounds?

(1) Germany beat New Zealand by 1 goal to 0.

(2) Spain beat New Zealand by 4 goals to 0.

(3) Spain beat South Africa by 2 goals to 0.

(4) Germany beat South Africa by 2 goals to 1.

36. Which one of the following statements is true about matches played in the first two rounds?

(1) Pakistan beat South Africa by 2 goals to 1. (2) Argentina beat Pakistan by 1 goal to 0.

(3) Germany beat Pakistan by 2 goals to 1. (4) Germany beat Spain by 2 goals to 1.

37. If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?

(1) Argentina (2) Germany (3) Spain (4) Cannot be determined

38. Which team finished at the top of the pool after five rounds of matches?

(1) Argentina (2) Germany (3) Spain (4) Cannot be determined


Since, the three integers are positive, the value of ‘n’cannot be equal to 1, therefore the value of ‘n’ = 4 orm = n – 1 = 3.Hence, the three consecutive positive integers are 3,4 and 5.Hence, option (1) is the correct choice.

24. 1

2 2 2 2 2 2

1 1 1 1 1 1S 1 1 ... 1

1 2 2 3 2007 2008= + + + + + + + + +

n 2 2

1 1T 1

n (n 1)= + +

+

4 3 2

2 2

n 2n 3n 2n 1

n (n 1)

+ + + +=

+

= 2

2 2

n n 1 11

n n n n

+ += +

+ +

2007 2007

nn 1 n 1

1 1S T 2007

n n 1= =

= = + − + ∑ ∑

12008

2008= −

Hence, option (1) is the correct choice.

25. 1

h

x

B

QNP

A

CR

M

S

Let, the height of the cylinder be ‘h’ cm and radiusbe ‘x’ cm.

ANQ∆ is similar to QSC∆

AN QS 10 h h

NQ SC x 4 x

−⇒ = ⇒ =

−

10 x 10 41

h 4 x h 4 x⇒ − = ⇒ =

− −

5h (4 x)

2∴ = −

Surface area of the cylinder PQSR

=22 x hx π + =

2 5x2 x (4 x

2

π + −

=2 2 25 3

2 x x 10x 2 10x x2 2

π − + = π −

=2

3 10 502 x

2 3 3

π − − +

Maximum value of surface area of the cylinder will

be at 10

x3

= .

Hence, option (1) is the correct choice.


The given information can be depicted as follows.(i)

3 houses on each side o f the roadR oad

(ii) Six houses – P, Q, R, S, T, U(iii) Colours – Red, Blue, Green, Orange, Yellow, White(iv) Different heights(v) T = tallest & opposite to Red(vi) Shortest opposite to Green(vii) U = orange & the position of U is: P/S U S/P(viii) R = yellow & opposite to P(ix) Q = Green & opposite to U(x) P = White & (S, Q) > P > R (in height)

From (iv), (v), (vi), (ix) & (x), T > (S, Q) > P > R > Uin terms of heightFrom (iv), (vii), (viii), (ix) & (x), we get the followingtwo cases.

R

5 2/3 1

4 (S hortest) 3 /2

1 2/3 5

3 /2 6 4

T

P S

Q Q

U

(Tallest)

U

T R

S P

Yellow Blue

W hite Red

G reen G reen

RO AD RO ADO R

O range O range

Blue

6

Ye llow

Red W hite

26. 4 Diagonally opposite to yellow is red.

27. 5 Second tallest house is either Q or S. So, we can notdetermine.


28. 2 Tallest house is T whose colour is Blue.

29. 5 Let volume of data transfer in India = Volume of datatransfer in Singapore = X

For INDIA:

ARDT for India ≈ $1 (approx)

∴ Revenue from data transfer = $X (approx)

Revenue from data transfer100 9% (approx)

Total Revenue× =

xTotal Revenue 100 (approx)

9⇒ ×;

For SINGAPORE:

ARDT = $9 (approx)

∴ Revenue from data transfer = $9X (approx)

Revenue from data transfer100 20.5% (approx)

Total Revenue× =

9xTotal Revenue 100 (approx)

20.5⇒ = ×

9x100

Total Revenue for Singapore 20.5 4 (approx)xTotal Revenue for India

1009

×= ≈

×

So, the statement given in option (5) is true.

30. 3 Let total Revenue of Sweden in 2010 = xTherefore total Revenue of India in 2010 = 2x

For Sweden in 2010:

ARDT = $6Revenue from data transfer = 2 × 18% of x

∴ Volume of data transfer = 2 18% of x

6

×

For India in 2010:

Let ARDT = y

Revenue from data transfer = 3 9% of 2x×

3 9%of 2xVolume of data transfer

y

×∴ =

Therefore2 18%of x 3 9% of 2x

6 y

× ×= y $9⇒ =

Therefore % change in ARDT of India

9 – 1100 800%

1= × =

31. 4 For UK:

( )Revenue from Data transfar100 30% approx

Total Revenue× =

Revenue from Data transfer 30

Total Revenue100

= ×

ARDT = $ 13 (approx)

∴ Volume of Data transfer 30 Total Revenue

100 13= ×

3Total Revenue

130≈ ×

For Spain:

( )Revenue from Data transfar100 15% approx

Total Revenue× =

ARDT = 6.5 (approx)

∴ Volume of Data transfer 15 Total Revenue

100 6.5= ×

3Total Revenue

130≈ ×

Similarly, we can check the other options and easilysee that the volume of data transfer is NOT the samefor given pair countries.

32. 2 Since Bhama got calls from all colleges, she has toscore marks in each section equal to at least themaximum of the cut-offs across colleges which means45, 45, 46 & 45 in section A, B, C, & D respectively.This makes her total to be 181 with which she willclear the overall cut-offs of all institutes also.

33. 3 Since we have to minimise the marks in a particularsection, we will maximise the marks in other 3 sections.Let us assume that marks obtained in each of thethree sections in which we are going to maximize thescore, is equal to 50. Now, the lowest overall cut-offis 171 & second lowest is 175. Hence Charlie musthave scored at least 175 – (50 + 50 + 50) = 25 marksin the remaining section.

Lets confirm whether he can clear sectional cut-offsalso with such a distribution. On seeing the sectionalcut-offs, we conclude what they can be cleared with50 marks each in section A, B & C and 25 marks insection D, which may enable Charlie to clear thesectional cut-off of section D for college 1, 2, 3 or 5.Hence answer is 25.


34. 3 Since we have to maximize Aditya’s marks, let usetake the base values of 50 marks in each section andtry to reduce that by minimum values to ensure hedoesn’t get any call. We notice that by reducing themarks obtained in section C to 41, we ensure colleges1, 2, 3 & 5 are ruled out. Now for colleges 4 & 6,reducing the marks obtained in section D to 43, ensuresthese colleges are also ruled out. Please note that weare reducing the score to 1 less than the minimum cut-off across all colleges for that particular section.In the other two sections A and B, Aditya may score 50each. So, the maximum possible aggregate marks = 50+ 50 + 41 + 43 = 184.


The given basic information can be collated as below:(i) Six teams – A, B, C, D, E, F(ii) Matches scheduled in two stages – I & II.(ii) No team plays against the same team more than once.(iv) No ties permitted.

As per the instructions given for stage – I, we canreach the following conclusions:

(a) As B lost at least one match, hence A won all the 3matches.

(b) The two teams who lost all the matches cannot be A(as explained above), cannot be B (E lost to B), cannotbe D (D won against C & F). Hence, the two teamsmust be C and F.

(c) F did not play against the top team (i.e. A).We get the following table for stage – I.

(To be read from rows)

A B C D E F

A X W W W

B L X W W

C L X L L

D L W X W

E L W X W

F L L L X

As per the instructions given for Stage-II, we can reach thefollowing conclusions.(d) A lost both its matches against E and F.(e) F won against A, hence is the bottom team

(out of C & F) which won both the matches⇒ F won against C as well.This also means that C lost both its matches againstB and F.

(f) Apart from A and C, one more team lost both thematches in Stage-II.That team can neither be E (A lost to E), nor B(as C lost to B), nor F (as F won both its matches).Hence, the team must be D.

We get the following table for Stage-II.

(To be read from Rows)

A B C D E F

A X L L

B X W W

C L X L

D L X L

E W W X

F W W X

35. 2 E & F defeated A. [Please note that in this

question option (1) and (5) were the same]

36. 4 B, E & F won both the matches in Stage-II.

37. 5 D & F won exactly two matches in the event.

38. 5 B & E has most wins, 4 each.

39. 1 Subscription in Europe in 2006 = 380 Mn USDSubscription in Europe in 2007 = 500 Mn USD

% change in 2007 500 – 380

100 30%380

= × ≈

Therefore subscription (based upon the growth rateof 2007 over 2006) in 2008 should have been= 500 × 1.3 = 650 Mn USD (approx)Therefore difference from the estimated subscrip-tion = 650 – 600 = 50 Mn USD (approx)[Please note that the unit is mentioned neither

in the question, nor in the options]

40. 1 Let total number of subscribers = 100xNumber of men = 60xTherefore number of men in 2010 = 60x × (1.05)7

= 84.42x (approx)Number of women = 40xTherefore number of women in 2010 = 40x × 1.17

= 77.94x (approx)Therefore total number of subscribers = 84.42x +77.94 = 162.36x% growth of subscribers

162.36x – 100x62.36 (approx)

100x= =

41. 4 Gap in 2008 = 780 – 600 = 180 Mn USDGap in 2009 = 810 – 700 = 110 Mn USD

Annual % change110 – 180

100 –39%180

= × =

Absolute change = 39% which is the highest.Among the other options, option (3) ’06-07’ is closest,but it will lead to only 22% change in gap.


42. 3 Growth rate of 2007 500 – 380

100 31.58%380

= × =

Growth rate of 2005 280 – 190

100 47.37%190

= × =

Therefore % change in growth rate of 2007 relativeto growth rate of 2005 is

47.37 – 31.58100 35%

47.37× ≈

43. 5 Since we do not know what are the share pricesduring different times of the day we cannot come toany conclusion. Hence (5)

44. 5 Suppose the prices of shares remains samethroughout the day then all the four given statementswould not hold true. Hence (5).

45. 1 As the prices are rising continuously, the earlier aperson invests, the more profitable it would be.Abdul invested in the beginning only and hence reapedin maximum return.Between Bikram and Chetan, Chetan always investedthe same amount but Bikarm invested more and moreamount towards the end. Hence Bikram got the mini-mum return.


Let the share price are 10 am, 11 am, 12 noon, 1 pm, 2 pm and3 pm be a, b, c ,d, e & f rupees respectively.

From information (i) we get, a > f …(I)

From information (ii) we geta) Dane made profit i.e. (a + b + c) < (d + e + f) …(II)

And, b) Emily made profit i.e. d

f ac

× > …(III)

Or, d × f > a × c …(IV)From information (iii) we get, e > f …(V)From information (iv) we get, a > c …(VI)

On combining in-equations (I) & (III) we get, c > d …(VII)On combining in-equations (I) and (VIII) we get,a + c > d + f …(VIII)On combining in-equations (II) and (VIII) we get,e > b …(IX)Hence, we get the sequence as (a > f > e > b) and (c > d).And also we know that ‘a’ is greater than both ‘c’ and ‘d’,therefore ‘a’ is the highest among the six mentioned variables.

46. 1 The price at 10 am i.e. ‘a’ is greater than prices atany other time.

47.1 and 4Since the price at 11 am i.e. ‘b’ is less than the price at2 pm (i.e. ‘c’), hence statement (1) is necessarily false.From in-equation (VII) we know that c > d.Hence statement (IV) is also necessarily false.

48. 3 Avg. Gross pay of HR department before transfer= Rs. 5000 × 1.7 = Rs. 8500Basic pay of the transferred person = Rs. 8000New allowance of the transferred person = (80 + 10)= 90% of the basic payNew Gross pay of the transferred person= Rs. 8000 × 1.9 = Rs. 15,200New average gross pay of HR

dept.15200 8500

Rs. 85006

− = +

= Rs. (8500 + 1116)

Percentage change 1116100

8500= × 13%≈

49. 3 Since increase in average age of the Finance dept. isone year, the age of the person moving from Mktg. toFinance is more than that moving from Finance toMarketing, by 1 × 20 = 20 years.Hence, due to this transfer, cumulative age of Marketingdepartment has gone down by 20 yrs. But since theaverage age of Mktg. dept. remaining unchanged, theperson moving from Marketing to HR has age = (Avg.age of Marketing) – 20 = 15 years.

New average age of HR dept.( ) ( )5 45 1 15

5 1

× + ×=

+ = 40 yrs.

50. 2 Total basic pay of HR= 5 × 5000 (existing) + 2 × 6000 (from Maintenance)+ 1 × 8000 (from Marketing) = Rs. 45,000

New average45,000

Rs. 5,6258

= =

Percentage change625

12.5%5000

= =

51. 1 Sentence A is incorrect as the spelling of ‘imigrant’ isnot correct , should be ‘immigrant’. Sentence D isincorrect because of a missing article and should be ‘the owner of a dry goods ….’. Sentence E is incorrectand should be ‘….. would later be known as…..’.Sentence C is incorrect. We require a comma between‘brother-in-law’ and ‘David Stern’.

52. 4 Sentence B should be’….its labour policy’ becausethe subject is Nike and we can’t substitute it with theplural pronoun ‘their’. Sentence C should be ‘Perhapssensing that the rising tide…’ as without ‘that’ thesentence structure is incomplete. Sentence E shouldbe ‘ ….an industry..’ as the word industry begins witha vowel so the appropriate article is ‘an’.

53. 3 Sentence B should be ‘…few millions…. ’Sentence Dshould be … reach the hundreds who are marooned..Sentence E is incorrect as per subject verb agreementand should be ‘…death count has begun’.

DATA INTERPRETATION QUESTION BANK EXERCISE 1 Directions for Qs. 1 to 2: Refer to the following data and answer the following questions. A B C

D E F G

H I

Each of the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 is represented by a different letter in the figure. A + B + C, C + D + E, E + F + G and G + H + I is equal to 13. 1. Which of the digits does E represent?

(1) 9 (2) 4 (3) 7 (4) 1 2. Which of the digits does D represent? (1) 8 (2) 7 (3) 3 (4) 7 or 8 Directions for Qs. 3 to 7: Refer to the following information and answer the following questions. In a group of 200 people, number of people having at least primary education : number of people having at least middle school education : number of people having at least high school education :: 7 : 3 : . 90 of these play football and 60 play hockey. 5 people in category III (defined as people having high school education) and one fourth each in category I and II (defined as people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above category the number of people playing only hockey equal the number of people playing only football. 2 people each in categories I and II and 1 person in category III play both the games. 2 people playing both games are uneducated (category IV). 5 people in category III play only hockey. Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under the four categories described above. 3. How many people have middle school education?

(1) 16 (2) 32 (3) 48 (4) 64 4. How many high school educated people do not play football?

(1) 6 (2) 8 (3) 10 (4) 12

5. How many people having middle school, but not high school, education play only football? (1) 2 (2) 7 (3) 11 (4) 15 6. How many people who completed primary school could not finish middle school? (1) 48 (2) 64 (3) 80 (4) 96 7. How many uneducated people play neither hockey nor football? (1) 15 (2) 20 (3) 23 (4) 28

Direction for Qs. 8 - 10: Refer to the following data and answer the following questions. A simple coding system, using cryptograms, is designed as below. Three concentric wheels each having all the alphabets and the number 0 to 9 are written around the rims of the wheels.

8. Suppose that a cryptogram system is made by rotating the inner wheel 2 alphabets to the right and

rotating the outer wheel 2 alphabets to the left. Starting with the inner wheel, what would APPLE be coded as? (1) BRRC7 (2) 8RNJC (3) 8CCNR (4) 8RNNC

9. How many cryptogram system can be totally made from this device? (Starting inner wheel) (1) 2315 (2) 1295 (3) 676 (4) Indeterminate 10. Assume that both the inner and outer wheels have been rotated one step, but you don’t know

whether left or right. What would the rotations be if HOCJ9 has to decode to a proper English word? (Starting inner wheel)

(1) Inner right, Outer right (2) Inner left, Outer left (3) Inner right, Outer left (4) Inner left, Outer right Directions for Qs. 11 to 13: Each of these questions contains six statements followed by 4 sets of combinations of 3. Choose the set in which the statements are most logically related. 11. A. All pianos are large B. All flutes are well turned C. All pianos are loud D. All flutes are loud E. All pianos are flutes F. All pianos are well tuned (1) FBE (2) CDF (3) BEF (4) BCF 12. A. All acetones are corrosive substances. B. All corrosive substances are acidic. C. All acetones are alkaline. D. Some acetones are alkaline and corrosive. E. All acetones are acidic. F. No oxide corrodes. (1) ACB (2) BDE (3) BCD (4) BAE

7

8

9 A B

C

D7

8

9 A B

D

7

8

9 A B

C

D

C

13. A. Some oils are refined B. Some oils are not brown. C. Some refined oils are acceptable. D. Only brown oils are acceptable. E. Some oils are not acceptable. F. Only refined oils are brown. (1) BDE (2) CFE (3) AEB (4) ABE Directions for Qs. 14-17: Refer to the following information and answer the following questions. In a village far far away, by name Foolistan, there are four kinds of people: Dumbos, Idiots, Fools and Morons. The village has each of these people in equal numbers, people in the village belong to exactly one of the four kinds. Everyday, people in this village have the habit of making assess of themselves. However, some rules are followed. A person may not make an ass of himself (or herself) at all. Idiots commit twice the number of blunders as do Dumbos, Fools thrice as many as Idiots and Morons four times as many as Fools. However, by a strange fact of the tribe, if even one person of a kind commits zero blunders, no one in the group commits a blunder. Every Dumbo commits the same number of blunders as every other Dumbo. Use these facts to answer the next four questions. 14. On a particular day, 66,000 blunders were committed. Which of the following is not possible?

(Assume the total population is 400) (1) A Fool did not commit any blunder (2) An Idiot did not commit any blunder (3) A Moron did not commit any blunder (4) None of these

15. The population of the village is 400. On a given day every group committed blunders, and Fools

as a group commit 1200 blunders. The total number of blunders committed on that day is: (1) 5000 (2) 6600 (3) 66000 (4) 6000 16. On a particular day, the Morons don’t commit any blunders, and the other groups may or may not

have committed blunders. Which of the following is the least number of blunders, which certainly satisfy the above the criteria? (Assume total population = 400)

(1) 600 (2) 100 (3) 2700 (4) 900 17. On a day, all four groups commit blunders and a Dumbo commits 3 blunders. If the population is

400, the total number of blunders on the day is: (1) 99 (2) 9900 (3) 9000 (4) 990 Directions for Qs. 18 to 20: Refer to the following information and answer the following questions. Shyam Kumar multiplier is a smart mathematician. While negotiating has salary with his prospective employer he worked out and proposed a novel salary plan, which his employer accepted as he was one of the smartest salesman around. According to the plan, his salary would increase every day of his employment such that on any day his income would be two rupees more than the square of the number of the days he has been employed for with the company. Back home his wife Renu congratulated him on working out an excellent deal and then together they planned their expenses in tune with the new salary plan. As they expected their income to be increasing on a daily basis — they planned their expenses in a way that the expenses of any day would be met by the day’s income itself, moreover they planned to make a net saving (which would be the difference of income and the expenses of the day) out of the day’s income. Thus they expected their expenses to be one rupee more than twice the number of days Shyam Kumar would have been employed for on that day, with the company.

18. On which day of his employment did Shyam Kumar Multiplier’s savings of a day exceed Rs. 100? (1) 10th (2) 11th (3) 12th (4) 13th 19. Shyam Kumar Multiplier wanted to get into Limca Book of Records. He eyed the category which

listed the person holding the record for the maximum salary increase in a single day. The person currently holding the record is Salim Khan who was given a raise of Rs. 12,000 in a single day. If Shyam Kumar were to beat his record he will have to remain in this job for a minimum of,

(1) 5999 days (2) 6000 days (3) 6001 days (4) 6002 days 20. Shyam and Renu planned to put each day’s savings into their savings bank account. They also

decided that they would regularly purchase Fixed Deposits in multiples of Rs. 300 from their savings in the account. They would purchase their first Fixed Deposit on

(1) 11th day (2) 12th day (3) 13th day (4) 14th day Directions for Qs. 21 – 25: Refer to the following information and answer following questions. Alord received a large order for stitching school uniforms from Mayflower school and Little Flower school. He has two cutters who will cut the fabric, five tailors who will do the stitching, and two assistants to stitch the buttons and button holes. Each of these nine persons will work for exactly 10 hours a day. Each of the May-flower uniforms requires 20 min. for cutting the fabric, one hour for stitching, and 15 min. for stitching buttons and button holes, whereas the Little Flower uniform requires 30 min., 1 hour, and 30 min. respectively for these activities. 21. What is the maximum number of little Flower uniforms that A lord can complete in a day? (1) 50 (2) 20 (3) 40 (4) 30 22. On particular day, Alord decided to complete 20 Little Flower uniforms. How many Mayflower

uniforms can he complete on that day? (1) 30 (2) 40 (3) 20 (4) 0 23. If Alord decides to complete 30 Little Flower uniforms only and no other on a particular day, how

many total man-hours will be idle? (1) 20 (2) 30 (3) 5 (4) 25 24. If he hires one more assistant, what is the maximum number of Mayflower uniforms that he can

complete in a day? (1) 40 (2) 50 (3) 60 (4) 30 25. A lord has the option to hire one more employee of any category. Which category should he hire

to get maximum increase in production capacity, assuming that he needs to stitch only Mayflower uniforms on that day?

(1) Tailor (2) Cutter (3) Assistant (4) Cannot be determined Directions for questions 26 to 35: Each questions is followed by two statements, A and B. Answer each question using the following instructions. Choose 1: if the question can be answered by using one of the statements alone, but cannot be

answered by using the other statement alone. Choose 2: if the question can be answered by using either statement alone. Choose 3: if the questions can be answered by using both the statements together, but cannot be

answered by using either statement alone. Choose 4: if the question cannot be answered even by using both the statements together. 26. What is the value of the two digit positive integer N? A. Four times N is 48 less than the square of the smallest two digit number. B. N is a prime number whose square lies between 150 and 250.

27. ABCD is a cyclic quadrilateral. Is ABCD a rectangle? A. AB⏐⏐ CD. B. ∠ A + ∠ C = 1800 28. What is the value of the positive integer n? A. The product of the numbers a, and b, which are respectively three less and two less than n,

is 0.

B. 2)!(n2

n!−=

29. What is the perimeter of the triangle ABC? One of its side is 10√3 units. A. ABC is the hypotenuse of the right angle triangle ABC. B. The sum of the areas of the semicircles described on the three sides of the triangle ABC is

100 π sq. units. 30. The cost price of an article is 100. Find the profit made by selling it. A. Ten percent discount was given on the list price and the profit percentage made is 25

percentage points more than the discount percent. B. List price is Rs.180 and profit percent is 1/5th of the mark up percentage. 31. The length of trains of traveling at 90km/hr crosses train B in 32 seconds. A. Train A traveling at 90 km/hr crosses train B in 32 seconds. B. Train A and B are not traveling in the opposite directions. 32. Find the value of the real number N, where N > 0? A. N is a two digits prime number less than 15, whose square and cube have the digit 1

occurring more than once. B. N is a composite number less than 10, whose square and cube have their sum of digits equal

to the number itself or a multiple of it.

33. Is 3

5n10 + an integer?

A. n is an integers. B. n is and natural integer. 34. Will A and B take more than 14½ days to complete the work working together? A. If they work on alternate days with A starting the work, they take 28½ days to complete the

work. B. If they work on alternate days with slower person among A and B starting the work, they

take 29 days to complete the work. 35. The length of train A and B are 4000m and 350 respectively. What is the speed of the train B? A. Train B crosses train A which is traveling at 60km/hr in 22 seconds. B. The speed of trains B is more than the speed of trains A.

Directions questions for 36 to 40: Study the following graph and answer the questions that follow.

PERCENTAGE SHARE OF VARIOUS MAKES OF CARS IN

THE MARKET

0102030405060708090

100

1994 1995 1996 1997 1998

Maruti Fiat Ambassador Ford Escort

NUMBER OF CARDS SOLD BY MARUTI (in '000s)

0

1000

2000

3000

4000

5000

1994 1995 1996 1997 1998

36. What is the number of Fiat cars sold in 1994 (in ‘000s)? (1) 750 (2) 500 (3) 1500 (4) can’t say 37. Which of the following statements is false? (1) The number of Fiat cars sold registered a decrease from 1995 to 1996. (2) The number if Fiat cars sold registered an increase from 1996 to 1997. (3) The number of Ambassador cars sold registered an increase from 1997 to 1998. (4) None of these. 38. Which of the following statements is/are true?

(A) The percentage decrease in the number of cars sold by Fiat from 1994 to1998 is 75% (B) The number of cars sold by Ford Escort in 1997 and 1998 is same. (C) The percentage increase in the number in the number of cars produced by Maruti in 1996, when compared to that of 1995 in more than 100% (1) A and C (2) B and C (3) A and B (4) None of these

39. In which of the following years, did the umber of ford Escorts sold register a decrease compared

to that in the previous year? (1) 1998 (2) 1996 (3) 1997 (4) Both1996 and 1998 40. The total number of cars sold is maximum in the year (1) 1995 (2) 1996 (3) 1997 (4) 1998 Directions questions for 41 to 45: These questions are based on the following data. 50,000 Units of brand X are being sold in the market at a price of Rs.1o/- unit. A competitive brand, Y, enter the market. The course of actions available for the company marketing brand X are (1) Cut the price of X by 50 %, which would result in an increase in the number of units sold of X by

30 % with a probability of 0.5 and 20% with a probability of 0.5 ((2) Advertise, which would cost Rs.2,00,00, but would result in an increase in the number of units

sold of X by 50% with a probability of 0.1, by 20% with a probability of 0.5 and 10% with a probability of 0.4.

(3) Remain silent, in which case, the probability of losing the market by 40 % is 0.5 and the probability of retaining its market is 0.5

41. Which is the best course of action to follow? (1) cut down the prices (2) Advertising

(3) remain silent (4) Cannot be determined 42. In which of the cases, does the market of X (number of units sold) increase the most? (1) cut down the prices (2) Advertising (3) Remaining silent (4) None of these 43. What is the net loss if course 1 is followed ? (Net Loss = Money realised originally – Money realized now) (1) Rs.87,500 (2) Rs.1,00,000 (3) Rs.1,87,500 (4) Rs.2,00,000 44. What is the revenue realised (net of advertising expenses) if Course 2 is followed? (1) Rs.4,00,000 (2) Rs.3,95,000 (3) Rs.3,12,500 (4) Rs.3,00,000 45. How much more/less in the net revenue realized by following course 2 than that realised by

following course 2 than that realised by following course 3? (1) Rs.5,000 less (2) Rs.5,000 more (3) Rs.50,000 (4) Rs.50,000 more DIRECTIONS for questions 46 to 50: Refer to the data below and answer the questions that follow. ABC limited produces a product P for which demand is unlimited and they can sell all they produce. They want to control costs and have three production plans from which to choose. The fixed cost incurred by the company is Rs.1lac, Rs.1.5lacs and Rs.1lac from plan I, II and III respectively. Given below is the graph of marginal cost of production virus number of units produced. It is also give that it can produce P in a batch of 1000 only.

0

1

2

3

4

5

6

7

1 2 3 4 5 6Unit productions (in '000)

Rs.

lacs

Plan 1 Plan 2 Plan 3

46. If production = 2000, then which of the three is best plan?

(1) Plan 1 (2) Plan 2 (3) Plan 3 (4) Plan 1 or Plan 2 47. If production = 3000 then which of the three is the best plan?

(1) Plan 1 (2) Plan 2 (3) Plan 3 (4) Plan 1 or Plan 2 48. If production < 3000 then which of the three is the best plan?

(1) Plan 1 (2) Plan 2 (3) Plan 3 (4) Plan 1 or Plan 2 49. If production > 4000 then which of the three is the best plan?

(1) Plan 1 (2) Plan 2 (3) Plan 3 (4) Plan 1 or Plan 2 50. For some reasons, the company cannot choose plan1, then 2 is best plan if;

(1) Production≤4000 (2) Production<4000 (3) Production=3000 or Production=4000 (4) Non of these

EXERCISE 2 Direction for Qs. 1to5 : Refer to the following information and the answer the following questions. People Power Corporation presently employs three Managers (A, B and C) and five recruitment agents (D, E, F, G and H). The company is planning to open a new office in San Jose to manage placement of software professionals in the US. It is planning to relocate two of the three managers and three of the five recruitment agents to the office at San Jose. As it is an organization which is highly people oriented the management wants to ensure that the individuals who do not function well together should not be made as a part of the team going to the US. The following information was available to the HR department of People Power Corporation.

Managers A and C are at each others throat and therefore cannot be sent as a team to the new office.

C and E are excellent performers in their own right. However, they do not function together as a team. They should be separated.

D and G have had a major misunderstanding during the last office picnic. After the picnic these two have not been in speaking terms and should therefore not be sent as a team.

D and F are competing for a promotion which is due in another 3 months. They should not be a team.

1. If D goes to the new office which of the following is (are) true?

I. C cannot go II. A cannot go III. H must also go (1) I only (2) II and III only (3) I and III only (4) I, II and III 2. If A is to be moved as one of the Managers, which of the following cannot be a possible working

unit? (1) ABDEH (2) ABFGH (3) ABEGH (4) ABDGH 3. If C and F are moved to the new office, how many combinations are possible? (1) 4 (2) 1 (3) 3 (4) 5 4. Given the group dynamics of the Managers and the recruitment agents, which of the following is

sure to find a berth in the San Jose office? (1) B (2) H (3) G (4) E 5. If C is sent to the San Jose office which member of the staff cannot go with C? (1) B (2) D (3) G (4) F Directions for Qs. 6 - 10: Refer to the following data and answer the following questions. It is a game based on the position you take in a clock. You are at the 1 O’clock position. You can move one step clockwise, 1 step anti clockwise or to a place that is diametrically opposite yours. For example, from 1 O’clock if you move clockwise you will be at 2 O’clock. As you start the game, you are at 1 O’clock position and your score is 1. If you move a step clockwise, add the value of the time in that position to your score to give you the new score. If you move a step anticlockwise, add the value of the time in that position and subtract 2 from your score. If you move a step diametrically opposite, add the value of the time in that position to your score and subtract 4 from your score to get the new score. You cannot get back to a position that you have already visited. 6. What will be your minimum score after the third move? (1) 10 (2) 7 (3) 11 (4) None of these

7. What will be your maximum score after the second move? (1) 16 (2) 18 (3) 20 (4) 24 8. If you had moved a step anticlockwise in the first move, you could not have reached one of the

following positions in the third move. (1) 10 O’clock (2) 5 O’clock (3) 7 O’clock (4) 6 O’clock 9. What is the shortest number of moves that you require to reach the 5 O’clock position When you

start from 1 O’clock position? (1) 4 (2) 3 (3) 5 (4) 2 10. A man said to a lady, “Your mother’s husband’s sister is my aunt.” How is the lady related to the

man? (1) Mother (2) Aunt (3) Sister (4) Grandmother 11. If P + Q means P is the brother of Q; P – Q means P is the mother of Q and P * Q means P is the

sister of Q. Which of the following means M is the maternal uncle of R, if you can assume a third person K to be involved in establishing the relationship?

(1) M-K*P (2) M+K*R (3) M+K-R (4) M+K+R Directions for Qs. 12 - 13: Refer to the following information and answer the following questions. A, B, C and D are four ladies who are friends of Elizabeth. On one Saturday the four of them visited Elizabeth at her weekend getaway. I. The time of each visit was as follows: A at 8 O’clock, B at 9 O’clock, C at 10 O’clock and D at 11

O clock. II. At least one woman visited Elizabeth between A and B. III. At least one of C or D visited Elizabeth before A. IV. C did not visit Elizabeth between B and D. 12. Who visited Elizabeth first? (1) A (2) B (3) C (4) D 13. Who visited Elizabeth last? (1) A (2) B (3) C (4) Insufficient data Directions for Qs. 14 - 18 : Refer to the following information and answer the following questions. Each of the questions is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question. Mark (1), If the question can be answered by using one of the statements alone, but cannot be

answered by using the other statement alone. Mark (2), If the question can be answered by using either statement alone. Mark (3), If the question can be answered by using both the statements together, but cannot be

answered using either statement alone. Mark (4), If the question cannot be answered even by using both the statements together. 14. Is one of X or Y a fraction? A. X2Y3 = 8 B. X is rational 15. A is a prime number. Is B a prime number? A. B = 9A + 7 B. AB is even 16. Is 3x + 10y even? A. x is even B. y is odd 17. Which amongst the three x, y and z (all real) is the greatest? A. x : y : z : : 6 : 8 : 11 B. xyz – y2 is positive

18. What is the speed at which L is driving? A. The ratio of the speeds of L and M is 3 : 5 B. L and M start from city X to Y simultaneously and as soon M reaches city Y he returns and

meets L on the way exactly 2 horus from the time they both left city X. Directions for Qs. 19 – 23: Refer to the following information and answer the following questions. Each question contains two statements in the question followed by four statements. Choose the alternative from the four statements which is logically related and follows the statements in the question. 19. No M are P. Some M are S (1) Some S are P 2. Some P are S (3) No S are M (4) Some S are not P 20. All M are P. All S are M (1) All P are S (2) All M are S (3) All S are P (4) None of the above 21. Some M are not P. All M are S (1) No S are P (2) All S are P (3) Some S are not P (4) No S are P 22. No P are M. Some S are not M. (1) No S are P (2) All P are S (3) Some M could be S (4) All S are P 23. All Critical Thinking classes are full. John found a class that wasn’t full (1) John might have found a Critical Thinking class (2) The class John found was not a Critical Thinking class (3) All Critical Thinking classes were not found (4) John was a dumb guy Directions for Qs.24– 25: Refer to the following information and answer following questions. Speaker: The great majority of people in this city have access to the best medical care available any where in the world. Opposition: There are thousand of poor in this city who cannot afford to pay to see a doctor. 24. Which of the following is true of the opposition’s comment? (1) It constitutes a hasty generalization on few examples (2) It cities statistical evidence which tends to corroborate the views of the speaker (3) It tries to compare two unrelated data and draws a contrarian conclusion (4) It is not necessarily inconsistent with the speaker’s remarks. 25. A possible objection that opposition could have fielded to the spearker’s comments would be to

point to the existence of (1) a city which has more doctors than this city (2) a city in which people are given better medical care than this city (3) a city which has a higher per capita hospital bed than this city (4) the amount spent on medical insurance for people of this city

DIRECTIONS for questions 26 to 30: Refer to the data below and answer the questions that follow.

Figure 1

0

100

200

300

400

500

600

75 80 85 90 95 2000Year

Pro

perty

Crim

es

Figure 2

0

10

20

30

40

50

60

75 80 85 90 95 2000Year

Vio

lent

Crim

es

The two graph above gives me crime statistics for the USA. Fig 1 give the variation of the number of property crimes per 1000 households with time. Property crimes consist of motor vehicle theft, theft and burglary. Fig 2 gives the number of violent crimes per 1000 population with time. Violent following can be divisible into three categories – aggravated assault, simple assault and robbery. The following facts are also given and may be used in answering the questions that follow. 1. The population of the USA between 1975 and 2050 is by the equation P= 2.3 (T-1950) + 157,

where P is the population in millions in the year T. 2. The number of persons per household can assumed to remain constant for the period 1975 to 2050. 26. Let x1 and x2 be the number of property crimes in 1975 and in 2000 expressed as a percentage of

the population, respectively. What is the ratio of x1 to x2? (1) 3 : 1 (2) 27 : 10 (3) 1 : 3 (4) 18 : 5 27. Assume that the total number of property crimes per year follow the following trend after 2000.

The total number of property crimes per year at the end of every 25 year is 0.71 times the number at the beginning. What is the number of property crimes per 1000 households in the year 2050?

(1) 63 (2) 90 (3) 129 (4) 180

28. In 2000, the number of aggravated assaults/1000 population was greater the number of robberies/1000 population by 1.8 and the number of simple assaults was three time the number of aggravated assaults. What was the total number of robberies in 2000?

(1) 1.1×106 (2) 1.1×103 (3) 3.9 (4) 3.9×103

29. Let y1 and y2 be the total number of violent crimes per year in 1975 and 2000, respectively. What

is y2 – y1 (1) 22 (2)-22 (3) 4.2 (4) none of these 30. The total number of property rimes in the year 200 was 1.45 times the total number of violent

crimes in the year 1975. what is the average number of person per household? (1) 2.1 (2) 3.2 (3) 4.2 (4) 4.9 DIRECTIONS for questions 31 to 35: Refer to the data below and answer the questions that follow. ABC is a firm which deals with furniture. Manufacturing of table requires three levels of assembly. The finished table is at first level. The leg assembly and table top are second level. The pieces that go into the leg assembly are at the third level which consist of shortrails, longrails and legs. One unit of table requires one unit of tabletop and one unit of leg assembly. One unit of leg assembly requires 2 units of shortrails, 2 units of longrails and 4 units. Orders are placed just in time to minimize storage. The lead time for activities are (Lead time is waiting time required to complete one activity)

Parts Weeks Assamble table 1 Finished leg assembly 1 Purchase legs 1 Purchase shortrails 1 Purchase longrails 1 Purchase table top 2

The availability of part at present time

Parts Units Table 50 Leg assembly 100 Legs 150 Shortrails 50 Longrails 0 Table top 50

Demand of finished Tables

Details Week 4 Week5 Week6 Demands (units) 200 150 100

31. For meeting the demand of 200 units of finished table of week 4, when would the first order of

tabletops be placed? (1) Week 1 (2) Week 3 (3) Week 4 (4) Week 5 32. What is the net requirement of legs for meeting the demand of week 4 finished table? (1) 200 (2) 50 (3) 400 (4) 800

33. When and how many units of shortrail would be placed for meeting the demand of finished table of week 6?

(1) 100 units in week 1 (2) 200 units in week 3 (3) 300 units in week 6 (4) Data insufficient 34. If in-hand units of legs are increased from 150 to 300, then what would be the net requirements of

legs for meeting the demand of finished table of week 5? (1) 1800, 900 (2) 2200, 1100 (3) 1600, 800 (4) 800, 400 35. The supplier of longrails has shiftedhis manufacturing unit to its new location. Because of this the

delivery time of long rail has been increased by 1 week. When would the order of longrails be placed to meet the week 5 demand of finished table?

(1) Week 1 (2) Week 4 (3) Week 5 (4) None of above DIRECTIONS for questions 36 to 40: Each of the following questions is by two statements. Mark [1], if the question can be answered by using any of the statements alone but not by using the

other statement alone. Mark [2], if the question can be answered only by using either of the statements alone. Mark [3], if the question can be answered only by using both the statements together. Mark [4], if the question cannot be answered. 36. a, b, c, d are positive integer. Which is the second smallest of these?

I. 3

c

2

b,

4

b

3

a<< II.

3

d

4

c,

6

d

3

a<<

37. LCM of two numbers A & a B is & is and HCF is 12. What is the number B?

I. A is not a factor B. II. B is greater than A.

38. What is the age of Ram?

I. Sum of the ages of Ram and Shyam was 60 five years back. II. Sum of the ages of Ram and Shyam would be 100 fifteen years from now.

39. What is the ratio of volume of sphere to of the cone?

I. Radius of the cone is twice that of the sphere. II. Height of the cone is equal to the radius of the sphere.

40. Who is/are the tallest among A, B, C, D and E?

I. D is the tallest among C, D and E. II. B, who is not shorter than D, is not the shorter of A and B.

Questions 41 to 43: are based on the following City College is selecting a four-person debate team. There are seven candidates of equal ability. X, Y and Z, who belong to Group A; and L, M, N and P who belong to Group B. The team must have two members from each group. Also, the members must be able to work well with the all the members of the other team. Debaters Y & L, Z & N, L & M are incompatible pairs. 41. If debater Y is rejected and M is selected, the team will consist of (1) L, M, X and Z (2) M, N, X and Z (3) M, N, P and X (4) M, P, X and Z. 42. If debater L is on the team, which other debaters must be on the team as well? (1) M, X and Z (2) N, X and Z (3) P, N and Z (4) P, X and Z

43. If both Y and Z are selected, which of the other debaters are thereby assured of a place on the team?

(1) Both L and M (2) Both M and P (3) Only N (4) Both N and P Directions: Q 44-50: The following table gives the number of AIDS cases over 2 years of selected countries.

All countries that have reported more than five hundred AIDS cases to the WHO in 1997 are listed here. The left column gives the total number of cases reported by each country for 1996, the middle column gives the 1996 rate (AIDS cases per 10000 population) and the last column shows the number of cases reported in early 1997. Most 1997 reports were for only the first quarter or a third of the year. Owing to reporting delays of six months or more, cases reported in 1997 actually were diagnosed in 1996. 44. Which country has reported the maximum number of AIDS cases to WHO during 1996?

(1) Brazil (2) United States (3) France (4) Italy

55. How many countries have reported 25000 AIDS cased in the early 1997? (1) Two (2) One (3) Three (4) None.

Country 1996 (In ‘000 cases)

1996 (Rate)

1997 (In ‘000 cases)

Argentina Australia Austria Bahamas Belgium Brazil Burundi Canada Chile Denmark Dominican Republic Ethiopia France French Guyana Greece Haiti Honduras Israel Italy Jamaica Japan Mexico Netherlands New Zealand Norway Portugal South Africa Sweden Switzerland United Kingdom United States Wet Germany Yugoslavia Zambia

51 342 85 78 85 1361 652 513 34 97 256 19 1852 45 53 332 58 13 888 37 34 499 215 30 35 44 46 73 163 653 21846 873 18 286

0.1 2.1 1.1 33.9 0.8 0.9 13.0 1.9 0.2 1.8 3.9 0.0 3.3 56.2 0.5 5.0 1.2 0.3 1.5 1.4 0.0 0.6 1.4 0.9 0.8 0.4 0.1 0.8 2.4 1.1 8.9 1.4 0.0 4.0

43 143 37 25 25 206 235 232 13 25 152 18 555 10 18 231 38 11 231 13 7 14 75 21 11 35 19 34 84 239 6442 222 12 218

46. The ratio of AIDS cases reported in early 1997 is 2 : 5 for (1) South Africa & Portugal (2) Israel & Denmark (3) Yugoslavia & Netherlands (4) West Germany & France 47. The number of countries for which 1996 (rate) [per 100,000] is more than five is (1) five (2) four (3) three (4) six 48. What is the population of Zambia on the basis of the reported cases of AIDS in 1996 (in

thousands)? (1) 650000 (2) 700000 (3) 72000 (4) 715000 49. Which of the following are true from the table?

I. The reported AIDS cases of Ethiopia, Japan and Yugoslavia as compared to the population is negligible.

II. The 1996 (rate) is highest for French Guyana though the reported cases are only 45000. III. The population of Haiti is 66400000 IV. France reported more than 2000 cases of AIDS in 1996.

(1) I & II (2) II & III (3) I, II & III (4) I, II & VI 50. The countries which have reported less than 2000 cases both in 1996 and early 1997 are (1) Japan, Ethiopia and Israel (2) Jamaica, Yugoslavia & Japan (3) Ethiopia, Chile & French Guyana (4) Ethiopia, Israel and Yugoslavia.

EXERCISE 3 DIRECTIONS for questions 1 to 10: Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question. Mark 1 if the question can be answered by using one of the statements alone, but cannot be answered by


Mark 2 if the question can be answered by using either statement alone.

Mark 3 if the question can be answered by using both statements together, but cannot be answered by

using either statement alone.

Mark 4 if the question cannot be answered even by using both the statements together.

1. One side of the triangle ABC is 5cm long. Is the largest angle in triangle ABC greater than 90°? I. Triangle ABC is a right angled triangle 4, II. Two sides of the triangle ABC are 3 cm and 4 cm long.

2. What is the number of institutes in Hyderabad that have an annual income of over Rs.5, 00, 000

and own a Laser Printer? I. 30% of the institutes in Hyderabad have an annual income of over Rs.5, 00, 000 II. 25% of the institutes in Hyderabad which have an annual income of over Rs.5,00,000

own a Laser Printer.

3. Is a >b? I. 8 - (a - b)3 is a positive number. II. 4 - (a-b)2 is a negative number.

4. There are two identical cubical boxes A and B which contain 8 and 27 balls respectively. The balls

are made of the same material. Which box is heavier? I. The balls are of different sizes. II. The boxes are not made of same material.

5. Is a/b defined where a and b are integers?

I. a is neither a positive number nor a negative number. II. b is neither a positive number nor a negative number.

6. What time does the clock show?

I. The angle between the hours hand and the minutes hand is 80°. II. The time is between 3 O'clock and 4 O'clock.

7. A ladder is leaning against a wall at a height of 9m at 8:00 a.m. and it started slipping. What is the distance

between the point at which the ladder is contacting the wall and point at which the ladder is contacting the floor at 8:30 a.m.? I. The length of the ladder is 15 m. II. The rate at which the top of the ladder is slipping is 2 cm per minute.

8. What is the speed of a particle at position x? I. The speed of the particle was 5 cm/sec at point X0 which is 5 cm away from x. II. The speed of the particle is increasing at the rate of 0.5 cm/sec every 1 cm it travels.

9. What is the ratio of two numbers p and q? I. p is 50% greater than q. II. p and q are respectively 87.5% and 25% greater than a third number r.

10. If each pencil costs Rs.2 and each pen costs Rs.3, then how many pens did I buy given that I

bought at least one pencil and at least one pen? I. I bought one pencil. II. I spent a total amount of Rs.8 buying pens and pencils.

DIRECTIONS for questions 11 to 14: These questions are based on the following information regarding the price changes that a certain pharmaceutical company is considering for its products.

Product Existing Price (Rs.) Revised Price (Rs.) Antacid 1.50 2.50 Anti Hypertensive 10.00 12.50 Expectorant 18.00/bottle 24.00/bottle Anti Asthmatic 20.00 26.00 Anti Pyretic 5.00 8.00

The prices for all the products except Expectorant are the prices of 10 tablets. 11. If a family has a hypertensive and an asthmatic patient, where the person with hypertension has to

consume three tablets of Anti Hypertensive per day and the asthmatic patient has to take two tablets of Anti Asthmatic every alternate day, what will be the increase in expenditure on two patients for 30 days? (l) Rs.40.50 (2) Rs.42.75 (3) Rs.46.50 (4) Rs.38.50

12. What is the percentage increase in the expenditure of a person for one year if he consumes 32

tablets of Antacid in one week? (1) 7½% (2) 6 ½ % (3) 62/3% (4) None of these

13. A person is prescribed to take two spoons of Expectorant thrice everyday for a period of, 20

weeks. Assuming that each bottle of Expectorant contains 90 spoons. Find the expenditure according to the existing prices. (1) Rs.200 (2) Rs.180 (3) Rs.168 (4) Rs.240

14. A person is prescribed a combination of antipyretic and anti-asthmatic such that he has to take one of

these before breakfast, the other after lunch and the one he had at breakfast at dinner also; if he consumed an antipyretic at the end of the dinner after the 7th day of the course, he started the course with (1) Anti-asthmatic (2) Antipyretic (3) Not possible to determine (4) None of the above

DIRECTIONS for questions 15 to 19: These questions are based on the pie diagrams given below. Shefali, a first year student of management from a well known institute of management in western India, was doing her internship with a leading public sector bank in India. Her project involved analyzing the market shares of various Indian companies that manufacture and sell fuels and lubes. Halfway through her project she managed to collect the following information from the sales figures of various companies.

Percentage shares of various companies in total sales of fuel (by value)

OICL30%

OTHERS15%

PRL10%

PHCL25%

PBCL20%

Percentage shares of various companies in total sales of lubes (by value)

OICL30%

OTHERS15%

PHCL25%

PBCL20%

PRL10%

Shefali's project guide, after reviewing the above information, pointed out the fact that the above figures were inclusive of the considerable volumes of inter-company sales that occur every year. Therefore the correct market shares of the companies should be arrived at after deducting the inter company sales figures from the present figures. Shefali then further collected the following information regarding the inter-company sales.

BUYER Sale value as a percentage of the total sales of the selling company SELLER PRL OICL PHCL PBCL OTHERS

Fuels - 50 10 - 40PRL Lubes - 30 - 10 60Fuels — — 15 20 10OICL Lubes - - 20 - 40Fuels - 20 - 20 20PHCL Lubes - 10 - 25 40Fuels - 30 10 - 35PBCL Lubes - 15 5 - 25Fuels - 10 5 10 - OTHERS Lubes - 15 5 15 -

15. By approximately what percentage did Shefali overestimate the correct value of the total sales of fuels? (1) 135% (2) 200% (3) 110% (4) 180%

16. If the correct sales figures are considered, then which of the following has the largest percentage

share by value of the sales of fuels and lubes put together? (1) PRL (2) OTHERS (3) OICL (4) PBCL

17. If for any company, Sales - Purchases = Profit, then neither fuels nor lubes were profitable for

(1) PRL (2) PHCL (3) OTHERS (4) OICL

Total Sales of fuels for the year 2000-2001 = Rs. 22, 400crores

Total Sales of lubes for the year 2000-2001 = Rs. 22, 400crores

18. Assuming the information given in the above question as true, which of the following had the maximum profitability for fuel? (1) OICL (2) PHCL (3) PBCL (4) OTHERS

19. Which of the following had the second largest percentage share by value when the correct sales

figures of fuels and lubes put together are considered? (1) OTHERS (2) PHCL (3) OICL (4) PBCL

DIRECTIONS for questions 20 to 23: These questions are based on the data given below. A paddy processing unit purchases 10,000 kg of paddy. After subjecting it to milling operation, the husk and rice are separated. The husk forms 5% of the total paddy weight. The rice so extracted from the paddy contains 6% of brokens or defective material in it. Cost of purchase of paddy is Rs.3.50/kg and the selling price of rice is Rs.8.00/kg. The broken material is sold at Rs.2.00/kg. The husk is sold atRs.0.50/kg. 20. What is the amount of paddy to be processed, such that the sale of the rice extracted from it excluding

brokens and husk fetches an amount of Rs.14, 288? (1) 2000 kg (2) 1786kg (3) 2500 kg (4) 1886 kg

21. Assuming that all the rice produced by processing 10,000 kg of paddy is sold, what would be the decrease in profits if the brokens in the operations increased to 8%? (1) Rs. 1,000 (2) Rs. 1,100 (3) Rs. 1, 140 (4) Rs. 1,200

22. Due to the evaporation of moisture, there is a 5% loss of weight before the processing of the. Paddy began. As a result the decrease in the weight of rice obtained (in kg) is (1) 450 kg (2) 500 kg (3) 447 kg (4) 475 kg

23. What is the amount realised on the sale of by products i.e., broken and husk on processing 5,000 kg of paddy (l) Rs.200 (2) Rs.180 (3) Rs.695 (4) Rs.190

DIRECTIONS for questions 24 to 27: These questions are based on the data given below. In a zoo, twelve animals, Elephant. Wolf Deer, Bear. Gorilla, Tiger. Antelope, Giraffe, Lion, Chimpanzee, Horse and Zibra are locked in twelve different cages from 1 through 12 (not necessarily in that order.) These cages are on either side of the path. Cages 1 through 6, in that order, are on the left side of the path and the cages 7 through 12, in that order, are on the right side of the path. Cage 1 is opposite Cage 7, Cage 2 is opposite Cage 8 and so on. The arrangement of the animals is as follows. 1. The Elephant is in the P1 cage and is diagonally opposite to the Wolf which is opposite to the

Chimpanzee. 2. The Bear is opposite to the Giraffe which is exactly in between the Gorilla and the Antelope. 3. The Deer is opposite to the Lion which is exactly in between the Wolf and the Tiger. 4. The Horse is diagonally opposite to the Chimpanzee. 24. If the Tiger is not opposite to the Gorilla, then which animal is adjacent to the Elephant?

(1) Antelope (2) Horse (3) Gorilla (4) Cannot be determined 25. In how many ways can the animals be arranged in the cage?

(l) One (2) Two (3) Three (4) Four 26. Which animal is exactly in between the Giraffe and the Deer?

(1) Antelope (2) Giraffe (3) Gorilla (4) Cannot be determined 27. If the Elephant is shifted to 12th cage and the Deer is adjacent to the Gorilla then which animal is

opposite to the Tiger? (1) Antelope (2) Lion (3) Gorilla (4) Deer

28. Five items A, B, C, D and E are kept in five different boxes numbered 1 to 5. Exactly one item is

kept in each box. C's box number is as much less than E's box number as E's box number is less 1 than A's box number. D is in box number 4 but not next to E. Then B is in box number (1) 3 (2) 1 (3) 5 (4) 4

Directions Q. 29 to 33: Study the following table and answer the question given below it. Number of different types of tyres of tyres sold by a company over the years (Numbers in lakh) Year A B C D E 1989 35 20 40 14 25 1990 40 15 55 20 35 1991 30 25 45 25 30 1992 25 30 50 30 35 1993 45 35 25 38 32 1994 42 28 34 42 30 1995 36 34 38 48 25 29. What was the approximate percentage increase in the number of D type tyres sold from 1992 to

1993? (1) 26 (2) 30 (3) 35 (4) 40 30. In which of the following years was the percentage of D type tyres sold to total number of tyres

sold the maximum among the given years? (1) 1992 (2) 1994 (3) 1990 (4) 1995 31. In the case of which of the following types of tyres was there continuous increase in sales over the

years? (1) B (2) E (3) D (4) C 32. What was the difference in the number of C type tyres sold in 1990 and 1994? (1) 21,000 (2) 2,10,000 (3) 2,50,000 (4) 21,00,000 33. The share of B type tyres in total sales of the company in 1994 was: (1) 13% (2) 14% (3) 15% (4) 16% DIRECTIONS for questions 34 to 36: These questions are based on the data given below. In the recently held Asian Games, an apartment in the games village was allotted to five sportsmen - Pranay, Qureshi, Rasool, Surendar and Tarif. They were practising for the games in which they were participating. The games in which they are participating are as follows. 1. No two players play the same number of games. 2. Exactly three players participate in swimming. 3. Tennis was the only game common among Pranay, Qureshi and Tarif. 4. Weightlifting is the most common game. 5. Qureshi and Rasool are the only chess players and when Surendar joins them they practise

weightlifting. 6. Cycling was the common game of Rasool and Tarif. 34. Which player plays all the five games?

(1) Pranay (2) Qureshi (3) Rasool (4) Surendar

35. Which among the following statements is definitely true? (1) The only common game among Pranay, Qureshi and Rasool is swimming. (2) The only common game between Qureshi and Tarif is cycling. (3) Qureshi and Rasool participate in ail the games except Tennis. (4) The number of players participating in each game is unique.

36. How many players participate in weightlifting?

(1) five (2) three (3) two (4) four DIRECTIONS for questions 37 to 38: Select the correct alternative from the given choices. 37. Eighty players numbered I through 80 are standing in a row, one behind the other, in the

increasing order of their numbers. The physical director of the players performed eight successive inspections of the players and in each of the respective inspections he sent the first 10, 20, 30, 40, 50, 60, 70 and 80 players, from the front of the row to the end of the row. Each time the players being sent back one after another. After these eight rounds of inspections what is the position of the player numbered 5? (1) 46th (2) 45th (3) 35th (4) None of these

38. Five friends A, B. C. D and F wear five different coloured shirts Red. White, Green, Blue, and

Black (not necessarily in that order) and five different coloured Trousers Red, White, Green, Blue and Black (not necessarily in that order) such that no person wears the shirt and the trouser of same colour. It is known that neither B nor E wears the Blue trouser while A wears a Black shirt. A. person has to wear only a White or Blue shirt with a White or Blue trouser. Which of the following gives a correct combination of the colour of A's trouser and the person wearing the Blue trouser given that D wears the Green shirt but not the Black trouser? (1) Green, D (2) Green, C (3) Red, D (4) cannot be determined

DIRECTIONS for questions 39 to 42: These questions are based on the pie charts given below

SECTORAL OUTLAY

1991- Total Outlay Rs. 2, 00, 000

Rural Developme

nt30%

Industrial15%

Medicine10%

Educations25%

Agriculture20%

1992- Total Outlay Rs. 2,50, 000

Industrial10%

Medicine15%

Rural Developmen

t50%

Educations10%

Agriculture15%

39. In 1992, the amount allocated to the sector recording a decrease in outlay of 8 percentage points

over the one year period exceeds the amount allocated to the sector recording an increase in outlay of 5 percentage points by an amount of (l) Rs.l0, 000 (2) Rs.12, 500 (3) Rs. 15, 000 (4) Rs. 17, 500

40. In the year in which the allocation to four sectors equals the allocation to Rural Development, the

outlay of the sector which has the maximum allocation out of these four sectors, exceeds that of the sector to which there was least allocation by (l) Rs.5, 000 (2) Rs. 10.000 (3) Rs.15, 000 (4) Rs.12, 500

41. The year in which allocation to Rural Development and other sectors are equal, the two sectors whose combined aggregate exceeds 25% but is less than 50% of the total allocation are (1) Agriculture and Medicine (2) Agricultural and Industrial (3) Medical and Education (4) None of the above

42. For the sector which records maximum percentage increase in allocation as compared to the

previous year, the difference between the outlay for the two years is (1) Rs.40, 000 (2) Rs. 5, 000 (3) Rs.50, 000 (4) None of these

DIRECTIONS for questions 43 to 46: These are based on the bar graph given below. PRODUCTION OF COTTON In thousands bales

0.6 0.6

1618

42 45

54

7276

8490

102

Manipur Sikkim Nagaland Tripura Assam W. Bengal

1993-94 1994-95

43. The total production in 1994-95 of the states that individually show a growth of more than 10%

from 1993-94 to 1994-95 forms what proportion of the total production for all the states for that year? (1) 82.1% (2) 91.7% (3) 93.6% (4) 85.8%

44. If x denotes maximum percentage increase in 1994-95 for any state and y denotes the least

percentage increase for any state in 1994-95, then which of the following relations between x and y is the most appropriate? (1) (x-y)2 = 0 (2) (x –y)2 = 5621 (3) x2/y2 is undefinable (4) y2/x2 is undefinable

45. By what percentage does the combined production in 1993-94 of the two largest cotton producing

states exceed the production of the state whose production was the closest to the average production of all the states that year? (1) 360% (2) 255% (3) 160% (4) None of these

46. The state which records 33.33% increase in production produces approximately what percentage

of total production for 1993-94? (1) 20 (2) 21 (3) 19 (4) 22

DIRECTIONS for questions 47 to 50: These questions are based on the following pie chart which represents the percentage of various trees in a fruit orchard consisting of 21, 600 trees and the table which represents percentages of fruit-yielding trees in each category of trees.

Apricot

PeachesCherries

Plums

Avocado

Fig

47. The number of fruit yielding Cherry trees in the orchard are

(1) 1701 (2) 4941 (3) 3402 (4) 5751 48. The number of fruit yielding apricot trees exceed the number of fruit yielding peach trees by

(1) 327 (2) 364 (3) 357 (4) 347

49. Which among the following has the greatest number of fruit yielding trees? (1) Avocado (2) Apricot (3) Peach (4) Plum

50. The fruit yielding plum trees from what percentage of fruit yielding peach trees?

(1) 112 (2) 110 (3) 107 (4) 101 DIRECTIONS for questions 51 to 55: These questions are based on the table given below.

PERFORMANCE OF EIGHT STUDENTS IN MOCK CAT Student code

Verbal Ability

Quantitative Ability

Reading Comprehension

Data Interpretation

√ x net √ x net √ x Net √ x Net S1 20 4 19 31 12 29 35 10 32.5 14 4 12 S2 42 8 40 18 4 16 40 10 37.5 20 5 18.75 S3 36 14 32.5 30 12 27 34 16 30 18 4 17 S4 7 4 6 12 8 10 32 12 29 14 4 13 S5 20 30 12.5 11 12 8 18 4 17 10 12 7 S6 40 10 37.5 30 20 25 30 20 25 15 5 12.5 S7 34 10 31.5 24 4 23 35 12 32 18 6 16.5 S8 28 20 23 32 16 28 30 16 26 20 4 19

√ → Number of questions correct x → Number of questions wrong net → Net score in the section

Type of tree

Percentage of fruit yielding trees in the category

Avocado 93 Apricot 87 Cherries 61 Fig 86 Plums 77 Peaches 78

Cut-off Marks

Area

Total number of questions in the section

Cutoff Marks

Verbal Ability 50 23 Quantitative Ability 50 18 Reading Comprehension 50 22 Data Interpretation 25 10

Students qualify in the test if they score more than or equal to cut off mark in all the sections. The sum of the net scores in all four sections together is called Grand Total. 51. Among the students who have qualified what is the maximum Grand Total?

(1) 106.5 (2) 108.5 (3) 100 (4) 103 52. What is the least Grand Total among the students who have qualified?

(1) 100 (2) 96 (3) 94 (4) 96.5

53. Who among the following committed maximum number of mistakes? (1) S1 (2) S2 (3) S3 (4) S7


I. The person who scored the maximum mark in Reading Comprehension did not qualify at the Exam.

II. The person who had the maximum Grand Total did not get maximum in any of the individual sections.

III. S8 attempted maximum number of questions among all the students. (1) Only I (2) Only I and ill (3) All three statements are true (4) Only I and II

55. Who among the following answered maximum number of questions correctly?

(1) S8 (2) S7 (3) S5 (4) S6

EXERCISE 4 DIRECTIONS for questions 1 to 5: Refer to data below and answer the questions that follow. In the two Tables below some statistics about consumption of electricity in India are given. Table 1 gives the electricity consumed per (1) 1000 population, (20 1000 sq. kms of area and (3) per1000

consumers, for the period 1950 to 1950. note that all the population in India does not consume electricity- only a fraction are actual consumers. The data is given in terms of GWH (Giga watt Hour) and 1 GWH = 109 WH.

Table 2 gives the number of consumers as well its break up into various categories for the same period. TABLE 1

Electricity Consumption in GWH

Year to 1950 1970 1980 1990 1993 1994 Per 1000 Population 0.016 0.09 0.253 0.253 0.299 0.32 Per 1000 Sq. kms area 1.7 15.4 25.1 64.4 80.8 88 Per 1000 Consumers 3.5 3.3 2.5 2.7 3.2 3.4

TABLE 2

Electricity of Consumers in Thousand

Year to 1950 1970 1980 1990 1993 1994 Domestic 1157 10165 22338 50389 60193 63406 Commercial 259 3206 4582 8002 9209 9558 Industrial 63 553 1150 2077 2337 2423 Agriculture 19 1571 4233 8631 9971 10372 Others 3 70 268 534 602 637 Total 1501 14665 32571 69633 82312 86399

1. Total electricity consumed by all the consumers in India in 1980 was

(1) 0.82×105 KWH (2) 0.82 ×107 KWH (3) 0.82×109 KWH (4) None of above

2. India’s total land area in 1994 was (1) 3.3×106 sq. kms (2) 3.3×107 sq. kms (3) 3.3× 108 sq. kms (4) 3.3×109 sq. kms 3. Let f1 andf2 be the fraction of the total population who were electricity

consumers in 1970 and 1980, respectively. What is the value of the ratiof1

f2

(1) 0.51 (2) 1.97 (3) 1.32 (4) Data insufficient 4. Consider the percentage rate of growth for the period 1980 to 1990 in the numbers of the four

types consumers Domestic, Commercial, Industrial and Agricultural. How many of these percentage rates of growth were more than the percentage rate of growth of the total number of consumers for the same period? (1) 0 (2) 1 (3) 2 (4) 3

5. What was the percentage increase in the number of Domestic consumers from 1970 to 1994?

(1) 223% (2) 374% (3) 524% (4) 612%

DIRECTIONS for questions 6 to10: Each of the following questions is followed by two statements. Mark [1], if the question can be answered by using any of the statements alone but not by using the

other statement alone. Mark [2], if the question can be answered by using either of the statements alone. Mark [3], if the question can be answered by using both the statements together. Mark [4], if the question can not be answered. 6. Is y a perfect square where x and y are natural numbers?

I. y is divisible by (x+1) and (x+2) II. y <200

7. Is a bag there are less than 40 marbles which are red, blue and black in colour. What is the probability of picking a black marble? I The probability of drawing a blue marble is 1/3. II. The probability of drawing a red marble is 1/24.

8. If 102 is perfectly divisible by a natural number x, what is the value of x?

I. x + 17 is divisible 3. II. X + 2is divisible by 4

9. The sum of the prices of 2 shares X and Y is Rs.160. what is the price of Y? III. When there is an increase of 10% in one of these of the shares and a decrease of 55 in the

other, there is a change of Rs.6 in Y. IV. 50 < x < 130

10. In ∆ABC. ∠A =700. What is the value of ∠C? I. ∠A -∠C < ∠B - ∠C II. B2 + C2 = 7300

DIRECTIONS for questions 11 to 14: Refer to the data and answer the questions that follow. Three leading drug manufacturers, ajit Pharma, and Chinku pharma each launch an atipyretic drug. Each company uses all or some of the 5 components A, B, C,D and E. the table below gives the composition of these components in their drug.

A B C D E Ajit Pharma 12 15 20 28 25 Bittu Pharma 37 15 13 15 20 Chinku Pharam 26 15 10 34 15

Above value are in percentage of composition. All manufactures produce their drug as a tablet of 300 mg. 11. .The effectiveness of components A, B, C, D are in the ratio 5 : 6 : 4 : 3, while E is just a sweetner

and does not have any therapeutic. Which of the following company’s tablet is most effective? (1) Ajit Pharma (2) Bittu Pharma (3) ChinkuPharma (4) Data Insufficient

12. If the side effects caused by drugs are proportional to the ratio of ‘s composition to the sum of B’s

and E’s composition, which drug has least side effect. (1) Ajit Pharma (2) Bittu Pharma (3) ChinkuPharma (4) Data Insufficient

13. Ajit Pharma finds that its sales are dipping, because it drug’s taste is too sweet. So, it decides to

decrease the composition of E and increase that C, keeping other composition unchanged. It also wants to make sure that the side effect is not more than double its previous value. What could be the maximum percentage of C’s composition in Ajit’s Drug? (Use data from the previous questions if necessary).

(1) 25% (2) 30% (3) 34% (4) 37%

14. If in all, million tables are produced by these 3 companies, per annum, the consumption of component C, annually would be:

(1) 60 kg (2) 90 kg (3) 105 kg (4) Data Insufficient DIRECTIONS for questions 15 to 19: Refer to the data below and answer the questions that follow. JET AIRWAYS 1ST august, 2002 to 31st October, 2002 (To & From) Special Festival Fares From Mumbai to

Current fares (R.)

Festival fares (Rs)

From Mumbai to Current fares (Rs)

Festival fares (Rs)

Delhi 6095 3920 Udaipur 4405 2213 Kolkata 6855 3320 Bhopal 4125 2371 Bangalore 4485 2839 Mangalore 4280 2446 Chennai 4905 2744 Nagpur 4200 2555 Hyderabad 4140 2443 Jodhpur 4935 2684 Ahedabad 3255 2017 Jaipur 5530 2917 Pune 2215 1295 Calicut 5060 3018 Indore 3360 1965 Cochin 6215 3248 Aurangabad 2745 2098 Thiruvananthapuram 6700 3312 To and From fares are same and the rates are effective from 1st August,2002 to 31st October,2002. 15. Ramesh, an executive of a company at Mumbai visits Delhi, Nagpur and Indors every month and

Mr. Ganesh visits Kolkata, Manglore and Hyderabad every mnth from Mumbai. Find the difference in th percentager benefit to the company between the rips of Ramesh and Ganesh in the festival month.

(1) 11 (2) 25 (3) 35 (4) none of these

16. With the discounts offered for Kolkata and Delhi tickets, how many different kinds of tickets can be bought respectively utilizing the festival benefit for other visits also

(1) 11 & 5 (2) 12 & 6 (3) 17 & 4 (4) 16 & 3 17. The largest absolute discount is what percentage of the lowest absolute discount? (1) 3.87% (2) 216% (3) 464% (4) 546% 18. What is the average discount in the air fare approximately? (1) Less than 10% (2) More than 50% (3) Less than 50% (4) None of these 19. Four executives of a company visited one of the four cities Delhi, Bhopal. Ahemdabad and Indore.

All of them left on 29th July, 2002 and came after a weeks visit, by the return flight of the same air lines. What would have been percentage saving in tickets expenditure if they had postponed their visit by one week, and returned after a week.

(1) 12% (2) 24% (3) 38% (4) 42% DIRECTONS for questions 20 to 24: Refer to the data below and answer the questions that follow. The table provides the percentage of total revenues accounted for the top 2 firms, top 4 firms and the top 190 firms in various industries. However, one of the data points in one of the industries is incorrect which is then corrected by adding or subtracting 4% from the incorrect data.

Industry Top2 form (% of

total industry) Top 4 Firms (% of total industry)

Top 10 Firms(% of total industry)

Steel 60 75 100 Oil & gas 50 80 100 Shipping 40 50 100 Leather 4 6 10 Textiles 8 18 30 Sp. Chem 3 5 7 Elevators 100 100 100 Refrigerators 25 40 60

20. Which is the incorrect data point and what is the correct data? (1) Top4firmsforOil & Gas, 75% (2) Top 4 firms for Leather,55 (3) Top 4 firms for Textiles,14% (4) Top 4 firms for Refrigerators, 45% 21. if the size of the largest steel firms is Rs5000 cr, which of the following cannot be the total size of

the steel industry? (1) 10,000 cr (2) 12,500 cr (3)15,000 cr (4) 17,000 cr 22. How many industry definitely have at least 20 firms in all? (1) 4 (2) 3 (3) 5 (4) 6 23. An industry faces restrictions if the top 2 firms form more than 40% of the industry and the top 4

firms more than 60% of the industry. An exception to this is if the largest firm in the industry is owned firms by the government. Which of the following is true?

(1) Government owned firms can exist in a maximum of 3 industries (2) 4 industries face restrictions.

(3) The ratio of the number of industries that face restrictions to the number of industries that do not face restrictions isles than 0.5.

(4) None of above. 24. If were least 2 mergers in the steel industry last year (the year before the data pertains to), how

many firms definitely existed in that industry last year? (1) 8 (2) 10 (3) 9 (4) 7 DIRECTIONS for Qns. 25 to 29: Consider the following statements where every person gets exactly one different dish:

1. Ria will not get soup unless Janet gets hot coffee. 2. Gia will not get gums unless Veena gets soup. 3. Veena will not get tea unless Gia gets soup. 4. Janet will not get gums unless Ria gets hot coffee. 5. Janet will not get hot coffee unless Veena gets gums. 6. Gia will not get hot coffee unless Ria gets tea. 7. Gia will not get tea unless Ria gets hot coffee. 8. Ria will not get hot coffee unless Gia gets soup. 9. Veena will not get gums unless Ria gets the hot coffee. 10. Janet will not get tea unless Ria gets gums. 11. Gia will not get soup unless Ria gets gums.

25. Who gets gums? (1)Ria (2)Gia (3) Janet (4) Veena

26. Who gets soup? (1)Janet (2)Veena (3) Gia (4) Ria 27. Who gets hot coffee? (1)Gia (2)Veena (3) Ria (4) Janet 28. Who does Janet get? (1)Hot coffee (2)Soup (3) Gums (4) Tea 29. Dileep, Martin and Salman married Ranjana, Vidisha and Karuna (not necessarily in that order).

Each of the couples has a son; their names being Saumitra, Shyam and Subhash. Further i. Ranjana married six months before Karuna did. ii. Salman was first to marry & Dileep, the last. Al the marriages took place in 1998

between February (month of first marriage) and September (month of last marriage). iii. None of the couples had a child within one year of their marriage. iv. Saumitra was born within 16 months of his parents’ wedding. He was not born between

August & Janauary both months inclusive v. Karuna’s son was born within 16 months of her marriage and Vidisha’s exactly 24

months after the marriage. vi. Subash was born an American citizen in Janaury.

Who are Saumitra’s parents

(1)Dileep-Ranjana (2)Salman-Karuna (3) Martin-Ranjana (4) Martin-Karuna

30. Sangt Kripalchand had been preaching daily how important it was not to tell a lie. At last, Seth

Jhuthamal decided to heed Sant’s teaching. So, henceforth, he would not tell a lie on Monday, Wednesday, Thursday and Saturday; on other days he would continue to tell lies only.

Presently, a customer comes to his jewellery shop and Seth Juthamal ties to close a sales deal. “But what is the guarantee that the jewellery is of specified parity” the customer asks. For today is Tuesday, the Santji’s beloved day, when I don’t speak a lie. “What if I make purchase tomorrow”, the customer enquires. “Tomorrow may be too late as being Saturday I may lie that day” insisted Sethji. So, this is how the conversation took place. What could be the day of this conversation?

(1)Friday (2)Tuesday (3) Sunday (4) Any one of these 31. Every month Chess Federation of India publishes ranking of Indian Chess Players. They actually

complement the FIDE lists which are brought out at longer intervals. It was seen, observing monthly lists for last tear, that top six players in the list remained same throughout the year but there was considerable mutual change of rankings among these six. Thus ranking for January 2003 as follows:

January 2003 was as follows:

1. P. Harikrishna 2. D. Barua 3. K. Humpy 4. S. Chanda 5. K. Ramesh 6. S.S Ganguli

The list of rankings for Feb 2003 had an entirely different look with each of the six ranked in a

position from the previous one. The following facts are known : 1. No one else had his/her ranking changed by as many places as D. Barua, whose change in

ranking was the greatest of the six. 2. The product of Chanda’s ranking for the two months was the same as product of Ganguli’s

ranking for the two months.

Who was ranked 5th in the list for February 2003. (1)P. Harikrishna (2)D. Barua (3) K. Humpy (4) None of these

32. In the following sum E E E EEE F F F XXX + G G G + YYY

J K LM JKLM where each of the different letters stand for a different digits, E stands for

(1)2 2 .3 (3) 4 (4) None of these DIERCTIONS for Questions 33 - 35: The coach of Indian Snooker and Billiards team has a novel way of providing them the required practice and improving the individual’s skill set. He does this through forming practice teams from among the team members after carefully considering relative strengths and weaknesses. Presently, he aims to reduce the number of practice teams from 4 – A1, A2, A3, A4 – to 3 to be called B1, B2 and B3. The players on team A1 are: A, B and C. The players on Team A2 are: D, E, F and G. The players on team A3 are: H and I. The players on team A4 are: J, K and L. A new team must, of course, have a minimum of two players. Other conditions are: 1. Each of the new teams (B teams) must contain at least one member from the four original teams

(A teams) 2. K and L have to be in separate teams 3. Any of the B teams cannot contain all the members of any of the A teams. 33. What could be the maximum strength of a B team? (1) 8 (2) 6 (3) 7 (4) 5 34. If one of the B teams is constituted of C, D, E, F and J only, which of the following groups cannot

completely represent one of the other B teams? (1) A, B, I (2) B, H, K (3) G, I, L (4) B, G, I, L 35. If a B team is constituted of A, C, D and K only, which of the following groups does not

completely represent one of the other B teams? (1) B, G, L (2) B, E, I (3) B, F, G, H (4) E, H, J, L DIRECTIONS for Q 36 - 37: Refer to the following data There are four bags on a shelf all in a straight horizontal line. Each bag contains a pair of socks and a tie. No bag contains a pair of socks and tie the same colour as the bag or each other. All four bags, pairs of socks and ties are either red, green, blue or yellow. No two bags are the same colour, no two ties are the same colour and no two pairs of socks are the same colour. The red tie is in the bag next to the bag containing the pair of green socks. The yellow socks are in the bag next to the green bag which is next to the bag containing the green tie. The bag on the far left is red. The blue socks are in the bag next to the bag containing the blue tie. The yellow bag is n’t next to the blue bag which is next to the bag containing the red socks. The green tie is in the blue bag or the yellow bag. The yellow tie is not in the red bag which is not, and is not next to the bag containing the yellow socks.

36. Which bag is the right most? (1) Yellow (2) Green (3) Blue (4) Yellow or Blue 37. Which combination of bag tie and socks (in that order) is in the extreme left? (1) Red- Blue-Green (2) Red–Green-Yellow (3) Red-Yellow-Red (4) Red-Yellow-Yellow

DIRECTIONS FOR Q. 38-39: Refer to the following data In a city state, government officials never tell the truth and those who are not government officials always tell the truth. A visitor meets three residents of the city state and asks one of them,” Are you a government official?” The first resident answer the question. The second native then reports that the first resident denied being a government official. The third resident says that the first resident is a government officials. 38. How many of these three residents are not government officials? (1) 1 (2) 3 (3) 2 (4) Insufficient data 39 What is the order in which the three residents statements are true/false (1) True, True, False (2) False, False, True (3) True, True, True (4) Insufficient data 40. In a batch of 120 postgraduate History students each student has to select at least one subject out

of American History, Ancient Indian History. Modern Indian History and History of Modern Europe. 90 students selected History of Modern Europe and an equal number. American History. 105 students selected Ancient Indian History and an equal number. Modern Indian History. AT least how many students selected all the four subjects.

(1) 75 (2) 45 (3) 30 (4) Insufficient data

EXERCISE 5 Directions: Q 1 to 4 are based on the following bar charts: LIQUOR SUPPLIED IN TAMIL NADU BY DISTILLERIES A, B, C, D, E (in lakh cases).

Q.1 Which of the five states manufactured liquor at the lowest cost? (1) Tamil Nadu (2) Delhi (3) The state which has the lowest value for (Wholesale Price – Excise duty) per litre (4) Cannot be determined Q.2 If Excise duty is levied before the goods leave the factory, then which of the following choices

shows the excise duty in ascending order for the year 1986? (1) ECABD (2) ADEBC (3) DCEBA (4) Cannot be determined Q.3 By what per cent do the excise duty rates between the closest among the five rates nearly differ? (1) 2 (2) 13 (3) 1/3 (4) Cannot be determined Q.4 If the Tamil Nadu Co., with the least simple annual growth in sales in the given period had shown

the same rate of growth as the one which grew fastest, what would that company’s sale have been in 1988, in lakh cases?

(1) 13 (2) 15.4 (3) 130 (4) Cannot be determined Directions Q 5 to 7 : Refer to the following Bar-chart (values are in Rs crore):

7.2611.92

9.35

12.07

6.41

10.78

12.89

3.57 4.215.795.753.15

05

101520253035404550

1986 1987 1988

The values of C, D and E to 1986 are 1.64, 1.05 and 2.45 respectively.

The order of distilleries is A to E from top to bottom.

100.5

67

141 143.9

65

020406080

100120140160

1984 1985 1986 1987 1988

Q.5 What is the average value of the contract secured during the years shown in the diagram? (1) Rs. 103.48 crore (2) Rs. 105 crore

(3) Rs. 100 crore (4) Rs. 125.2 crore Q.6 Considering 1985 as the performance base of 100% to which other performances may be referred,

which of the following most closely represents the set of Project Export Performance indices for ’84, ’85, ‘86’, ’87, ’88?

(1) 150, 100, 211, 216, 97 (2) 100, 67, 141, 144, 65 (3) 150, 100, 200, 215, 100 (4) 120, 100, 220, 230, 68 Q.7 Which is the year in which the highest percentage decline is seen in the value of contract secured

compared to the preceding year? (1) 1985 (2) 1988 (3) 1984 (4) 1986 Directions Q 8 to 13 :The table below shows the estimated cost (in Rs. lakh) of a project of laying a railway line between two places.

1988 1989 1990 1991 1. Surveying 41.5 7.5 2.2 0.5 2. Cement - 95.0 80.0 75.0 3. Steel - 70.0 45.0 60.0 4. Bricks - 15.0 12.0 16.0 5. Other building material

- 25.0 18.0 21.0

6. Labour 2.1 25.0 20.0 18.0 7. Administration 7.5 15.0 15.0 14.0 8. Contingencies 1.0 15.0 4.2 5.0 Total 52.1 267.5 196.4 209.5

Q.8 If the cost of materials rises by 5% each year from 1990 onwards, by how much w ill the

estimates fall short? (1) Rs. 11.4 lakh (2) Rs. 16.4 lakh

(3) Rs. 21.4 lakh (4) Rs. 26.4 lakh Q.9 What ratio does cost of material bear to labour cost approximately? (1) 4 : 1 (2) 8 : 1 (3) 12 : 1 (4) 16 : 1 Q.10 The total expenditure is required to be kept within Rs. 700 lakh by making a cut equally in all the

years, on expenditure of administration. What will be the percentage cut for 1989? (1) 22.6 (2) 32.6 (3) 42.6 (4) 52.6 Q.11 If the length of line to be laid each year is in proportion to the provision for material and labour

cost, what fraction of the total length is proposed to be completed in the third year? (1) 0.9 (2) 0.7 (3) 0.6 (4) 0.3 Q.12 After preparing the estimate, the provision for contingencies is felt inadequate and is therefore

doubled. By what percent does the total estimate increase? (1) 3.47 (2) 2.45 (3) 1.50 (4) 3.62 Q.13 It is found at the end of 1990, that the entire amount estimated for the project has been spent. But

for 1991, the actual amount spent is equal to that which was estimated. By what per cent approximately has the actual expenditure exceeded the estimate?

(1) 39 (2) 29 (3) 19 (4) 9

Directions for Q. 14 to 18: The first table gives the number of saris (of all the eight colours) stocked in six regional showrooms. The second gives the number of saris (of all the eight colours) sold in these six regional showrooms. The third table gives the percentage of saris sold to saris stocked for each colour in each region. The fourth table gives the percentage of saris of a specific colour sold within that region. The fifth table gives the percentage of saris of a specific colour sold across all the regions. Study the tables and for each of the following questions, choose the best alternative. Table 1 Region Blue Green Magent

a Brown Orange Red Violet Yellow Total

1 267 585 244 318 132 173 195 83 1994 2 341 480 99 199 234 119 200 109 1781 3 279 496 107 126 100 82 172 106 1468 4 198 307 62 221 65 96 124 91 1164 5 194 338 120 113 82 60 125 124 1156 6 158 261 133 104 71 158 128 82 1095 Total 1437 2454 765 1081 684 688 944 595 8658 Table 2 Region Blue Green Magent


1 122 164 71 165 40 84 97 45 788 2 124 200 37 78 67 47 73 50 676 3 21 57 7 24 9 14 20 11 163 4 79 85 22 164 18 46 43 54 511 5 29 36 22 17 9 18 19 16 166 6 1 3 2 2 1 3 2 4 18 Total 376 545 161 450 144 212 254 180 2322

Table 3 Region Blue Green Magent


1 46 28 29 52 30 49 50 54 40 2 36 42 37 39 29 39 37 46 38 3 8 11 7 19 9 17 12 10 11 4 40 28 35 74 28 48 35 59 44 5 15 11 18 15 11 30 15 13 14 6 1 1 2 2 1 2 2 5 2 All 26 22 21 42 21 31 27 30 Table 4 Region Blue Green Magent


1 15 21 9 22 4 11 12 6 100 2 18 30 5 12 10 7 11 7 100 3 13 35 4 15 6 9 12 7 100 4 15 17 4 32 4 9 8 11 100 5 17 22 13 10 5 11 11 10 100 6 6 14 11 11 6 17 11 22 100

Table 5 Region Blue Green Magent

a Brown Orange Red Violet Yellow

1 32 30 44 37 28 40 38 25 2 33 37 23 17 47 22 29 28 3 6 10 4 5 6 7 8 6 4 21 16 14 36 13 22 17 30 5 8 7 14 4 6 8 7 9 6 0 1 1 0 1 1 1 2 Total 100 100 100 100 100 100 100 100 Q.14 In which region is the maximum percentage of blue saris sold? (1) 2 (2) 3 (3) 1 (4) 4 Q.15 Out of its total sates, which region sold the minimum percentage of green saris? (1) 1 (2) 6 (3) 4 (4) 2 Q.16 Which region sold the maximum percentage of magenta saris out of the total sales of magenta

saris? (1) 3 (2) 4 (3) 2 (4) 1 Q.17 Which colour is the most popular in region 1? (1) Blue (2) Brown (3) Green (4) Violet Q.18 Which region-colour combination accounts for the highest percentage of sales to stock?

(1) (1, Brown) (2) (2, Yellow) (3) (4, Brown) (4) (5, Red)

Directions for Q. 19 to 22 : The table below give the achievements of Agricultural Development Programmes from 1983-84 to 1988-89.

Programme 83-84 84-85 85-86 86-87 87-88 88-89

Irrigation (Cumulative in Million Hectares)

Major & Medium 22.05 22.70 23.20 24.0 24.60 25.32

Minor 28.60 32.77 32.77 34.20 34.20 35.14

High yielding varieties (Million Hectares)

1. Paddy 16.90 18.20 19.70 18.70 21.70 22.80

2. Wheat 15.90 16.10 16.80 17.80 19.40 19.10

3. Jowar 3.10 3.50 3.90 4.40 5.30 5.10

4. Bajra 2.90 3.60 4.60 4.70 5.40 5.20

5. Maize 1.40 1.60 1.60 1.70 1.90 2.00

Consumption of Chemical fertilisers (Million tons)

1. Nitrogen 3.42 3.68 4.07 4.22 5.20 5.49

2. Phosphate 1.11 1.21 1.32 1.44 1.73 1.89

3. Potash 0.59 0.62 0.67 0.73 0.78 0.84

Q.19 How much area, in million hectares, was brought under irrigation during the year 1986-87? (1) 58.20 (2) 1.43 (3) 0.80 (4) 2.23 Q.20 The consumption of chemical fertiliser per hectare of gross cropped area is lowest for the year (1) 1984-85 (2) 1985-86 (3) 1986-87 (4) 1987-88 Q.21 It is possible that a part of the minor irrigated area is brought under major and medium areas. In

which year has this definitely happened? (1) 1984-85 (2) 1985-86 (3) 1986-87 (4) 1987-88 Q.22 In which year does the area cropped under high yielding varieties show a decline for the maximum

number of crops? (1) 1988-89 (2) 1985-86 (3) 1986-87 (4) None of these Directions for Q. 23 to 30: Each of the following questions is followed by two statements. Mark 1, if the question can be answered with the help of statement 1 alone. Mark 2, if the question can be answered with the help of statement 2 alone. Mark 3, if both statement 1 and statement 2 are needed to answer the question, and Mark 4, if the question cannot be answered even with the help of both the statements. Q.23 How long did Mr. X take for the 5000 km journey with 10 stopovers?

(1) The ith stopover lasted i2 minutes. (2) The average speed between any two stopovers was 66 kmph.

Q.24 A man distributed 43 chocolates to his children. How many of his children are older than five

years? (1) A child older than five gets 5 chocolates. (2) A child 5 years or younger gets 6 chocolates.

Q.25 If R is an integer between 1 & 9, and P - R = 2370, what is the value of R? (1) P is divisible by 4. (2) P is divisible by 9. Q.26 Is (x-1 - y-1)/x-2 - y-2) > 1? (1) x + y > 0.

(2) X and y are positive integers and each is greater than 2. Q.27 x, y, and z are three positive odd integers. Is x + z divisible by 4? (1) y - x = 2 (2) z - y = 2 Q.28 Ramu went by car from Calcutta to Trivandrum via Madras, without any stopping breaks. The

average speed for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum? (1) The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras. (2) The average speed from Madras to Trivandrum was twice that of the average speed from

Calcutta to Madras.

Q.29 X is older than Y, Z is younger than W and V is as old as Y. Is Z younger than X? (1) W may not be older than V (2) W is not older than V Q.30 The unit price of product P1 is non-increasing and that of product P2 is decreasing. Five years

hence, which product will be costlier? (1) Current unit price of P1 is twice that of P2. (2) 5 years ago, unit price of P2 was twice that of P1.

Directions Q. 31 to 35: Each of these items has a question followed by two statements. As the answer, mark 1, if the questions can be answered with the help of both the statements but not with the help of

either statement itself. 2, if the question can not be answered even with the help of both the statements. 3, if the question can be answered with the help of statement II alone 4, if the question can be answered with the help of statement I alone Q.31 What is value of x, if x and y are consecutive positive even integers? I. (x - y)² = 4. II. (x + y)² < 100 Q.32 What is the profit percent? I. The cost price is 80% of the selling price. II. The profit is Rs. 50. Q.33 What is the length of the rectangle ABCD? I. Area of the rectangle is 48 square units.

II. Length of the diagonal is 10 units Q.34 What is the price of bananas? I. With Rs.84, I can buy 14 bananas and 35 oranges. II. If price of bananas if reduced by 50% then we can buy 48 bananas in Rs.12. Q.35 What is the first term of an arithmetic progression of positive integers? I. Sum of the squares of the first and second term is 116. II. The fifth term is divisible by 7.

EXERCISE 6 Directions: Q. 1 to 4: are based on the table and information given below. Bankatal works x hours a day and rests y hours a day. This pattern continues for 1 week, with an exactly opposite pattern next week, and so on for four weeks. Every fifth week he has a different pattern. When he works longer than he rests, his wage per hour is twice of what he earns per hour when he rests longer than he works. The following are his daily working hours for the weeks numbered 1 to 13:

1st week 5th week 9th week 13th week Rest 2 3 4 - Work 5 7 6 8

A week consists of six days and a month consists of 4 weeks. Q.1 What is his salary for first month? (1) 1440 (2) 2040 (3) 1320 (4) 1680 Q.2 Referring to the data given in Q. 187, Bankatlal’s average monthly salary at the end of the first

four months will be: (1) 1760 (2) 2040 (3) 1830 (4) 1680 Q.3 The new manager Kushaldas stipulated that Rs. 5 be deducted for every hour of rest and Rs.25 be

paid per hour starting the 9th week, then what will be the change in Bankatlal’s salary for the 3rd month? (Hourly deductions and salaries are constant for all weeks starting 9th week).

(1) 540 (2) 480 (3) 240 (4) 0 Q.4 Using the data in the previous questions, what will be the total earning of Bankatlal at the end of

sixteen weeks. (1) 7320 (2) 7800 (3) 8400 (4) 7680 Directions: Q 5 to 9 are based on the table given below: Machine M1 as well as Machine M2 can independently produce either Product P or Product Q. The times taken by machines M1 and M2 (in minutes) to produce one unit of product P and Q are given in the table below: (Each machine works 8 hours per day).

Product M1 M2 P 10 8 Q 6 6

Q.5 What is the maximum number of units that can be manufactured in one day? (1) 140 (2) 160 (3) 120 (4) 180 Q.6 If the number of units of P is to be 3 times that of Q, what is the minimum idle time for maximum

total units manufactured? (1) 0 minutes (2) 24 minutes

(3) 1 hour (4) 2 hours Q.7 If equal quantities of both are to be produced, then out of the four choices given below, the least

efficient way would be: (1) 48 of each with 3 minutes idle (2) 64 of each with 12 minutes idle

(3) 53 of each with 10 minutes idle (4) 71 of each with 9 minutes idle.

Q.8 If M1 works at half its normal efficiency, what is the maximum number of units produced, if at least one unit of each must be produced?

(1) 96 (2) 89 (3) 100 (4) 119 Q.9 What is the least number of machine hours required to produce 30 pieces of P and 25 pieces of Q? (1) 6 hours 30 minutes (2) 7 hours 24 minutes (3) 5 hours 48 minutes (4) 4 hours 6 minutes Directions: Q. 10 to 14 are based on the information given below: A company produces five types of shirts - A, B, C, D, E - using cloth of three qualities - High, Medium and Low - using dyes of three qualities - High, Medium, and Low. The following tables give, respectively: 1. The number of shirts (of each category) produced, in thousands. 2. The percentage distribution of cloth quality in each type of shirt, and 3. The percentage distribution of dye quality in each type of shirt. Note: Each shirt requires 1.5 meters of cloth. Distribution of cloth (%) Distribution of dye (%) Shirt Type

Number (000)

Shirt Type

High Medium Low Shirt Type

High Medium Low

A 20 A 80 20 - A 70 15 15 B 30 B 30 40 30 B 20 50 30 C 30 C - 70 30 C - 60 40 D 10 D - 60 40 D - 40 60 E 10 E - 10 90 E - 20 80 Q.10 What is the total requirement of cloth?

(1) 150,000 m (2) 200,000 m (3) 225,000 m (4) 250,000 m

Q.11 How many metres of high quality cloth is consumed by A-shirts? (1) 8,000 m (2) 112,000 m

(3) 24,000 m .(4) 30,000 m Q.12 What is the ratio of low-quality dye used for C-shirts to that used for D-shirts? (1) 3 : 2 (2) 2 : 1 (3) 1 : 2 (4) 2 : 3 Q.13 How many metres of low-quality cloth is consumed? (1) 22,500 (2) 46,500 (3) 60,000 (4) 40,000 Q.14 What is the ratio of the three qualities of dyes in high-quality cloth? (1) 2 : 3 : 5 (2) 1 : 2 : 5 (3) 7 : 9 : 10 (4) None of the above.

For 15 to 19 use the following data:

A manufacturer can choose from any of the three types of tests available for checking the quality of his product. The graph gives the relatives costs for each of these tests for a given percentage of defective pieces.

Q.15 dopting Test-2 will be feasible if the percentage of defective pieces (p) lies between: (1) 0.10 to 0.020 (2) 0.20 to 0.30 (3) 0.05 to 0.20 (4) 0.00 to 0.05

Q.16 If p is equal to 0.2, then which test will be feasible? (1)either 1 or 2 (2) 2 only (3) 3 only (4) either 2 or 3 Q.17 When will Test-3 be feasible? (1) p > 0.2 (2) 0.1 < p < 0.2

(3) 0.05 < p < 0.1 (4) p < 0.05 Q.18 When is Test-1 feasible? (1) p < 0.05 (2) 0.0 < p < 0.2

(3) 0.1 < p < 0.2 (4) 0.05 to 0.2 Q.19 If p < 0.2, then the best alternative will be: (1) Test-2 (2) Test-3 (3) Test-1 (4) Not Test-3 DIRECTIONS for Q. 20 to 26: The table below provides the data for production of ferrous and non-ferrous metals in million dollars for the year 1990 and % change for the three periods for the entire world and regionwise.

Non-Ferrous Metals Ferrous Metals Annual %change Annual %change

Value 1990

1980-90 1989 1990

Region Value 1990

1980-90 1989 1990 8660 6 4 11 World 11350 6 4 12 2308 8 7 15 Asia 2590 8 10 23 670 5 8 14 Japan 665 5 11 20 348 15 6 18 China + HK + Taiwan 393 15 18 28 908 9 8 19 Asian 1075 8 11 25 1408 7 5 11 North America 2632 9 11 17 502 9 7 18 Latin America 678 12 -3 15 3415 4 0 3 Western Europe 4490 4 1 5 3151 4 0 2 European Union (15) 4133 4 2 5 378 7 0 24 C./E Europe/ Baltic

States/USSR 423 5 -12 13

162 8 1 14 Central Europe 255 10 -1 13 147 - 1 34 USSR 80 - -23 12 203 3 10 27 Africa 297 4 -3 7 368 7 28 46 Middle East 300 6 1 14

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

Test 1Test 2Test 3

Relative Cost

% defective

Q.20 In which of the following regions production of Non-ferrous metals exceeded that of ferrous metals in 1989?

(1) Asean (2) China + HK + Taiwan (3) Japan (4) Middle East Q.21 What was the following regions production of Ferrous metals in million dollars by developing

economies of Asia in 1990 (In Asia Japan is the only developed economy)? (1) 1256 (2) 1568 (3) 1925 (4) 1638

Q.22 Which of the following values is closest to world production of ferrous metals in the year 1988

(million dollars)? (1) 13200 (2) 9000 (3) 7500 (4) 9750

Q.23 What percentage of the world production of non-ferrous metals was contributed by non-EU countries of Western European in 1980?

(1) 6% (2) 36% (3) 3% (4) Indeterminate Q.24 What was the CAGR of ferrous metals production between the year 1988-90 in USSR,

Central/East Central/East Europe, European Union, Batlic States and non-EU-Western Europe economies? (1) 2% (2) 4.1% (3) 3% (4) 0.40%

Q.25 Which of the following is not true?

(1) None ferrous metals production as a percentage of ferrous metals production in the year 1990 was highest for USSR.

(2) China accounted for less than 4 percent of all metals production in 1990. (3) Africa contributed to less than 2 percent of all metals production in 1990. (4) USSR witnessed the second highest annual rate of growth on non-ferrous metals production in

1990. Q.26 What is value of total metals production of Western of Western Europe in 1988 (million dollars)?

(1) 7730 (2) 7550 (3) 7900 (4) 8300

DIRECTIONS for Q 27 - 13: Each question is followed by two statements A and B. Answer each question using the following instructions. Choose (1) if the question can be answered by using statement A alone but not by using B alone. Choose (2) if the question can be answered by using statement B alone but not by using A alone. Choose (3) if the question can be answered by using both the statements together, but cannot be

answered using either statement alone. Choose (4) if the question cannot be answered even by using both the statements together. Q.27 What is the ratio of radii of the circumcircle and the incircle of a polygon of 12 sides

(A) The polygon is a regular one of side 8 cm. (B) One angle measures 150°

Q.28 A newspaper boy has 3 TOI, 2 ET and 3 HT in his bag (kept at random). He takes out 2

newspapers at random, without replacement. Does he retain at least one ET? (A) He takes out 5 more newspapers at random of which there is at least one TOI, one ET and

one HT (B) He takes out 5 more newspapers at random and there are 2 TOI and 2 HT among them

Q.29 Determine the value of the function f(x) = aloga x

(A) a is a positive real number such that twice of ‘a’ is 8 more than ‘a’ itself (B) x is 12 less than half of itself

Q.30 If a sequence of numbers a1, a2, a3, …. is given by the rule an

2 = an+1, does a multiple of 3 appear in the sequence? (A) a1 (B) an

Q.31 Which of the three bowlers in the series of test matches took most wickets?

(I) The first and the third bowlers took twice as many wickets as the second bowler (II) The second and the third bowlers took three times as many wickets as the first bowler.

Q.32 What is the price of mangoes per kg? I. Ten kg of mangoes and two dozens of oranges cost Rs. 252.

II. Two kg of mangoes could be bought in exchange for one dozen oranges. Q.33 Is x + y - z + t even? I. x + y + t is even. II. tz is odd. Q.34 What is the area of the triangle?

I. Two sides are 41 cm each II. The altitude to the third side is 9 cm long.

DATA INTERPRETATION ANSWER KEY

Q.No Ex 1 Q.No

Ex 2 Q.No

Ex 3 Q.No Ex 4 Q.No

Ex 5 Q.No

Ex 6

1 2 1 3 1 2 1 4 1 4 1 12 4 2 4 2 4 2 1 2 4 2 33 3 3 2 3 3 3 2 3 4 3 24 3 4 1 4 4 4 2 4 4 4 25 3 5 2 5 1 5 3 5 1 5 26 2 6 4 6 4 6 4 6 2 6 17 4 7 3 7 1 7 3 7 2 7 38 4 8 4 8 4 8 3 8 2 8 49 2 9 2 9 2 9 3 9 2 9 1

10 3 10 3 10 1 10 3 10 3 10 111 3 11 3 11 1 11 2 11 4 11 312 4 12 2 12 4 12 3 12 1 12 213 1 13 3 13 2 13 2 13 2 13 214 4 14 3 14 3 14 4 14 1 14 315 2 15 1 15 1 15 4 15 2 15 316 2 16 3 16 3 16 3 16 4 16 417 2 17 4 17 3 17 4 17 2 17 118 3 18 4 18 2 18 3 18 3 18 119 3 19 4 19 1 19 2 19 4 19 420 1 20 3 20 1 20 3 20 1 20 321 3 21 3 21 3 21 4 21 4 21 322 1 22 3 22 4 22 2 22 1 22 423 2 23 2 23 3 23 4 23 3 23 324 2 24 4 24 3 24 2 24 3 24 325 1 25 2 25 2 25 1 25 2 25 326 2 26 1 26 4 26 3 26 2 26 227 4 27 1 27 3 27 2 27 3 27 128 1 28 1 28 3 28 4 28 3 28 429 3 29 3 29 1 29 3 29 2 29 230 2 30 2 30 4 30 3 30 4 30 131 1 31 1 31 3 31 2 31 2 31 332 2 32 2 32 4 32 4 32 4 32 333 1 33 2 33 4 33 2 33 1 33 334 2 34 2 34 2 34 1 34 3 34 335 4 35 1 35 3 35 1 35 4 36 2 36 3 36 4 36 3 37 4 37 3 37 2 37 1 38 4 38 4 38 2 38 3 39 4 39 3 39 2 39 4 40 2 40 4 40 4 40 3 41 3 41 4 41 1 42 1 42 4 42 4 43 3 43 2 43 4 44 2 44 2 44 3 45 1 45 3 45 4 Q.No Ex 3 46 1 46 4 46 3 51 1 47 4 47 2 47 2 52 2 48 1 48 4 48 1 53 3 49 4 49 1 49 2 54 1 50 1 50 4 50 3 55 4

EXPLANATIONS

EXERCISE 1 Direction for Qs. 1 to 2 : Refer to the following data for the following solutions.

9 3 1 A B (2) C (6) (5) (7) D 8 (4) E 4 (8) F 7 (1) G 2 (3) H 5 (9) I 6

∴E represents 4 and D represents 7 or 8. 1. (2) 2. (4) Directions for Qs. 3 to 7: Refer to the following data for the following solutions.

Let ‘x’ people have high school education. ∴ 3x have middle school education and 7x have primary school education. Also as all and middle school educational people have primary school education and all high school educated people have middle school education, number of people in Category I = 4x, Category II = 2x, Category III = x. ∴Number of people Category I and II, who do not play any game = x and x/2 respectively. ∴Number of people playing only hockey = Number of people playing only football.

=4

432

223

223 −

=−− x

x

andx respectively

Also number of people in category III playing only hockey = 2

6−x = 5 = ⇒ x = 16.

3. (3) 3x = 48 people have middle school education.

4. (3) Number of high school education who do not play football = 5 + 2

6−x = 10.

5. (3) Number of people having middle school education but not high school education who

play only football = 2

6−x = 11.

6. (2) Number of such people = Number of people having primary school education - No. of people having middle school education = 7x – 3x = 4x = 64. 7. (4) Number of educated people playing football only = 39.

Number of educated people playing hockey only = 39. ∴Number of an uneducated people playing football = 90 – (39 + 5) = 46 and number of uneducated people playing hockey = 60 – (39 + 5) = 16. Out of these 2 play both games. ∴ No. of uneducated people playing at least one game = 46 + 16 - 2 = 60. No. of uneducated people = 200 – 7x = 200 – 112 = 88. ∴ 88 – 60 = 28 uneducated people do not play any game.

8. (4) Right turns: Actual letter – 2, 2 left turns : Actual letter + 2 A (inner) : 8; P (outer) : R ; P (inner): N; L (outer) : N; E (inner) : C ∴ APPLE would be coded as 8RNNC. 9. (2) Total alphabets + number on a wheel = 26 + 10 = 36 per wheel Total combinations = (36 x 36) – 1 = 1295 (one is where all wheels are aligned)

10. (3) 4 combinations possible : Inner L, Outer L, Inner R, Outer R, Inner L, Outer R and Inner R, Outer L. Translate HOCJ9 back in each of the four above, and the only one which would reproduce an

English an English word (INDIA) is inner R, outer L. 11. (3) From the given options, only (3) i.e. BEF are logically related. 12. (4) Statements BAE are logically related. Hence this is the answer. 13. (1) By combining Statements B and D, we can deduce the statements E. Hence BDE are logically

related. 14. (4) 15. (2) It is given that, Blunders committed by Idiots (I) = 2 (Dumbos) ……(i) Blunders committed by Fools (F) = 3 (Idiots) and ………. (ii) Blunders committed by Morons (M) = 4 (Fools) ………… (iii)

As, Fools commit 1200 blunders, hence Moron commit 4800 blunders, Idiots, commit 400 blunders & Dumbos commit 200 blunders from (i) , (ii) & (iii).

Hence total numbers of blunders committed = 1200 + 4800 + 400 + 200 = 6600.

16. (2) The population in each group = 4

400 = 100

Let us assume that if Dumbos commit the lest number of blunders i.e. 1, hence blunders committed by Dumbos group = 1 x 100 = 100.

Note: Others may & may not commit blunders. Hence (2).

17. (2) As the population is same in each groups, hence Dumbo’s population =4

400 = 100.

As every Dumbo commits the same number of blunders as every other Dumbo, so total blunders committed by Dumbos = 3 x 100 = 300. Now using equations as shown in Q. 135, Blunders committed by Idiots, Fools & Morons are respectively 600, 1800 and 7200.

∴Total number of blunders of the day = 300 + 600 + 1800 + 7200 = 9900. Direction for Qs. 18 to 20: Refer to the following data for the following solutions. Equation Salary = n2 + 2 where n > 1 ………….. (1) Expenses = 2n + 1 where n > 1 ……….. (2) Saving = n2 – 2n + 1 where n > 1 ………….. (3) 18. (3) Putting the value of savings in equation (3), 100 = n2 – 2n + 1 ⇒ n2 – 2n – 99 = 0, we get n = 11.

Hence the savings would exceed Rs. 100 on 12th day. 19. (3) Putting the value of n in eq.n (1) Salary = n2 + 2 When n = 6000 Salary = Rs. 36000002 When n = 6001 Salary = Rs. 36012003

∴Increase in salary = 36012003 – 36000002 = Rs. 12001. Thus he will have to remain in his job for minimum 6001 days to break the record.

20. (1) Putting different values of n starting from 1 in eqn 3 and adding all the savings up to 11th day, Total saving = Rs. 385, so on 11th day they will buy a first fixed deposit.

Direction for Qs. 21 to 25 : Refer to the following table for the following solutions.

MAYFLOWER LITTLEFLOWER CUTTING 20 mins 30 mins STITCHING 60 mins 60 mins STITCHING BUTTON 15 mins 30 mins AND BUTTON HOLES

The time given in the table is for per uniform to be stitched. 21. (3) No. of working hours for each person = 10 hour ∴Total time available for cutters in a day = 20 hours = 1200 mins. Max. No. of uniform that 2 cutters can cut for Little Flower in a day = 1200/30 = 40

Time required for stitching 40 uniform = 40 x 60 = 2400 min and Alord has 5 tailors for stitching that means the Total available time is (5 X 10 x 60) = 3000 mins.

Hence maximum number of Little Flower uniforms can be completed in a day = 40. 22. (1) To complete 20 Little Flower uniforms, Time consumed by Cutters = 20 x 30 = 600 mins Time consumed by Tailors = 20 x 60 = 1200 mins Time consumed by Assistants = 20 x 30 = 600 mins Time available for Cutters = (1200 – 600) = 600 mins Time available for Tailors = (3000 – 1200) = 1800 mins Time available for Assistant = (1200 – 600) = 600 mins

Max. No. of uniform that 2 cutters can cut for May Flowers uniform in a day = 600/20 = 30 Time required to stitch 30 uniforms = (30 x 60) = 1800 min and is exactly equal to the time available for tailors. Hence No. of Mayflower uniform that can be completed on that day is 30.

23. (2) (1) To complete 30 Little Flower uniforms, Time consumed by Cutters = (30 x 30) = 900 mins Time consumed by tailors = (30 x 60) = 1800 mins Time consumed by assistants = (30 x 30) = 900 mins Time available for cutters = (1200 – 900) = 300 mins Time available for tailors = (3000 – 1800) = 1200 mins Time available for Assistant = (1200 – 900) = 300 mins

As they are not working in this available time it is the idle time. Hence total man hours that are idle = (300 + 1200 + 300) = 1800 mins = 30 hours.

24. (2) Hiring one more assistance increases the time available for stitching buttons and button holes. Max. No. of uniform those cutter can cut for Mayflower in a day = 1200/20 = 60 Time required by Tailors to stitch 60 uniforms = (60 x 60) = 3600 mins, whereas time available is 3000 mins only.

Hence maximum No. of uniform that can be stitched in a day = 3000/60 = 50 Time consumed by assistant to stitch buttons to 50 uniform = (50 x 50) = 750 mins Time available for assistant = (3 x 10 x 60) = 1800 mins.

Hence 50 uniforms can be completed in a day.

25. (1) Max. number of uniforms that can be cut by those 2 cutters in a day for MayFlower is 60. And the buttons and buttonholes can be easily stitched by the 2 assistant for these 60 uniforms in a day in the time available for them. While 5 tailors can stitch only 50 uniforms in the available time. Hence, A lord will hire 1 tailor to get maximum increase in production capacity in a day.

26. (2) From statement A alone 4n + 48 = 102 4n = 52 n= 13 A alone is sufficient. From statement B alone: Numbers whose squares lie between 150 and 250 are 13, 14 and 15 Among these A, only 13 is a prime number. :. B alone is sufficient.

27. (4) Even upon using both the statements we can only conclude that two of the opposite sides are parallel and sum of 2 angles is 180°. In order to conclude that ABCD is a rectangle which is also a cyclic quadrilateral we also need to know whether the opposite sides are equal in length.

28. (1) From A (n - 3) (n - 2) = 0 n = 2 or 3 ∴A alone is not sufficient From B Only for n = 2

10!1

2)!(22

2!i.e.2)!(n

2

n!

==

−=−=

B alone is sufficient. 29. (3) From A Form B

Given, sum of areas of semi-circles x, y and z is 100π If BC = a cm, AC = b cm, AB = c cm. Area of semi-circle x is π/2 a2/4 cm2

Area of semi circle y is π/2 c2/4 cm2

Area of semi circlezx is π/2 b2/4 cm2 ½ π/4 (a2 + b2 +c2) =100π a2 + b2 + c2 = 400 We know that in ∆ABC a2 = b2 +c2 = ∴2 (b2 + c2) = 800 b2 + c2 = 400 b2 + c2 = a2 = 400 ⇒ a = 20 ⇒ b or c = 10√3 and ⇒ the sides are 10, 10√3, 20 ∴ the perimeter = 30 + 10√3 cm

30. (2) From A profit % is 35% (i.e. 10 +25)⇒ profit = Rs.35 From B Mankup% = 80% ⇒ profit % = 1/5 x 80 = 16%

A

B

CA C

B

xy

z

profit = Rs.16 ∴ Either statement is sufficient

31.(1) From A alone. Tram A takes 30 seconds to cross tram B if it were stationary. Either the trains were moving in the same directions where the speed of train A is greater than the speed of the tram B or the trains are moving in the opposite direction. If they the trains were moving in the opposite direction, A would have taken less than 30 seconds to cross B.

Therefore the trains are moving in same direction and the speed of the train B = ⎟⎠⎞

⎜⎝⎛

×−5

18

32

75090

B alone is not sufficient.

32.(2) From statement A only 11 is the two digit prime which satisfies the condition. i.e. 112= 121 113 = 1331 From statement B only 9 is such number when 92= 81 and 8 + 1 = 9 93 = 729 and 7 + 2 + 9 = 18

33. (1) From A

n can take negative values for which3

5n10 +

is not an integer and for positive values of n, 10n + 5 will result in a number which has the sum of its digits equal to 6 which is a multiple of 3,

∴3

5n10 + is an integer if n is positive

From A, n can be negative or positive

From B, n can be only positive and hence3

5n10 +is an integer.

34. (2) From statement A alone, A worked for 14 ½ days and B worked for 14 days, so they together will be able to finish the work in less than 14½ . So A alone is sufficient. From statement B alone, When the slower person starts the work, the work takes 29 days. So, when the faster person starts the work, the work would be completed in less than 29days. So, they together need less than 29/2 days to complete the work. So B alone is sufficient.

35. (4) From statement A alone, two cases are possible Case 1 The two trains are travelling in the same direction. In this case, the speed of train B must be more than that of train A. Case 2 The two trains are travelling in the opposite direction In this case, if speed of train B = 60 km/hr time taken to cross each other

= 22.58

18

560)(60

750=

×+

∴Speed of train B must be greater than 60 km/hr i.e. greater than speed of train A. Since both the cases are possible, nothing can be concluded. even after using statement B, both cases remain.

36.(2) Number of Maruthi cars sold in 1 994 = 40% =1000,000 Number of Fiat cars sold in 1994 » 20%

= 500,000

37.(4) Fiat in1995 → ⎟⎠⎞

⎜⎝⎛

×150040

301125

Fiat in 1996 → ⎟⎠⎞

⎜⎝⎛

× 0055

15818 30

Fiat in 1997 → ⎟⎠⎞

⎜⎝⎛

×150045

351167

Ambassador in 1997 → 334 Ambassador in 1998 → 423 On observation we can see that all the statements are true.

38.(4) Choice A is false Number of cars sold by Fiat in 1994 (in thousands)

1000××40

100

100

20

Number of cars sold by Fiat in 1 996 (in thousands)

7

1002000

70

100

100

5=××

∴% decrease is close to 71 % Choice (2) is false Although percentage share is same for the two years, the total production is different. Choice (3) is false. The increase in total production is from 1500 to 3000, which is exactly 100%

39.(4) Ford Escort in 1995 → 750

Ford Escort in 1996 → 272.7 Ford Escort in 1997 → 333.3 Ford Escort in 1998 → 285.7

40.(2) Total number of cars sold in 1995 → 1500 x 100/40 1996 → 3000 x 100/55 → Maximum 1997 → 1500 x 100/45 1998 → 2000 x 100/70

Solutions for questions 41 to 45: Originally money realised by sales = 10 x 50000 = 5,00,000 Money realised from (3) = 5.00,000 - 0.5 x 0.4 x 5,00,000 = 4,00,000 Money realised from (2) = 5,00.000 [0.1 x 0.5 + 0.2 x 0.5 + 0.1 x 0.4] - 2,00,000 + 5,00,000 = 3,95,000 Money realised from (1)

= 0.5 x 50000 [1 + 0.5 x 0.3 + 0.5 x 0.2 ] = 3,12,500 41. (3) Hence the most profitable option would be to remain silent.

42. (1)

43. (3) Loss = 5,00,000-3,12,500= 1,87.500.

44. (2) As calculated above, it is Rs.3.95,000

45. (1) Net revenue from course 2 = 3.95 lakhs

Net revenue from course 3 = 4.00 lakhs

∴Rs.5000 less

For answer to questions 46 to 50:

Production Total cost= Fixed cost+ Variable cost Plan 1 Plan 2 Plan 3 1000 2 3 4 2000 3 3.5 4.5 3000 4 4 5 4000 5 5 5.5 5000 5.5 6.5 6 6000 6.5 7.5 6

Now all the questions can be answered.

46. (1) 47. (4) 48. (1) 49. (4) 50. (1)

EXERCISE 2 Direction for Qs. 1 to 5: Refer to the following information the following solutions. From clues I & III we can conclude that B is always present and one only one of A & C is always present. Also note that when D goes than the only combination possible agents is D-E-G and from clues IV, in such a case A should be included. 1. (3) 2. (4) 3. (2) From clues IV & VI we conclude that F – G – H are the recruitment agents that should be

included. Hence only one combination is possible. 4. (1) 5. (2) From previous solutions we know that F, G and B all can go with C, Directions for Qs. 6 to10 : Refer to the following table for the following solutions. The following table gives the moves that can be made for the mentioned conditions. The underlined positions indicate your position after nth move. 6. (4) 7. (3) 8. (4) By moving a step anticlockwise in the first move, you reach at 12 O’clock. From here you can

reach (1) 10’O Clock through 12 – 11 - 10 (2) 5 ‘O clock through 12 – 6 – 5 (3) 7 ‘O Clock through 12 – 6 – 7. But you cannot reach 6 ‘O Clock. 9. (2) 10. (3) Your mother’s husband ⇒ your father. Your father’s sister ⇒ your aunt. So, the lady’s aunt is the

man’s aunt ⇒ the man and the lady are brother and sister. 11.(3) M is the maternal uncle of R means m is the brother of R‘s mother (say K) i.e., M + K – R. Direction for Qs. 12 to 13 : Refer to the following information for the following solutions. We are given that A visited at 8 O’clock. Now from III we conclude that A visited at 8 p.m. Now from I we concluded that B has to visit at 9 a.m. otherwise nobody will be able to visit in between A & B. Now if D were to visit at 11 p.m. then condition IV will get violated hence we concluded that D visited at 11 a.m. and C visited at 10 p.m. From here all the questions are answered. 12. (2) 13. (3) 14. (3) As X2Y3 = 8, either X or Y or both are fractional. From statement B, we get that X is rational.

Move Minimum Score Maximum Score Reaching 5 O’clock 0th 1 = 1 1 = 1 1

1st 7 – 4 = 3 12 – 2 = 10 12 2nd 1 – 4 = 3 11 – 2 = 9 11 / 6

3rd 2 = 2 - 5

4th - - -

Total 3 20 -

Therefore, X2 is either and integer or a fraction. Therefore, X2 = 3

8γ

will either be an integer or

a fraction, So either X or Y is a fraction. 15. (1) Statement A alone is sufficient to say that B is not prime. However, statement B alone is not

sufficient. 16. (3) From statement A we can conclude that 3x is even. As y is an integer (by virtue of it being odd)

from statement B, we can conclude that 10y is even. The sum of two even numbers will be even. 17. (4) From statement A we cannot conclusively state which of the three is largest as they could all be

positive or negative. From statement B we know that xyz is positive as xyz – y2 (as y2 will always be positive for real values of y) is positive. This is possible in two cases, I. All of x, y and z are positive in this case z is the greatest II. Y is negative and one of x and z is negative. Hence we cannot conclude even if we combine the two statements.

18. (4) From both the statements we know the ratio of the speeds and the times at which they met.

Without knowing the distance between the two cities X and Y, we will not be able to find out the speed of L or M.

19. (4) Those S which are M are not P. Hence some S are not P. 20. (3) 21. (3) Those ‘M’ are not ‘P’ are ‘S’ because all ‘M’ are ‘S’ 22. (3) Important link here is ‘could’. 23. (2) 24. (4) Because the minority might consist of thousand of people, the opposition might not be inconsistent

with the speaker’s remarks. 25. (2) 26. (1) Since the number of persons per household can be assumed to be a constant, the ratio of x1 to x2 is

the same as the ratio of the number of property crimes per1000 households in 1975 to that in 2000.

This value is 1:3180

560= .

27. (1) Let the number of households in thousands be T1 in 2000 and T2 in 2050. The total number of

property crimes in 2000 is, therefore, T1 × 180. This will reduce to T1 × 180 × 0.71 × 0.71. The number of property crimes per thousands households in 2050 is, therefore, T1 × 180 × 0.71 × 0.71/T2/ Since the number of persons per households remains constant, the ratio of T1/ T2 is the same as the ratio of the populations. The ratio of the populations is (157+ 2.3 × 50)/ (157 +2.3 × 100). The required answer comes out to be approximately 63.

28. (1) Let x be the number of aggravated assaults per thousand population. The number of robberies is x

– 1.8 and the number of simple assaults is 3x. From the graph, we get the sum of all the three as 27. Hence x – 1.8 + x+{ 3x = 27, giving x = 5.76 and x – 1.8 = 3.96. The total number of robberies is, therefore, (3.96/1000) × (1.57 + 2.3 × 50) ×106 = 1.1 × 106.

29. (3) 30. (2) The number of property crimes in 2000 was 180 × H where H is the number of households in the

thousands in 2000.

The number of violent crimes in 1975 was 49 × P1 where P1 is the population in 1975 in

thousands. Therefore, 180 P149

H

×× = 1.45 which gives

1.45

3.67

H

P1=

The quantity required is H

P2where P2 is the population in 2000.

But P2/ P1= 214.5

272

252.3157

502.3157=

×+

×+. Therefore P2/ H= 3.2

1.45

3.67

214.5

272≈× .

31. (1) Week 1, for detailed solution refer the table below. 32. (2) 50, for detailed solution refer the table below. 33. (2) 200 units’ week 3, for detailed solution refer the table below. The gross requirement of leg is 200 and 600 in week 3 out of 300 in – hand units of legs, 200 units

would be used for wek2 requirement and the rest units would be used for meeting the requirements of week 3. Therefore net requirement of week would be 600 – 100 = 500 units of legs for meeting the demand of finished table of week 5.

34. (2) For meeting the additional demand of 200 tables Shortrails = 4 ×200 = 800 Legs = 8 × 200 = 1600

Total shortrails = 300 + 800 = 1100 Total legs = 600 + 1600= 2200. 35. (1) Details of components available on a particular week. Figure in bracket represent the week to which components belong.

Details Week1 Week 2 Week 3 Week 4 Week 5 Week 6 Table 50 50+50 100 200 150 Leg assembly 100 100 – 50 = 50(4) 100(4) 150(6) 100(6) Legs 150 150 + 50=200(6) 600(5) 400(6) Shortrails 50 50 + 50 = 100(4) 300(5) 200(6) Longrails 0 100 (4) 300(5) 200(6) Top 50 50 – 50 = 0 100(4) 150(5) 100(6)

Details of component ordered on a particular week.

Details Week1 Week 2 Week 3 Week 4 Week 5 Week 6 Table Leg assembly Legs 50(4) 600(5) 400(6) Shortrails 50(4) 300(5) 200(6) Longrails 100(4) 300(5) 200(6) Top 100(4) 150(5) 100(4)

Week 1 As lead – time increased by 1 week so planned order release would be by one week ahead.

36. (3) I. 4

b

3

a<

3

c

2

b<

⇒ 4a < 3b ⇒ 3b < 2c

⇒ a < b ⇒ b < c (as both a & b are positive) ( ∴b & c are positive) But, this is not sufficient as nothing is known about d till now

II. 6

d

4

a<

3

d

4

c<

⇒ 6a < 4d ⇒ 3c < 4d ⇒ a < d

This means a < d, but nothing can be concluded about the value of d compared to b or c. When we combine I & II, We get 3b < 2c or 9b < 6c & 3c < 4d or 6c < 8d Which can be represented as 9b< 6c < 8d ⇒ 9b < 8d ⇒ b < d

We know that b < c & a < b. this shows that a is smallest and b the second smallest number, even thought which is greater between c & d cannot be decided.

37. (3) LCM & HCF of A & B are 72& 12 respectively. ∴ LCM × HCF = A × B ⇒ 72 × 12 = A × B Values (A, B) can take so that HCF will be 12 & LCM 72 are (12, 72) and

(24, 36) I. A is not a factor of B, which means A and B can take either 123 and 72 or24 and 36 as

together values but not necessarily in the same order i.e., A = 72 and B = 12 OR A = 36 and B = 24 OR A = 24 and B = 36 II. B is greater than A. This means B can be either 72or 36.

Hence II alone is not sufficient. Combining, I & II, we get A = 24 & B = 36. Hence, the answer is (3).

38. (4) I. Let R & S be the ages of Ram & Shyam respectively. Age of Ram 5 years back = R – 5 & Shyam = S - 5 ∴(R - 5) + (S – 5) = 60 or R + S = 70 …(1) Hence, I alone is not sufficient.

II. Ages of Ram & Shyam fifteen years hence will be R + 15 & S + 15 ∴(R + 15) + ( S + 15) = 100 ∴ R + S = 70 …..(2) Hence, II alone is not sufficient . Combining I & II, We are getting the same equation in both cases, hence we cannot we conclude what are the ages of Ram & shyam respectively.

39. (3) Let r & R be the radius of sphere & cone respectively. Let h be the height of the cone.

Volume of sphere = 3πr3

4

Volume of cone = h2πR3

1

I. Radius of cone, R = 2r

∴Volume of sphere = 3πr3

4& volume of cone = h24rπ

3

1×

Ratio of volume of sphere to that of cone = h

r

h24rπ3

1

3πr3

4

=×

. Hence, I is not sufficient.

II. Height of the cone, h = r. But, this alone cannot give us the ratio. Hence, II is also not sufficient. Combining I & II

Ratio = h

r= 1 (∴r = h)

40. (4) I. D is the tallest among C, D & E. But, we don't know anything about

A & B. Hence, I is not sufficient. II. B is not shorter than D, means B is either taller than or equal to D, But, this is not

sufficient, as nothing is known about C & E. Combining I & II, We get that D is the tallest of C, D & E. And B not shorter of A & B. Between B & D it is opt

known whether they are equal or B is taller, which means either B is the tallest in the group or A; B & D both are the tallest in the group hence we cannot decide.

41. (4) It y is dropped, XZ must be selected. Since Z is there, N cannot be taken hence M and P must be

taken. 42. (4) It L is taken, we cannot take Y hence XZ must be taken and also P. 43. (2) If Y and Z are taken, L and N cannot be taken hence M and P must be taken 44. (2) Visually, we see US has reported more than 21,000 cases. 45. (3) Bahamas, Belgium, Denmark 46. (4) West Germany = 222, France 555 Reqd ratio = 222 : 555 = 2 : 5 47. (2) Bahamas, Burundi, French Guyana and US. 48. (4) 4% of x = 286,000 hence x = 715,000. 49. (1) Only I and II are true. 50. (4) Ethiopia, Israel and Yugoslavia.

EXERCISE 3 1. (2) Using I above since ABC is a right angled triangle and the largest angle

= 90⇒ I alone is sufficient. Using II above since 32 + 42 = 52 ABC is a right angled triangle and the largest angle = 90". => II alone is sufficient.

2. (4) Since the actual number of institutes in Hyderabad is not mentioned, even both the statements are insufficient.

3. (3) From I 8- (a-b)3>0

⇒ 8 > (a - b)3 ⇒ (a-b)3 < 8 ⇒ a-b < 2 - (1) Nothing can be said about this. From II 4- (a-b)2 < 0 ⇒ 4 < (a - b)2 ⇒ (a-b)2 > 4 ⇒ | (a - b)| > 2 ⇒ a - b > 2 or ⇒ a-b<-2- (2) ⇒ From equation (1) and (2) we can see that a-b < -2 ⇒ a < b

4. (4) Since the weights of the balls mentioned are not given, ft is not possible to determine the heavier

box. 5. (1) B alone is sufficient because the statement implies b = 0

∴ a/b is not defined.

6. (4) Since the angle given is 80' in (I) and the time between 3' clock and 4" clock in (II), we can see that there can be two values, hence no unique answer possible.

7. (1) From (I) the dotted line is the ladder at say 8:30 A.M. since we want the height h of the ladder (i.e the point from where ladder touches the wall to the point the ladder touches the floor) and since the length of the ladder is given in statement (I). Answer can be got from (I) alone. Statement (II) will not give the length of the ladder.

8. (4) From statement I, we cannot find the speed at x. Similarly from statement II also, nothing is given about point x. But from I and II, two possibilities arise, i.e. one case if the particle is moving from x0 to x then the particles speed at x would be 7.5 cm/s second case If the particle is going from x to x0, the speed of the particle at x would be 2.5 cm/sec, Since no unique answer can be found.

9. (2) As per statement alone if q = 100 then p = 150 ∴ p/q = 150/100 = 3/2 As per Statement II alone if r = 100 then p =187.5 and q= 125 so, p/q = 187.5/125

9mh

XX0 5cm

X0X 5cm 5 cm/sec

∴the question can be answered statement I alone or statement II alone.

10. (1) As per statement II alone, a sum of Rs.8 can be arrived at by adding 2 and 3 in the form 2 + 3x2 =

8 i.e. one pencil and two pens 11. (1) Three tablets/day would mean the hypertensive has to be taken 90 times in 30 days

The increase 2.50……> 10 tablets hence for 2.50 x 9 = 22.50 for 90 tablets Asthmatic has to consume…> 30 tablets 6.00x3= 18.00 ∴The total increase = 22.50 +18 = 40.50

12. (4) %32

661003

2100

1.50

1.00=×=×

13. (2) He has to consume = 2 x 3 x 7 x 20 = 840

spoons 90 spoons …….. 1 bottle 840 spoons …… 10 bottles

since he cannot buy 3

19 bottles;

hence expenditure according to the existing prices = 10x18.00 = Rs. 180

14. (3) Since he may change the order in which he takes the tablets it is not possible to determine

15. (1) To arrive at the correct value of the total sales of Fuels the inter company sales figures should be

subtracted from the present total sales. To be subtracted from 100% PRL ⇒ 50 + 10 + 40 = 100% i.e. has sold all its sales to other companies only ⇒ correct sales = 0% OICL⇒ 15 + 20 + 10 = 45 ⇒ (100 - 45)% of 30% = 16.5% PHCL ⇒ 20 + 20 + 20 = 60 ⇒ (100 - 60)% of 25% = 10% PBCL ⇒ 30 + 10 + 35 = 75 ⇒ (100 - 75)% of 20% = 5% OTHERS ⇒ 10 + 5 + 10 = 25 ⇒ (100 - 25)% of 15% = 11.25% ∴ Actual sales: = (0 + 16.5 + 10 + 5 + 11.25) = 42.75% of given sales ∴% by which total sales of fuels were over estimated

135%10042.5

42.75)(100≅×

−

16. (3) The correct sales figures

= (100 - % sales to other companies) x % share of total sales given = (100-M) x p (say) ∴M should be minimum and p maximum. By observation this is true for OICL in case of Fuels and for PBCL for lubes. (Note that OTHERS and PRL are eliminated) Calculations between PBCL and OICL OICL: = (100 - 45) x 30% x 25 + (100 - 60) x 15% x S (where S = sales of lubes and since sales of fuels = 25) ≅ .45

For PBCL = (100 - 75) x 20% x 25 + (100 - 45) % x 30% x S ≅ 0.275 S ∴Clearly it is maximum for OICL

17. (3) We need to find that company for which Total sales are less than total purchases = S-P is minimum (and -ve) i.e. S is minimum and P is maximum S is from the pie chart and P is the sum of purchases obtained from the columns in the table. By observation alone OTHERS have purchased far more than any of the rest. And its sales are also minimal for both lubes and fuels.

18. (2) For maximum Profitability. Sales - Purchases should be maximum. ∴ S - P must be maximum For ICL, the total Purchases are 17.5% and ∴ Profitability = 30 - 17.5 = 12.5% [i.e. 50% of PRL + 20% of PHCL + 30% of PBCL + 10% of OTHERS] Similarly, for PHCL Profitability = 25 - 8.25 = 16.75 for PBCL Profitability = 20 - 12.5 = 8/5% and for others, there is Negative Profitability as we have seen in 2127.

19. (1) The correct sates figures for Fuels have already been calculated in solution (1) and in similar manner we calculate those of lubes OTHERS ⇒ [100 - (15+5+15)] x 25% = 16.25% PHCL ⇒ [100 - (10+25+40)] x 20% = 5% OICL ⇒ [100-(20+40)] x 15% = 6% PBCL ⇒ [100 - (15+5+25)] x 30% = 16.5% Now total sales of lubes =% x that of fuels ⇒ effect values for above are OTHERS ⇒ 8.125 PHCL ⇒ 2.5% (of total sales of fuels) OICL ⇒ 3% PBCL ⇒ 8.25% The total correct sales value of fuels and lubes put together maximum is for OTHERS ⇒ 11.25 + 8.125 =19.375 PBCL⇒ 5+ 8.25 =13.25% OICL ⇒ 16.5 + 3 = 19.5% PHCL⇒ 10 + 2.5 = 12.5% ∴OTHERS is second in terms of (correct) total value of sales of fuels and lubes put together.

20. (1) Let the amount of paddy to be processed = q kg. the amount of rice it yields = q x 0.95 = 0.95 q out of this if you exclude 6% broken

0.893q100

610.95q =− ⎟

⎠⎞

⎜⎝⎛

∴So the rice you get = 0.893q ∴0.893q x 8 = 14.288 0.893q = 1786 q = 2000 kg.

21. (3) The rice produced by processing 10.000 kg of paddy = 9,500 kg. if the brokens increase by 2% of 9,500 ⇒ 190 kg of additional brokens 190 kg of fine nee less ⇒190 x 8 = 1520 but this is offset by 190 x 2 = 380 profit over sale of additional brokens 1, 520 – 380 = Rs.1, 140

22. (4) 5% loss of weight would imply = 0.05 x 10,000 = 500kg.

the rice extracted will be = 9,500 x 100

95= 9025

the decrease will be = 9, 500 - 9025 = 475 kg.

23. (3) Proceedings from sale of husk =

5000 x 0.05 x2

1 = Rs.125

proceedings from the sale of brokens =

5000 x 0.95 x 100

6x 2 = 570

hence amount realised = Rs.570 + Rs 125 = Rs.695 Solutions for questions 24 to 27:

‘It-is given that the cages are as follows. Antelope Gorilla

Elephant Gorilla Giraffe Antelope Deer 1 2 3 4 5 Chimpanzee Horse Zebra Bear Tiger Lion

6 7 8 9 10 11 Wolf 12

From statement (1) we get elephant is in 1st cage, wolf is in 12th cage and chimpanzee is in 6th cage. From statement (3) we get lion is in 11th cage, deer is in 5th cage and tiger is in 10th cage. From statement (4) we get horse is in 7th cage From statement (2) we get bear is in 9th cage, and zebra is in 8th cage and giraffe is in 3rd cage. Either Antelope or Gorilla is in the 2nd cage or 4th cage. 24. (3) If tiger is not opposite to Gorilla, then the order of the animals are as follows.

Elephant Gorilla Giraffe Antelope Deer Chimpanzee Horse Zebra Bear Tiger Lion Wolf Then Gorilla is adjacent to Elephant.

25. (2) The animals can be arranged in two ways. 26. (4) Either Gorilla or Antelope is in between Giraffe and deer. 27. (3) If elephant is shifted to the 12tH cage and deer is adjacent to gorilla, then the order in which the

animals are arranged in the cages is Wolf Lion Tiger Bear Zebra Horse Chimpanzee Deer Gorilla Giraffe Elephant Gorilla is opposite to tiger.

28. (3) 1 2 3 4 5

C E A D B C, E, A are in that order as C's number is less than E's as E's is less than A's. Hence C, D and A can only take box numbers 1, 2 and 3. Therefore B has to be in box number 5.

29. (1) (38 - 30)/30 = 26% 30. (4) Visually, we see D is more in 1995 while total is more or less constant 31. (3) 32. (4) 55 - 34 = 21lakh. 33. (4) 28/176 = 16%.

Solutions for questions 34 to 38: It is given that the number of games played by each player is different, i.e. one player plays one game, another plays two games and so on. With the given information we can conclude that

Chess Swimming Weightlifting Cycling Tennis Pranay × √ √ Qureshi √ √ √ Rasool × √ √ Surendar × √ Tarif × × √ √

From (6) Tarif does not plays weightlifting because cycling is the only common of Rasool and Tarif. 3 players participates in swimming and the most common game is weightlifting. Hence 4 players participates in weightlifting, From (6), Rasool does not play Tennis All the players play at least two games except Surender. From Statement (1) we get Surender plays only one game and Qureshi plays all the five games and Pranay do not play cycling, From (3) Tarif do not play swimming. Hence, the final arrangement is as follows.

Chess Swimming Weightlifting Cycling Tennis Pranay × √ √ × √ Qureshi √ √ √ √ √ Rasool √ √ √ √ × Surendar × × √ × × Tarif × × × √ √

34. (2) Qureshi plays all the five games. 35. (3) The common game among Pranay, Qureshi and Rasool are swimming and weight lifting. Hence

(1) is not true. The common game among Qureshi and Tarif is cycling and tennis. Hence (2) is not true. All the four games except Tennis are played by Qureshi and Rasool is true.

36. (4) Four players participate in weight lifting. 37. (2) When the first 10, 20, (and so on) players are sent back in that order the row is gradually "and

completely reversed after every 80 players who are sent back. Total number of players sent back = 10 + 20 +.... 80 = 360 i.e. (80 x 4) * 40 ^ effectively only the first 40 players have been sent to the end of the row and hence the player numbered 5 will be in the 40 + 5 = 45th position.

38. (2) It is given that A wears Black shirt means A cannot wear black trouser, blue trouser, white trouser. Hence he wears either Red or Green trouser Similarly, D wears Green shirt means he cannot wear green trouser, black trouser, white trouser. Hence he wears either Red or Black trouser. It is also given that D does not wear Black trouser. Hence D weans Red trouser and A wears Green trouser. It was also given that neither B nor E wears the Blue trouser. Hence, C wears the Blue trouser.

Solutions for questions39 to 42: 39. (2) The sector recording a decrease of 8 percentage points is medicine the sector recording a 5

percentage of points increase is education the difference in amounts allocated in 1992 will be

12,500100

102,50,000

100

152,50,000 =×−×

40. (4) The year in 4 sectors = Rural Development is 1992; the difference between maximum and

minimum allocations is

⎟⎠⎞

⎜⎝⎛

−100

10

100

152,50,000

= Rs.12,500100

52,50,000 =×=

41. (1) In the year 1992 medicine + agriculture is 15% + 15% = 30% 42. (4) The maximum percentage increase is for the rural development

∴the difference in outlay for two years 1, 25, 000 - 80, 000 = Rs.45, 000 43. (4) The states with a growth greater than 10% are Sikkim, Tripura, Assam, West Bengal.

Total production = 0.6 + 18 + 45 + 72 + 84 + 102 = 321.6 Production of states which show more than 10% increase = 321 .6 - (0.6 + 45) = 276 276/321 = 85.8%

44. (3) The maximum % increase in 1994-95 is for the state of Tripura which is 33.33%. Where as the least percentage decrease is zero in case of Manipur ∴ x2/y2 is undefinable.

45. (4) The average production for 1993-94

46=+++++

690 76 54 42 16 0.6

and the state which is closest to that is Nagaland which is 42 (closest to average production) The average production of all the states for year 1995-94 =

90 76 54 42 16 0.6 278.6

46.46

278= = average production

The state is Nagaland with 42 (closest to average production) ∴The production of Assam + West Bengal = 166

300%10042

42166=×

−

46. (3) The state which records 33% increase is Tripura has 19% of the lot at production for the year

1993-94.

47. (2) Total trees = 21.600 Cherries are 37.5% of total = 3/8 x 21600 - 8100 Fruit yielding cherry tree are 61% of 8100 = 3/5x8100+ 1% of 8100 = 4860 + 81 = 4941

48. (1) Apricot fruit yielding trees = 12.5% of 87% of 21600. = 10.87% of 21600 Peach fruit yielding trees = 12% of 78% of 21600 = 9.36% of 21600 ∴10.87% of 21600- 9.36% of 21600 = 1.51% of 21600 = 327

49. (2) Avercado = 11%x93%of2l600

= 10.23% of 21600 Apricot = 12/5% of 87% of 21600

= 10.87% of 21600. Peach = 12% of 78% of 21600 = 9.36% of 21600 Plum = 13% of 77% of 21600 = 10.01% of 21600 By observation Apricot has the greatest number of fruit yielding trees.

50. (3) The percentage of fruit yielding plum trees as a percentage of fruit yielding peach trees is

107%1009.36

10.01=×

51. (1) Only S3, S6, S7 and S8 have qualified and among these it is dear (by addition) that 106.5 marks is

the highest for S3. 52. (2) The four people who have qualified are 1

S3 (106.5); S6(105) S7 (103) and S8 (96)

53. (3) Adding the total number of mistakes. S1 = 30 mistakes S2 = 27 mistakes S3 = 46 mistakes S7 = 30 mistakes

54. (1) (a) Maximum score in RC is 37.5 and was secured by S2. yet he did not qualify. Hence statement I is true.

(b) 82 is the person with the maximum grand total and he did get the maximum in VA and RC sections arid hence statement II is false.

(c) S6 has made maximum attempts. Not S8. Hence statement III is false. Hence only statement I is true.

55. (4) Maximum number of questions answered correctly by S8 is 110 S7 is111 S5 is 59

S6 is 115

EXERCISE 4 1. (4) From Table 2, we see that in 1980, the total number of consumers ere 32571 ×103 and from Table

1, the average energy consumption per 1000consumerswas2.5 GWH. Hence the total energy

consumption would be 32.6 × 106 1000

2.5× GWH ≈ 0.82 × 1011 KWH. Hence (4)

2. (1) The total electricity consumed in 1994 (obtained from the number of consumers and the average energy consumption per consumer) is 0.86 × 105 × 3.5 GWH. This is also equal to the area average consumption per sq. km.

Hence the area is equal to 0.86× 105 =

⎟⎠⎞

⎜⎝⎛

1000

883.4

3.3 × 106 sq. kms. Hence (1)

3. (2) Let C1 and C2 be the number of consumers in 1970 and 1980 respectively, let P1 and P2 be the

populations in 1970 and 1980 respectively. Then 0.134

0.09

P2

N2P1

N1

and2.5

3.3

C2

N2C1

N1

==

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

. Since f1

=P1

C1and f2 =

P2

C2, the required

ratio 1.97

0.134

0.092.5

3.3

f1

f2≈=

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

. Hence (2)

4. (2) We use Table 2 to obtain the ratios of the number (1990 to 1980) of consumers for Domestic, Commercial, Industrial, agricultural and Total. The values are 2.26, 1.75, 1.81, 2.04, and 2.14 respectively. Hence (2)

5. (3) The number of Domestic consumers in 1970 and were 10165 and 63406 thousands respectively giving a percentage increase of approximately 524%. Hence (3)

6. (4) Both the statements individually or combined are not sufficient 62 = 36 divisible by 2 & 3 or 52 =25 not divisible by two consecutive numbers. Hence (4)

7. (3) Since the probability of drawing a red marble is24

1and the number of marbles < 40, ∴the number

of marbles in the bag is 24, of which one is red.

From I The probability of drawing a blue marble is 3

1,

∴the number of blue marbles is 8 ∴number of black marbles 24 – (1 + 8) = 15

∴The probability of drawing a black marbles is 8

5

24

15= .

∴Both statements are necessary. Alternatively,

Using both the statements, the probability of drawing a black marbles 1 - ⎟⎠⎞

⎜⎝⎛

+3

1

24

1

(since there are only red, blue and black marbles). Hence (3)

8. (3) Possible values of x can be 1, 2, 3, 6, 17, 34, 51, 102 Form I : x + 17 is divisible by 3 ∴x + 2 is also divisible by 3 which is possible when x = 1or 34 From II : x + 2 is divisible by 4 which is possible when x = 2, 6, 34

∴Using both statements, we have only one common value of x, i.e., 34. Hence (3) 9. (3) From I : Y can either be Rs.60 or Rs.120 From Y = 60, X = 100

When Y = 120, X = 40 From II, x > 50, therefore the 2nd case does not apply.

∴x =100; y =60 ∴Both statements are required. Hence (3) 10. (3) From I : ∠B > ∠A From II : We know B + C = 1100 ∴(B + C)2 =12,100 B2 + 2BC + C2 = 12,100 ∴BC= 2400

∴B + 01102400=

B

B – 110B + 2400 = 0 B = 80 OR B = 30 B > A ∴∠B = 1800 – (70 + 80)0 ∠C = 300 ∴Both statements are necessary. Hence (3)

11. (2) Let the effectiveness of A, B, C and D be 5x, 6x, 4x and 3x respectively then, total effectiveness of Ajit’s drug ⇒ 12 × 5x + 15 × 6x + 20× 4x + 28× 3x = 314x that of Bittu’s and drug ⇒ 37 × 5x + 15 × 6x + 13× 4x + 15× 3x = 372x that of Chinku’s drug ⇒ 26 × 5x + 15 × 6x + 10× 4x + 34× 3x = 362x

Alternatively,

The most effective drug B is in equal proportion in all drugs. Now the second most effective is A, Ajit‘s pharma can be easily eliminated as it has very less proportion of A compared to Bittu’s and Chinku’s drug. Again, Ajit pharma: 37× 5+ 13 × 4+ 15 × 3 = 82

Bittu’s pharma : 26 × 5 + 10 × 4 + 34 × 3 = 272 Hence (2)

12. (3) Side effect EB

C

+

For Ajit’s drug, it I, 2

1

2515

20=

+

For Bittu’s drug, it is, 0.372015

13=

+

Fro Chinku’s drug, it is,3

1

1515

10=

+. Hence (3)

13. (2) Let the new composition of E be 25 – x and that of be 20 + x.

then, 12515

20≤

−++

xx

20 + x ≤ 20 x ≤ 10

∴Maximum composition of C is 20 + 10 = 30%. Hence (2)

14. (4) We cannot answer this, unless the production of individual companies are given. Hence (4) 15. (4) 16. (3) The discount in Kolkata ticket is Rs.3535 and the discount in Delhi ticket is Rs. 2175

So with Rs.3535 ticket for 17 destination can be bought (any one of them except Delhi0 and with Rs.2175 tickets for 4 destinations i.e. Ahemedabad, Pune, Indore and Aurangabad can be bought (any one of them 0. So answer is 17 & 4. Hence (3)

17. (4) Maximum discount in numerical terms is in Kolkata ticket. It is 6855 – 3320 = Rs. 3535 Lowest discount same way for Aurangabad is 647 Rs. So Rs. 3535 is almost 546% of Rs. 647. Hence, (4) 18. (3) less than 50% 19. (2)

Case I Case II To From To From

Delhi 6095 3920 3920 3920 Bhopal 4125 2371 2371 2371 Ahemedabad 3255 2017 2017 2017 indore 3360 1965 1965 1965 16835 10273 10273 10273

So Expenditure in I case =27108 So Expenditure in II case = 20546 The solving in the second case = 6562it is approx. 24%. Hence (2) 20. (3) From the options, it is obvious that only the top 4% numbers must be evaluated.

The average size of the 3rd and 4th largest firms must be less than or equal to the average size of the first two firms. Based on an inspection, the jump in textiles appears to be very large. The average fro the 3rd and

4th firms is 52

8)(18=

−. However, the first two firms’ average is only 4

2

8= . Hence, it is

incorrect and needs to be corrected by subtracting 4%. Hence (3) Only option (3) shows the correction by 4%.

21. (4) The solution lies in estimating the size of the largest firms as a proportion of the total industry.

Since the 3rd largest firms ≥ average of the 3rd and 4th firms, The 3rd largest firms ≥ 2

60)(75−or

7.5% Hence, the 2nd largest firms ≥ 7.5% or the largest firms ⇐ 60 – 7.5 = 52.5% Also, largest firms ≥ average of the top 2 firms Hence, the largest firms ≥ 60/2 or 30%.

Hence, the size of the steel industry is between 0.525

5000 (about 9500) and (16667)

0.3

5000. Hence, (4)

is not possible Hence (4) 22. (2) It is obvious that steel, oil & gas shipping and Elevators have less than 20 firms. Now, the average size of the top 10 firms ≥ the average size of all the remaining firms. Consider

the leather industry. The average size of the top 10 firms = 1%10

10= . Hence, each of the

remaining firms cannot be larger than 1% and there must be at least 901

90= such firms. In all,

then there must be at least 100 firms. Similarity, Textiles has at least 17 firms. Hence, leather, textiles and chemicals definitely have at

least 20 firms. Hence (2)

23. (4) Option (1) is a red herring and is false. Applying these rules, it can be seen that a maximum of 3 industries can face restrictions (Steel, Oil & Gas and Elevator). We do not know the number of industries where the largest firms is government owned. Hence, options (2) and (3) cannot be evaluated. Hence (4)

24. (2) Consider the current year. Maximum possible size of the 4th largest firms = average of 3rd and 4th

largest firms= 2

60)(75−= 7.55 of the industry. Assuming the remaining firms (the firms other

than the top 4 firms) are the same size (7.5%), there would have been 7.5

75)100 − or 3.33 or 4 firms

other than the top 4. Hence, a total of at least 8 firms in this year. There were at least 2 mergers last year. Hence, last year’s minimum = 8 + 2 =10. Hence (2)

25-28. For this caselet consider possibilities one by one. E.g. first suppose Ria gets soup then Janet gets hot coffee (statement 1), Venna gets gums (statement 5) and Ria gets hot coffee (statement 9) which contradicts our supposition; hence, rejected. Next suppose Gia gets soup then Ria gets gums (statement 11). Then if Janet get hot coffee, Veena gets gums (statement 5), which is not possible. So, Janet gets tea and remaining Veena gets hot coffee. 25. (1) 26. (3) 27. (2) 28. (4) 29. (3) 30. (3) 31. (2) 32. (4)

33. (2) Two other teams each must have at least 3 members. 34. (1) This team contains members from two of the original teams only. 35. (1) Since neither of two new teams has any member from team A3, both members of A3 will have to be

accommodated in the third team which, however, is not allowed.

36. (3) 37. (1)

38-39 The second resident always speaks truth (so, not a govt. official) First speaker may speak truth (IS not & denies being a govt. official) or may tell a lie (is a govt. official but denies being one) – in either case denying being a govt. official. If first resident speaks truth the third one tells a lie and vice-versa.

38. (3) 39. (4)

40. (3) History of Modern Europe (HME) + American History (AH) = 90 + 90 = 180, but there are only 120 students. Thus, at least 60 students selected both of the above subjects. HME and AM + Ancient Indian History (AIH) = 60 + 105 = 165. Thus, again, as there are only 120 students, at least 45 would have taken all three of above. Using the same logic, (45 + 105) – 120 = 30 students at least would select all the four subjects.

EXERCISE 5

1. (4) The data is insufficient as the manufacturing cost of the liquor is not mentioned anywhere for any

of the states. 2. (4) The data is insufficient, as the excise duty per litre for the year 1986 is not mentioned. 3. (4) The data is insufficient, as the amount of liquor supplied to four states is not mentioned. The

amount of liquor supplied in Tamil Nadu is only mentioned and moreover for the first bar graph the year is not mentioned.

4. (4) The data is insufficient as the sales for the period is not mentioned in the question. Therefore, the answer is 4.

5. (1) The average value of the contract secured during the years = (100.5 + 67 + 141 + 143.9 + 65)/5 = 103.48

6. (2) Considering 1985 as the performance base of 100% i.e. 67 = 100% the figure for the indices for different years are shown in the table below:

Index is calculated as 67 = 100 (Base year 1985) Index for 1984 is therefore = 100/67 × 100.5 = 150 (contract secured is 100.5) 7. (2) There is decline in contract secured only in the year 85 and 88 compared to the previous year. The

highest % decline in the value of contract secured is for year 1988 = {(143.9 - 65)/143.9} × 100 = 54.82%

8. (2) The estimated cost of material in 1990 = 80 + 45 + 12 + 18 = 155. The estimate cost in 1991 = 75 + 60 + 16 + 21 = 172

Cost of material rises by 5% and hence, the estimated cost will rise by the amount =.05 × (155 + 172) = 16.35.

9. (2) The ratio of cost of materials to labour cost = Total cost of material for the years/Total labour cost for the years Using the above formulae, the ratio comes as 8 : 1

10. (3) The total expenditure is required to be kept within Rs. 700 lakh. The estimated total expenditure = Rs. (52.1 + 267.5 + 196.4 + 209.5) = Rs. 725.5 lakh

The amount to be cut down = Rs. (725.25 - 700) = Rs. 25.5 lakh This amount is cut equally in all the years on expenditure of administration and hence cut in each year = Rs. 25.5/4 = Rs. 6.375 lakh.

% cut for year 1986 = (6.375/15) × 100 = 42.5%. 11. (4) Let the total length of the railway line to be laid is x km in the given years. Length of line is proportional to the provision for material and labour cost.

That means x kms is laid for Rs. (sum of material and labour cost for the given years). For Rs. 597.1 lakh, x km line is laid Therefore by Rs. 175 lakh, (x/597.1) X 175 = 0.3x 12. (1) Total estimate = Rs. 725.5 Lakh; Estimate of contingencies = Rs. 25.2 lakh

Now the estimate of contingencies is doubled as it is felt inadequate = Rs. 50.4 % increase in total estimate = (25.2/725.5) × 100 = 3.47%

13. (2) At the end of 1990, the entire amount for the project has been spent = 725.5 lakh. For 1991, the amount spent = Rs. 209.5. The total amount spent on the project is Rs. (725.5 + 209.5) = Rs. 935 lakh. % by which the actual expenditure exceeds the estimated = {(209.5/725.5)} × 100 = 28.8%

14. (1) Referring table 5, we can directly say that % of blue sari sold is maximum in the region 2 = 33% 15. (2) Referring table 4, we can say directly say that minimum % of green sari is sold in region 6 = 14% 16. (4) Referring table 5, it is quite obvious that % of magenta saris sold is maximum for region 1 = 44% 17. (2) The popularity of any colour in any region can be checked by looking the % sale of that colour in

that region i.e. referring table 4. The most popular colour in region 12 is brown 18. (3) Refer to table 3 to know % of saris sold to saris stocked for each colour in each region.

The region-colour combination that accounts for the highest % of sales to stock is (4, Brown) = 74%

19. (4) The area which was brought under irrigation in 1986-87 = (24 - 23.2) + (34.2 - 32.77) = 2.23

million hectares 20. (1) Consumption of chemical fertilisers per hectare of gross cropped area is given by {Total

consumption of chemical fertiliser/gross cropped area} The consumption of chemical fertiliser per hectare of gross cropped are is lowest for the year 1984-85 = (3.68 + 1.21 + 0.62)/173.1 = 0.0318 ton per hectare

21. (4) In year 1987-88 a part of minor irrigated area is brought under major and medium areas as it was the cumulative figures and hence data for minor irrigation for 1987-88 must be greater than the previous year, but it is not so.

22. (1) Refer to the table showing High yielding varieties. In year 1988-89, wheat jowar and bajra shows a decline from previous year and that is the maximum number of crop.

23. (3) The travelling time was 5000/66 hours. The stopping time was 12 + 22 + 32 + … + 10² minutes. 24. (3) If the number of children older than 5 years of age is x and the number of children younger than 5

years of age is y, then 5x + 6y = 43. The only values of x and y satisfying the equation are x = 5 and y = 3.

25. (2) P lies between 2371 and 2379. If P is divisible by 4, it could be 2372 or 2376. But if it is divisible by 9, it can only be 2376.

26. (2) [(x-1 - y-1)/(x-2 - y-2)] = (1/x - 1/y)(1/x² - 1/y²) = 1/(1/x + 1/y). If x and y are both greater than 2, 1/x and 1/y are both less than 0.5. Hence 1/x + 1/y is less than 1, or its reciprocal is greater than 1.

27. (3) x + z = 2x + (y - x) + (z - y) = 2x + 2 + 2 = 2x + 4. Since x is odd (dos not have a factor 2), 2x + 4 is not divisible by 4.

28. (3) Let the average speed from C to M be s, and the distance be x. Then from M to T, the speed is 2s and the distance is 0.3x. Average speed of the entire journey = distance / time = (x + 0.3x) / (x/s + 0.3x/2s) = 2.6s/2.3 = 40.

29. (2) If w is not older than V, he is younger than or the same age as Y. Hence Z is younger than X. 30. (4) The change in the prices of the two products over the next five years cannot be determined. 31. (2) x - y will always be 2. x + y < 10 does not specify the numbers. 32. (4) If CP is 80% of SP, then SP is 125% of CP, or the profit is 25%. 33. (1) If the length is I, the breadth is 48/1, and the diagonal is √[i² + (48/l)²] = 10. Hence I can be found. 34. (3) If a price reduction of 50% enables me to buy 48 bananas in Rs. 12, I can buy 48 bananas for Rs.

24 at the original price. ∴ The price of a banana is 50 paise. 35. (4) The only two positive numbers whose squares add up to 116 are 4 and 10.

EXERCISE 6 Direction for 1 to 4: First of all derive a general formula for Bankatlal’s monthly salary

1 week 2 week 3 week 4 week Hours of rest X Y X Y Working hrs. Y X Y X

Thus for every month, 1st & 3rd week and 2nd week must be identical. Salary per day in 1st & 3rd week = KY, where k = wage per hour Salary per day in 2nd & 4th week = kX/2 Total monthly salary = 1{ky + kX/2} = 6k(2Y + X), where x = hours of rest per day, Y = working hours per day in the 1st week of the month. Direction for 1 to 4 1. (1) Fro the 1st month X = 2, Y = 5, so total salary = 6x 20 (2x 5 + 2) = Rs. 1440. 2. (3) Total salary for 4 months = [1440 + 120 {(2 × 7 + 3) + (2x 6 + 4) + (2x 8)}] = Rs. 7320

Average Salary = 4

7320= Rs.1830.

3. (2) Under New Scheme salary per day in 9th & 11th week = 25 × 6 - 5x4 = Rs. 130 Under New Scheme salary per day in 10th & 12th week = 25 × 4 - 4x6 = Rs. 70

Under New Scheme total salary for 3rd month = 12 (130 + 70) = Rs. 2400 Under previous scheme total salary for 3rd month = 120 (2 × 6 + 4) = Rs. 1920

Difference = 2400 - 1920 = Rs. 480. 4. (2) As per the conditions salary for first 3 months = (!440 + 2040 + 2400) = Rs. 5880 For 4th month salary per day in 13th & 15th week = 8 × 25 = Rs. 200 For 4th month salary per day in 14th & 16th week = - 8 × 5 = (- 40) Total salary for 4th month = 12 (200 - 40) = Rs. 1920 Total salary for 16 weeks = {1440 + 2040 + 2400 + 19 5. (2) In order to manufacture maximum number of units, make Q on both the machines as time taken

for manufacturing one unit of Q is less on both the machines. And maximum number of units obtained = {(8 + 8) × 60}/6 = 160.

6. (1) As per the given condition number of units of P should be three times that of Q. One unit of P takes less time on M2 as compared to that on M1. So manufacture P on all the time available on M1, number of units of P obtained = (8 × 60)/8 = 60. Now number of units of Q required to fulfil the given condition = (60/3) = 20. Time taken to manufacture 20 units of Q on M2 = 20 × 6 = 120 min. Remaining time available on machine M2 = (8 × 60) - (120) = 360 min. In this time manufacture 3 units of P followed by 1 unit of Q & continue till all the available time is utilised. Time taken to manufacture 3 units of P & 1 unit of Q on M1 = (3 × 8 + 6) = 30 min. Thus in 360 min 36 units of P & 12 units of Q will be manufactured & idle time will be zero.

7. (3) Here four different method is given and to compare each method we will bring them into common

platform so that we can compare them. Taking the LCM of 48, 64, 53 and 71 which will give total number quantities to be manufactured and hence we will see which method is taking maximum idle machine hour to manufactured this number of quantities. LCM of 48, 64, 53 and 71 = 722496

By method a) Total idle machine hours (722496 × 3)/48 = 45156 min b) Total idle machine hours (722496 × 12)/64 = 135468 min c) Total idle machine hours (722496 × 10) = 136320 min d) Total idle machine hours (722496 × 9)/71 = 91584

From above it is very clear that method c) is maximum idle hours hence it is the least efficient method. Answer is 3).

8. (4) If M1 works at half of its normal efficiency, time taken by M1 to manufacture 1 unit of P = 20

min. and Q = 12 min. And now maximum number of units obtained = (8 × 60)/12 + (8 × 60 - 8)/6 + 1 = (41 + 472/6) = 119 (consider only complete units).

9. (1) In order to take minimum time manufacture P on M2 & Q on M1. Number of machine hours

required = (30 × 8 + 25 × 6)/60 = 6.50 hours. 10. (1) Total requirement of cloth = Total number of shirts x cloth required per shirt = (20 + 30 + 30 + 10

+ 10) 1000 × 1.5 = 150,000 m. 11. (3) Total quantity of high quality cloth consumed by A shirts = (80% of 20000) × 1.5 = (4/5) × 30000

= 24,000 m. 12. (2) Required Ratio = (40% of 30000)/(60% of 10,000) = 2 : 1. 13. (2) Total low quality cloth consumed = 1.5 {(3/10)x60 + (2/5) × 10 + (9/10) × 10} 1000 = 46,500 m. 14. (3) 15. (3) One can logically assume that a test will be feasible if its relative cost is lower than that of any other

test. Test -2 has the lowest relative cost in the range 0.05% to 0.2%, so the answer is (c). 16. (4) For p = 0.2, both, Test-2 and Test - 3 have the same relative cost, so both of them are feasible. 17. (1) Test-3 has the lowest relative cost for the range p > 0.2, so Test - 3 will be the best option to adopt

for p > 0.2. 18. (1) In the range 0.00 < p < 0.05, Test - 1 has the lowest relative cost, so the answer is (a), i.e. p < 0.05. 19. (4) If p < 0.2, then initially Test-1 is more feasible, while thereafter, Test -2 is

a better option. While we cannot say from the data given in the question, which of these two tests is better, we can definitely say that Test-3 is the most expensive test for the range p < 0.2.

20. (3) 21. (3) 22. (4) 23. (3)

24. (3) 25. (3) 26. (2) 27. (1)

28. (4) 29. (2) 30. (1) 31. (3)

32. (3) dozen organs are equivalent to 4 kg mangoes, hence 14 kg mangoes cost Rs. 252.

33. (3) If tz is odd, both t and z are odd. If x + y + t is even, x + y + t - z odd. 34. (3) If the altitude to the base of an isosceles triangle is known, the base can be found, and hence the

area.

Solid DI Set 1 Question For Questions 1 to 5 read the following instructions: Nine horses participated in a horse tournament. Five races were held in this tournament. The winner of a race gets 5 points, 2nd gets 3 and the 3rd gets 1. The table gives the points tally.

One race is held between five horses. The first race is held among the first 5 horses from the left in the above table. Out of these horses, A drops out of the race and a new horse. ie. F enters into the race. In the next race, B drops out and G enters and so on. It is also given that H is the only horse that scored in 2 consecutive races. Q.1 What was the position of horse F in race 4? a. 4th b. 2nd c. 3nd d. cannot be determined e.1st Q.2 What is the ratio of the points scored by “G” and E in race 5? a. 1:3 b. 3:1 c. 1:5 d. cannot be determined e. 5:1 Q.3 The first 3 rankers of the race 3 in some order? a .C,E,G b. D,E,F c. C,D,F d. C,E,F e. C,G,F Q.4 D could have come third in which of the following races? a. Race 1 b. Race 3 c. Race 4 d. Race 5 e. cannot be determined Q.5 Suppose if C had 6 points and E had 7 points while the points of the rest of the horses remain unchanged then E could’ve come second in a. One race b. Two races c. At most one race d. At most 2 races e. cannot be determined Answer: For Solid DI Set 1

The table of the winners is as follows:

So 1-b, 2-d, 3-a, 4-c

For 5 interchange the places of C and E in race 1. Hence the answer is d, 5-d

Solid DI Set - 2 Question For Questions 1 to 5 read the following instructions: The following Table gives the number of students in all the different classes of Indian Public school in the years 2050 and 2051 respectively.

Race1 A C E Race2 B F D Race3 C E/G G/E Race4 H F D Race5 H G/E E/G

1

Class

Students in the year 2050

Students in the year 2051

VII 120 140 VIII 84 100 IX 72 70 X 64 60 XI 48 56 XII 36 54

It is known that i. New students join the school only in class VII ii. No student leaves the school before passing out from class XII iii. The students, who fail, have to repeat the year. Q.1 If no student of class XI failed in the year 2020, then what is the pass percentage of class XII for the year 2050? a. 22.66% b. 16.66% c. 83.33% d. 77.77% e. None of these Q.2 If the new joiners in the year 2051 were 76, then the number of students failed in class XII in the year 2050? a. 10 b. 14 c. 8 d. 16 e. 20 Q.3 How many students of class IX failed in the year 2050, if no student of class XI failed in the year 2050? a. 12 b. 8 c.10 d. 14 e. None of these Q.4 If number of students of class VII failed in the year 2050 is 64, then what is the total number of students failed in the year 2050? a. 150 b. 182 c. 195 d. 164 e. 176

Q.5 The highest pass percentage of class VII can be? a. 55% b. 60% c. 58% d. 50% e. 65%

Answer: For Solid DI Set 2 A general formula here is Strength (c, y) = Pass(c-1,y-1) + Fail(c,y-1) Where c is the class and y is the year.

1. No. of failures in class XII in 2050 is 54-48=6. Hence the pass percentage is 5/6*100.ie 83.33

2. Back track and obtain the failures and passes in that particular year from the formula. Answer is 16.

3. Same procedure, start from the bottom. Answer is 20.

4. This is a supplement of question. no 7. Answer is 182.

5.The highest pass percentage for class VII can be obtained only when class XI has no failures( because, all the other classes have certainly a min number of failures). You’ll get it as 66. so its 66/120 ie.55%

1-c ,2-d, 3-e, 4-b, 5-a

2

Solid DI Set - 3 Question For Questions 1 to 5 read the following instructions: Six people A,B,C,D,E and F are standing in a row(from left to right) in that order. A is at place 1, B is at place 2 and so on. They are rehearsing a dance sequence for a dance competition. When the signal is given the following 3 steps are performed. Step 1: They break away and form a triangular formation with 4 and 5 in front of 1, 2 and 3 and between 1 and 2 and 2 and 3 respectively, while 6 is in front of 4 and 5. Step 2: Then 6 goes a step backward and joins between 4 and 5 who form the front row now. Step 3: After a few dance moves, both these rows merge with the person in front of 1 joining between 1 and 2 and so on. These 3 steps form a round. These steps are repeatedly performed till the dancers attain their original positions. This is called one sequence. Q.1 How many times are step 1, step2 and step 3 are performed before one sequence? a. 8 b. 6 c. 4 d. 5 e. 10 Q.2 At which place is C after the completion of the penultimate round? a. 1 b. 3 c. 5 d. 2 e. 6 Q.3 How many members come to their original positions at least once before the sequence ends? a. 1 b. 2 c. 3 d. 4 e. 5 Q.4 Suppose their initial positions were in the order mentioned before but from right to left, and the steps 1 and 2 remain the same while in step 3 the person in front of 3 joins between 3 and 2 and so on to form a single row.

How many rounds before this sequence ends? a. 4 b. 6 c.8 d. 10 e. They never come back to their original positions Q.5 In the above mentioned sequence, how many members come back to their original position at least once before the sequence ends? a. 2 b. 3 c. 4 d. 5 e. 6

Answer: For Solid DI Set 3 A B C D E F is the initial formation.

Step1: A B C D E F Step 2: A B C D F E Step 3: A D B F C E

This is completion of Round 1. After 5 rounds the formation will again be A B C D E F.

3

1-d, 2-d, 3-a

Another formation is F E D C B A

Step 1: C B A E D F Step 2: C B A E F D Step 3: C E B F A D

From this formation it takes 6 rounds to complete a sequence. 4-b, 5-e

Solid DI Set - 4 Questions For Questions 1 to 5 read the following instructions: 12 Hockey teams participated in a tournament. These teams were equally distributed into 2 pools A and B. In the 1st round, each team played a match against all the other teams in the same pool. Top 3 teams with highest average (from both the pools) went to the next round, where all the six teams played against each other once. Again the top 3 teams with highest average qualified to the finals. In the final round, all the 3 teams played against each other and the team with the highest average was declared the winner. Scoring: A win earns 4 points, loss earns -2, and a tie will result in 2 each. Average = Total points/ Number of matches The following table shows the points tally

Teams A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 Total 28 0 10 0 16 6 -6 26 6 12 4 14 Average 2.33 0 1 0 1.6 1.2 -1.2 2.16 1.2 1.2 0.8 1.16

Also --The winner of the tournament won both its matches in the finals --the total points earned by all the teams (Played in the second round) after second round are 100. Q.1 Which 2 teams do not play against each other in the finals? a. A1,B2 b. A1,B6 c. A5,B2 d. B2,B6 e. none of these Q.2 Find the number of matches won by A2 and A4 a. 0 b. 1 c. 2 d. 3 e. cannot be determined Q.3 How many points did the second runner up earn in the finals? a. -4 b. 2 c. 4 d. 0 e. cannot be determined Q.4 After round 2, the highest average of any team can be a. 2 b. 2.4 c. 2.6 d. 2.8 e. cannot be determined Q.5 The first runner up of the tournament was a. A1 b. B1 c. B6 d. B4 e. None of these

4

Answer: For Solid DI Set 4

The teams playing in second round are A1, A3 A5,B2,B4 and B6. Final is played between B2, B6 and A1. Total points earned by the teams which dropped out in second round are 10 + 16 +12 =38. So points earned by B2, B6 and A1 after round 2 is 100-38 = 62. Total points earned by these teams after final round = 28 +26+14=68, ie. They together earned 6 points in the 3 matches happened in the final round. A1 won both its matches in final ie. It got 8 points. So the points earned in these 2 matches =4+4-2-2 =4 points. So the match between B2 and B6 resulted in 2 points. Hence it cannot be a draw.

Suppose, B2 had lost that match , then it must’ve lost 4 points in the final round , while B6 must’ve gained 2 points which means it’s points after second round must’ve been 12, equal to that of B4, which contradicts the fact that top 3 with highest average made it to the finals. Hence B2 must’ve won the B2 v/s B6 encounter. That means B2’s points after second round must’ve been 24. while B6’s must’ve been 18.

Hence 1-c, 2-c, 3-a, 4-b, 5-e

Solid DI Set - 5 Question For Questions 1 to 5 read the following instructions: Friday morning, local pediatrician Dr. Johnson N. Johnson had appointments with five infants scheduled at 9:00, 9:30, 10:00, 10:30, and 11:00. Each of the five, including the Ortiz baby, is a different number--1, 2, 3, 4, or 5--of months old. The following notes are available. 1. Immediately after seeing infant Beth, Dr. Johnson examined the Majors infant, who is 2 months younger than Beth. 2. Erica isn't the one of the five who is 1 month old. 3. The doctor saw David later in the morning than the 1-month-old. 4. The 9:30 appointment was with the 3-month-old baby. 5. The Luce infant isn't the one who is 5 months of age. 6. Dr. Johnson saw the Nash infant, then examined Alice, who is 2 months older than the Nash baby. 7. The pediatrician's 10:00 appointment was with Chad, who isn't the Majors or the Nash baby. 8. The Prior baby isn't the 1-month-old and wasn't the doctor's 9:00 examinee. Q.1. How old(in months) is infant Beth? a. 1 b. 2 c. 3 d. 4 e. 5 Q.2 At what time did infant Erica meet the doctor? a. 9 b. 9:30 c.10 d. 10:30 e.11 Q.3 Whose baby is infant Chad? a. Ortiz b. Majors c. Luce d. Nash e. Prior Q.4 Which of the following is not correct w.r.t infant David a. He is Nash’s baby b. He is 2 months old c. His appointment was at 11.00 d. none of these e. His appointment was at 10:30 Q.5 Who was the last infant to meet the doctor? a. Alice b. David c. Chad d. Erica e. Beth

5

Answer: For Solid DI SET 5

By clue 7, Dr. Johnson saw infant Chad at 10:00, the middle appointment of the five. By clue 1, Dr. Johnson saw Beth and then the Majors baby, while by clue 6, he saw the Nash baby and then Alice. Since Beth is 2 months older than the Majors infant (1) and Alice is 2 months older than the Nash infant (6), Beth can't be the Nash baby and Alice be the Majors infant (the only way possible to combine the two clues), so four different babies are named between the two clues. Since Chad is neither the Majors nor the Nash baby (7), either Dr. Johnson saw Beth at 9:00 and the Nash child at 10:30, or he saw the Nash child at 9:00 and Beth at 10:30. Trying the latter case, he would have examined Alice at 10:00 (6) and the Majors baby at 11:00 (1). By clue 4, Alice would be 3 months old, with the Nash baby then 1 month old. However, neither Erica (2) nor David (3) could be the Nash infant, so this arrangement cannot work. Dr. Johnson's 9:00 patient was Beth, with the Majors baby his 9:30 (1); and he saw the Nash infant at 10:30 and Alice at 11:00 (6). The Majors baby is 3 months (4) and Beth 5 months (1) old. By clue 3, David is the Nash child and Chad the 1-month-old. Erica is the Majors baby. By clue 6, David Nash is 2 and Alice 4 months old. Beth is neither the Luce (5) nor Prior (8) infant and is the Ortiz baby. Chad's surname is Luce and Alice's Prior (8). In sum, Dr. Johnson saw the five babies as follows:

• 9:00 - Beth Ortiz, 5 months • 9:30 - Erica Majors, 3 months • 10:00 - Chad Luce, 1 month • 10:30 - David Nash, 2 months • 11:00 - Alice Prior, 4 months

Hence 1-e, 2-b, 3-c, 4-c, 5-a

Solid DI Set - 6 Question

Directions for Q.1 to Q.5: Read the information given below and answer the questions that follow.

Five friends (Avinash, Vijay, Alok, Vivek and Rajiv) went to a hotel and ordered five different soups (Tomato, Chicken, Vegetable, Corn and Mutton), followed by lunch. After lunch, they ordered five different desserts. (Mango, Pista, Vanilla, Tutti-Fruti and Casatta). (i) Avinash ordered for vegetable soup and Mango ice-cream (ii) Vivek didn't order mutton soup but ordered Vanilla ice-cream (iii) Vijay is a vegetarian who ordered Tutti-Fruti ice-cream (iv) The person who ordered corn-soup also ordered Pista ice-cream while Rajiv ordered Casatta ice-cream

1. Who among the following ordered Tomato soup? (1) Avinash (2) Vijay (3) Alok (4) Vivek

2. Which among the following soups was ordered by Vivek? (1) Vegetable (2) Corn (3) Chicken (4) Mutton

3. Which of the following combinations is FALSE? (1) Rajiv - Chicken soup (2) Tomato soup - Tutti Fruti ice-cream (3) Chicken soup - Vivek (4) Alok - Corn soup

4. Which of the following ice-creams was ordered by Alok? (1) Vanilla (2) Tutti-Fruti (3) Mango (4) Pista

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5. Which of the following combinations is TRUE? (1) Avinash - Tomato soup - Tutti-Fruti ice-cream (2) Vijay - Corn soup - Mango ice-cream (3) Alok - Mutton soup - Pista ice-cream (4) Vivek - Chicken soup - Vanilla ice-cream

Answer: For Solid DI SET 6 Make a table as below

Avinash Vijay Alok Vivek Rajiv Tomato X X X X Chicken X X X X

Veg X X X X Corn X X X X Mut X X X X

Mango X X X X Pista X X X X Vani X X X X T.F X X X X Cass X X X X

1. Ans.(2) 2. Ans.(3) 3. Ans.(1) 4. Ans.(4) 5. Ans.(4)


1. If (a) '1 2 3' stands for These are boys', (b) '1 3 4' stands for 'boys are naughty' and (c) '1 4 5' stands for 'Naughty boys sing', which numeral stands for 'naughty'? (1) 1 (2) 2 (3) 3 (4) 4

2. In a certain code 'BROAD' is written as 'ASNBC'. How is 'PLUGH' written in that code? (1) OMTHG (2) QMTHG (3) QMTFG (4) OMTGH

Answer: For Solid DI SET 7 A1) Correct answer is (4) 1 = boys, 2 = these, 3 = are, 4 = naughty, 5 = sing

A2) Correct answer is (1)

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p stands for Preceding letter and s for Succeeding letter. Coding is done by taking the preceding and succeeding letters alternately

Solid DI Set - 8 Question An Inspector has discovered that 5 people were involved in the murder of Miss Batliwala. Nine suspects are short listed by him. Maina, Naina and Raina are women. Ooman, sangha, Topaz, Unni Vasu and Wagle are men. Through intelligent deliberation and analysis, Ghote has also made a checklist of points. I) There were at least two women involved in the crime. II) Raina will never collude with Ooman. III) Sangha and Topaz will always commit crimes together. IV) Unni and Vasu never work together. A). If Maina was involved in the crime and Naina is not, which statements given below are true necessarily. I) Either Unni or Vassu but not both are involved. II) Sangha and Topaz will be involved 1. I only 2. II only 3. Both I and II 4. Either I or II B) Greatest number of combinations are possible if which of the following are definitely involved in the crime. 1. Sangha and Topaz 2. Vasu 3. Raina 4. Wagle C) Which of the following statements is definitely true ? I) If only two women are involved in the crime Sangha and Topaz must be involved. II) If Raina is not involved in the crime, Ooman must be involved. III) If either Maina or Naina is not involved in the crime Sangha and Topaz must be involved. 1. I only 2. I and III only 3. II only 4. III only

Answer: For Solid DI SET 8 A) Correct answer is 2. Women : M, N and R Men ; O, S, T, U , V & W If M is involved and N is not means that R must be involved so 3 men, of which O is not a part, of must be involved so analysing given statements : either U or V but both not involved This means that U or V can pair up only with S & T But S & T have the option of choosing W. So U or V must not necessarily be involved so statement I is not necessarily true

B) Correct answer is 1. If V is involved U cannot be involved If R involved O cannot be involved since We require 2 more men of which U and O are not available so the option is S & T.

C) Correct answer is 4. M and N can pair with U +W + O or V + W + O. If R is not involved, it can give options like M and N with S + T +U or S + T + V or S + T + W so is definitely not true.

Solid DI Set - 9 Question 1) Find the word which does not fit in the group. (1) D A B (2) H E F (3) T S R (4) P 0 N

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2) Insert the missing word from the brackets. 54 (HIDE) 98 53 (....) 16 (1) FACE (2) 6135 (3) HIDE (4) ECAF

3) Which will come next in the series? N Q L S J U – (1) W (2) T (3) I (4) H

Answer: For Solid DI SET 9 A1) Correct answer is (3) All other options contain a vowel (A, E, I, 0, U) as the middle term.

A2) Correct answer is (1) Numbers outside the brackets denote the alphabet, a = 1, b = 2, c = 3. HIDE has numbers 4,5,8 and 9. For second series, we get EC and AF which are then reversed t A3) Correct answer is (4) Alternate letters are one letter away in the alphabetical order. There are two sets one beginning with N-L-J and hence H, the other beginning with Q-S-U. The former is descending, while the latter is ascending. Solid DI Set - 10 Question At the IIM 5 areas of specilisation are available. They are Marketing, finance, production, personnel and systems. However it is necessary for any student to take up a combnination of two of the above. Based on common preference, preset combinations called moducles are offered, coded M001, M002, M003, M004 and M005. Each allows two specialisations such that every specilisation is assigend to two modules. Further to allow for uncommon prefercences a student is allowed to take up more than one commbination in such a manner that the specialisation common to the two modules is necessarily dropped. However, a smart student, by manipulating combinations, may be able to specialise in more than two subjects. Additional information is as follows : M001 has not been assigned production. M003 has not been assigned marketing. M004 has not been assigend finance. By choosing M001 and M003 one may specialise in marketing and systems. By choosing M001 and M002 one may specialise in Marketing, production finance and personnel. By choosing M001 and M004 one may specialise in finance and personeel . 1. What is the maximum number of modules any person may take to specialise in at least two areas ? 1. 2 2. 4 3. 5 4. 3 2. Which of the following number of specialisations is impossible ? 1. 2 2. 3 3. 4 4. None of these 3. Personnel is available in modules 1. M002 and M003 2. M001 and M003 3. M002 and M004 4. M003 and M005 4. Finance is available in modules 1. M001 and M003 2. M003 and M004 3. M002 and M003 4. M001 and M004

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Answer: For Solid DI Set 10 1) 2 2) 2 3) 3 4) 1

The main thing is that if any specialisation is common to the 2 modules selected it gets dropped and is not a specialisation. M001 does not have production and M003 does not have marketing. But their combination gives us marketing and systems so M001 must have marketing since Moo1 and M002 have 4 different subjects three must be no common specialisation and M002 will not have marketing but will have production M003 will have systems included because it is not a part of M001 so M001 will have finance or personnel and it will be common to M003. Since the M001 and M004 combination does not have marketing as a specialisation it means that they have marketing in common. Since they have finance and personnel in common M001 has finance and M004 has personnel. So M002 also has personnel. So M003 must also have finance. This leaves M005 with production and systems.

Solid DI Set - 11 Question There are two ethnic groups, the Dravids and the Aryans. No marriage is permitted within a group. After marriage, men become a part of their wives’ group; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at a time and marriage to a direct descendant is forbidden.

1. A Dravid male could have a. an uncle in either group b. a Dravid daughter c. a Dravid son d. an Aryan son-in-law

2. Which of the following is not permitted under the rules stated? a. a Dravid man marrying his father’s sister. b. an Aryan woman marrying her mother’s brother. c. a widower born Aryan, marrying his brother’s widow. d. a widower marrying his wife’s sister.

3. If widowers and divorced males had retained the group they had upon marrying, which of the following would be permissible, assuming that no previous marriage had occurred? a. a woman marrying her dead sister’s husband. b. a woman marrying her divorced daughter’s ex-husband. c. a widower marrying his brother’s daughter d. a divorced male his ex-wife’s divorced sister in law.

Answer: For Solid DI SET 11 1) The key to remember in this question is that when it says “Dravid male” they refer to his group when he was born, and not after he gets married. I will shorten Dravid to D and Aryan to A. Given that, the answer is trivial. You can eliminate b and c immediately, since a D must be married to an A, becomes an A, his children (sons and daughters) are A’s. Option d is similarly eliminated since his daughter A, must marry a D. That leaves option a, which can be quickly verified. An uncle could be maternal or paternal. His paternal uncle could be a D (if unmarried), or an A (if married). His maternal uncle could be an A (if unmarried), or a D (if married). Hence option a) is correct.

2) Try and eliminate each option. Option a) D marrying his father’s sister(A).Possible. Option b) A marrying her mother’s (A) brother (A). Not possible. Option c) A widower born A, therefore now A, marrying his brother (A)’s widow (D). Possible.

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Option d) A widower X, marrying his wife’s (X’) sister (X’). Possible. Hence answer is b)

3)Once again eliminate each option: Option a) A woman X marrying her dead sister X’s husband (X (because he retains X after his wife died). X-> X not possible. Option b) A woman X marrying her divorced daughter X’s ex-husband (X). Not possible. Option c) A widower X (born X’, but X after marriage, retained after his wife’s death), marrying his brother (X’)’s daughter (X) (since daughter will get her mother’s group which must be X). Not possible. Option d) A divorced male X (born X’) marrying his ex-wife’s (X)’s divorced sister-in-law (X’ or X). Sister-in-law can be the wife’s husband’s sister -> (potentially her husband’s sister (heaven forbid!), who would be an X’) or her brother’s wife (also an X’). Either way X, marrying an X’ makes it permissible.


In 2001 census, the following data regarding two village ‘Rajgarh’ and ‘Sukhgarh’ was found I. Rajgarh has 2104 more males the Sukhgarh II. Sukhgarh has 2041 fewer females than Rajgarh III. Sukhgarh has 687 more males than females IV. Rajgarh has 750 fewer females than males

1. What is the total number of males in Rajgarh and Sukhgarh? 1. 11,924 2. 10,510 3. 12,510 4. Cannot be determined

2. What is the difference between the number of males in Sukhgarh and the number of females in Rajgarh? 1. 27,961 2. 1,354 3. 2,747 4. Cannot be determined.


1.1 Let x be number of males in Rajgarh, z the number of males in Sukhgarh, y the number of females in Rajgarh, and t the number of females in Sukhgarh. Check the options if x + z = 11924. Then x = 7014, z = 4910, y = 6264 and t = 4223 So, all other equations (ii) , (iii) and (iv) are satisfied. 2. 2 Here y – t = 2041 and z – t = 687 So, y – z = 1354


A hedge fund has recently acquired four companies - BOB, MOB, ZOB and DOB. The sales of DOB are half that of BOB whereas the profits of DOB are double that of BOB. The expenses of ZOB are Rs 3 crores less than that of DOB whereas the profit of MOB is Rs 1 Crore less than that of ZOB. The expenses of BOB are three times that of DOB. It is also known that the sales of ZOB are Rs 15 crores or one-fourth that of MOB. The auditing firm has also reported that sales of DOB are Rs 10 crores more than that of ZOB and the expenses of BOB are 90% of its own sales.

Q1) The total sales of all the four companies is (Rs crores): a) 200 b) 150 c) 125 d) 160

Q2) The expenses of BOB exceed that of ZOB by (Rs crores): a) 34 b) 43 c) 33 d) 62

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Q3) Which company had the maximum profits? a) BOB b) MOB c) ZOB d) DOB

Q4) The expenses of MOB exceed the profits of BOB by (Rs crores): a) 51 b) 52 c) 53 d) 54

Q5) Total profits of the four companies are (Rs. Crores): a) 15 b) 20 c) 25 d) 40

Q6) The profits of MOB form what percentage of the expenses of ZOB? a) 16% b) 20% c) 15% d) 23%


Based on the information given, best way to solve this is to make a table. May seem tedious initially but would save you time for answering other questions

Sales Expenses ProfitsBOB 2 X = 5 0.9 x 50 = 45 50 – 45 = 5MOB 60 60 – 2 = 58 B – 1 = 3 – 1 = 2ZOB 15 A – 3 = 12 B = 15 – 12 = 3DOB X = 25 A = 45/3 = 15 2 x 5 = 10Total 150 130 20 A1) Correct answer is (b) A2) Correct answer is (c) A3) Correct answer is (d) A4) Correct answer is (c) A5) Correct answer is (b) A6) Correct answer is (a)


For questions in this test, use the following answer choices

a) If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone. b) If the question can be answered by using either statement alone. c) If the question can be answered by using both statements together, but cannot be answered by using either statement alone. d) If the question cannot be answered based on the information provided

1) Average of ten numbers s 15.34. If the fifth number is incorrect then what would be the average of the remaining nine numbers?

I. In the given ten numbers the average of the first five numbers is 14.35 and the average of the last six numbers is 15.43.

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II. In the given ten numbers, the average of the first six numbers is 14.38 and the average of the last six numbers is 15.40.

2) Is the prime number p equal to 37? I. p = n2 + 1, where n is an integer II. p2 is greater than 200

Answer: For Solid DI SET 14 A1) Correct answer is (a) Only A alone is sufficient. From B, we can get only the sum of the fifth and the sixth numbers.

A2) Correct answer is (d) Since 142 = 196 and 152 = 225, if follows from (B) that p > 14

In (A) the expression n2 + 1 can represent a prime number less than 37, equal to 37, or greater than 37, depending on the value of n. For example, if n = 4, the 42 + 1 = 17; if n = 6, then 62 + 1 = 37; if n = 10, then 102 + 1 = 101; and 17, 37, and 101 are all prime numbers. Thus, (A) alone is not sufficient Both the statements together are not sufficient

Solid DI Set - 15 Question For questions in this test, use the following answer choices

a) If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone. b) If the question can be answered by using either statement alone. c) If the question can be answered by using both statements together, but cannot be answered by using either statement alone. d) If the question cannot be answered based on the information provided

1) Two schools decide to send their students to a picnic on the same day. How many students attend the picnic from the first school?

I. 40 students in all attend the picnic II. If you multiply the number of students from first school with the number of students from the second school, the answer is 300

2) Radhesh is a class X student and is practicing for his board exam. He draws a circle of radius 9.6 cm. He also draws a chord, whose length is I. If you measure the perpendicular distance from the centre of the centre of the circle to the chord, you get 6 cm II. If you draw a triangle with two end points being the end points of the chord and the third point touching the circle, the 3rd angle is 80 degrees

Answer: For Solid DI SET 15 A1) Correct answer is (d)

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While at first glance, you may be tempted to answer ©, since there are two linear equations and two variables, as you try to solve the question you will get two answers 30 and 10. So you can’t say which one of those applies to the first school

A2) Correct answer is (a). Statement I allows you get the answer since the perpendicular from the centre of the circle to the chord is going to bisect the chord. Then using Pythagoras theorem, you can calculate the length of the ½ chord Statement II doesn’t provide you any concrete information to be useful


Mr. Malik went to US on a business trip and rented a car to drive from his hotel to the plant that he was visiting. Being new to driving in US, he was very cautious and wanted to ensure he drove within the speed limits. The graph below shows the speed he was driving at different times of the day

1) For what percent of the time was he driving at 40 miles per hour or faster? a) 20 b) 45 c) 40 d) 50 Q2) How far, in miles, did Mr. Malik drive between 8:30 and 9:00? a) 0 b) 20 c) 30 d) 40

Q3) The total distance traveled by Mr. Malik is a) less than 50 miles b) between 50 and 100 miles c) greater than 100 miles d) Can’t be calculated

Q4) How much time Mr. Malik would have taken if he had traveled the whole distance at the average speed of 40 miles per hr? a) 2 hrs b) 2.8 hrs c) 2.4 hrs d) 3 hrs

Answer: For Solid DI SET 16 A1) Correct answer is (d) A quick glance at the graph will show you that x axis has equally spaced intervals. Out of the 5 intervals that he drove, for 2.5 of those the graph on y axis is above 40, so 50%

A2) Correct answer is (d) Since his speed was 40 miles per hr, he would have driven 40 miles

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A3) Correct answer is (b) Take the average speed for 30min. intervals and divided by 2 (since each interval is ½ hr) ( 37.5 + 40 + 45 + 40 + 30 )/2 = 192.5 / 2 = 96.125

A4) Correct answer is (c) Use data from previous question re distance traveled 96.125 / 40 = 2.4 hrs approx.


Two shopkeepers go to buy newly designed weights from the trade fair. In a particular shop the salesman asks their limits of weighing at a time. Both of them tell their limit as 120 kg at a time. The salesman shows them the price list as: Any weight less than 10 kg ? Rs. 10 per piece More than 11 kg but less than 50 kg ? Rs. 20 per piece More than 51 kg but less than 100 kg ? Rs. 30 per piece. More than 100 kg ? Rs. 50 per piece. The salesman gave them two options:

In the 1st option, the shopkeepers might have to put the weights on both sides. He gave them an example: Suppose you want to weigh 7 kg, so put 10 kg on weight side and put 3 kg on the goods side. In the second option, the shopkeeper did not need to put the weights on goods side. 1. If the 1st shopkeeper opts for the 1st option, what is the minimum number of weights he would need to buy at the lowest cost? 1. 8 2. 10 3. 5 4. None of these 2. The 2nd shopkeeper opts for the 2nd option. What is the min. no. of weights he would need to buy at the lowest cost? 1. 5 2. 7 3. 10 4. None of these 3. One of them needed as much more amount as the other has left after purchase. Suppose both of them left their home with the same amount. Who borrowed and what amount was borrowed? 1. First shopkeeper borrowed Rs. 30 2. Second shopkeeper borrowed Rs. 30 3. Second shopkeeper borrowed Rs. 15 4. First shopkeeper borrowed Rs. 15

Answer: For Solid DI SET 17 A1) Correct answer is (3) In the first option, the minimum no. of weights needed is 5. The weights are 1 kg, 3 kg, 9 kg, 27 kg, 81 kg.

A2) Correct answer is (2) In the second option , the minimum no. of weights needed is 7. The weights are 1 kg, 2 kg, 4 kg, 8 kg,16 kg, 32 kg, 64 kg.

A3) Correct answer is (3) First shopkeeper needs 3 x 10 + 1 x 20 + 1 x 30 = Rs. 80 Second shopkeeper needs 4 x 10 + 2 x 20 + 1 x 30 = Rs. 110 Therefore Second shopkeeper needed to borrow Rs. 110-80/2 = Rs. 15

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The following is the list of instructions to be followed Step1: x=0 A=2 B=3 Step2: If X<5 then do Steps3-6 otherwise Step7 Step3: Y=A+B replace A by B, replace B by Y Step4: Type Y Step5: Increase X by 2 Step6: Goto Step2 Step7: Exit 1.When X=4 what value of Y is typed? 1] 12 2] 8 3] 13 4] 5 5] 8 2.Suppose Step5 is replace by 'Increase X by 5' then what would be the last value of Y typed? 1] 5 2] 4 3] 6 4] 9 5] 8 3. After the set of instructions is over at Step 7 what is the value of X 1] 5 2] 4 3] 3 4] 7 5] 8

Answer: For Solid DI SET 18 1. While X=0, Y=5, A=3, B=5 While X=2, Y=8, A=5, B=8 While X=4, Y=13, A=8, B=13 Hence [3] 2. While X=0, Y=5, A=3, B=5 If X is increased by 5 further values of Y will not be calculated. Hence [1] 3. The last value of X is 4 Hence [2] Solid DI Set – 19 Question Five brothers have among them a pair of twins who are neither the oldest nor the youngest. E is older than C but younger than B. D is younger than 3 brothers 1) The youngest is 1] A 2] B 3] C 4] D 2). One of the twin pair is 1] B 2] C 3] D 4] E 3). The eldest is 1] A 2] B 3] C 4] E 4) The one who has as many elder brothers as younger brothers is 1] A 2] B 3] E 4] none of these 5) Who is the fourth brother 1] A 2] B 3] D 4] E

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Answer: For Solid DI SET 19 The following table explains the answers

1 2 3 4 5 B E A D C

1) [3] 2) [4] 3) [2] 4) [1] 5) [3] Solid DI Set - 20 Question Each item has a question followed by two statements each giving some data.

• Mark 1 if the question can be answered by using one of the statements alone; but cannot be answered by using other statement alone.

• Mark 2 if the question can be answered by using either statement alone. • Mark 3 if the question can be answered by using both statements together, but cannot be answered by

using either statement alone. • Mark 4 if the question cannot be answered even by using both the statement together.

1) a and b are two positive numbers. How many of them are old? I. Multiplication of b with an odd number gives an even number II. a2 – b is even. 1] 1 2] 2 3] 3 4] 4 2)A, B, C, D have to stand in a queue in descending order of their heights. Who stands first? I. D was not the last, A was not the first. II. The first is not C and B was not the tallest. 1] 1 2] 2 3] 3 4] 4 3) Of two boxes of sweets A and B, which costs more? I. The box A has 32 sweets of one kind and box B has 24 sweets of another kind. II. 6 sweets of box B cost more than 8 sweets of box A. 1] 1 2] 2 3] 3 4] 4

Answer: For Solid DI SET 20 1) From statement I - b is even but nothing can be said about a From statement II, a2 - b is even only if both are of the same parity (odd or even),which means a is also even. Therefore none of a and b are odd. Using both statements we can answer the question. Choice (3) 2) Taking II and I we get A, B, C are not the tallest, hence D has to be the tallest. Thus D stands first. Choice (3) 3) From statement I, the price cannot be calculated.

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From statement II, 6 sweets of B>8 sweets of A or 24 sweets of B > 32 sweets of A Hence, we can say box B is more expensive than box A. Choice (3) Solid DI Set - 21 Question Each item has a question followed by two statements each giving some data.

• Mark 1 if the question can be answered by using one of the statements alone; but cannot be answered by using other statement alone.

• Mark 2 if the question can be answered by using either statement alone. • Mark 3 if the question can be answered by using both statements together, but cannot be answered by

using either statement alone. • Mark 4 if the question cannot be answered even by using both the statement together.

1) How many boys are there in the class? I. The number of boys in the class is 8 more than the number of girls in the class, which is five times the difference between the number of girls and boys in the class. II . The number of girls in the class is four less than half the total number of students in the class. 1] 1 2] 2 3] 3 4] 4 2) How many guests attended the party hosted by Rajesh? He invited 60 people for the party. I. 12 of the invitees expressed their inability to attend the party where as another 12 did not get back to Rajesh nor did they attend the party later on. II. 50% of the invitiees confirmed that they would attend the party, but only 80% of them actually attended the party. 1] 1 2] 2 3] 3 4] 4 Answer: For Solid DI SET 21 1) From statement I B = G + 8 G = 5 x (B – G) = 5 x 8 = 40 B = 48 From statement II G + 4 N/2 Choice (1) 2) From statement I only 60 people, 12 have expressed inability and 12 have not come. Still nothing can be said about the other 24. From statement II though 80% of 50% did come. No information on the other 50% is given. Choice (4) Solid DI Set - 22 Question Priya has agreed to feed a friend’s dog for a full week, running from Monday to Sunday. A total of seven brands of dog food are available, of which exactly five, M, N, O, P and Q are protein-enriched, and exactly two, R and S, are vitamin-enriched. Priya must adhere to the following feeding instructions. On each of the seven days, a different brand of dog food must be fed. Protein-enriched dog food cannot be fed for more than two consecutive days. R must be fed earlier in the week than S. M must be fed earlier in the week than R. M must be fed earlier in the week than Q and exactly four of the other brands must be fed between N and Q.

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1) Which of the following brands must be scheduled to be fed on Wednesday? [1] M [2] O [3] P [4] R 2). If Q is scheduled to be fed on Sunday, which of the following could also be true? [1] R and O are scheduled to be fed on consecutive days. [2] N is scheduled to be fed earlier than M. [3] Two days intervene between the day O is fed and the day P is fed. [4] P is scheduled to be fed on Tuesday. 3) Which of the following pair of brands could be scheduled to be fed on consecutive days? [1] M and O [2] N and P [3] O and S [4] Q and R Answer: For Solid DI SET 22 The possible combinations that meet all the conditions Mon Tue Wed Thurs Fri Sat Sun a) N M R O/P S Q P/Q b) M N R O/P S P/O Q 1. [3] 2. [1] 3. [3] Solid DI Set - 23 Question DIRECTIONS for the questions 1 to 3 A quack- Dr. Fool’s Paradise- fools his customers by claiming to predict future using a unique method. He has three parrots kept in three different cages. Each cage has three cards with a single non-zero digit inscribed on every card. No two cards have the same number & no cage contains two cards with digits totalling ten. Further, the total of three cards in the first cage is greater by two than the total in the second cage & by four than that of third cage. When a customer asks for his prediction, the quack lets out three parrots which randomly picks one card out of their respective cages. Before the prediction is made, the quack totals the digits on the three picked cards & charges the customer the same number of rupees as the total of the cards. One day a customer paid seven rupees for his prediction. 1. What is the lowest payment possible? (1) Rs. 5 (2) Rs. 7 (3) Rs. 6 (4) Rs. 8 2. What is the maximum possible amount that anyone can pay? (1) Rs. 22 (2) Rs. 23 (3) Rs. 24 (4) Rs. 25 3. Which of the following payments can never be made by any customer? (1) Rs. 19 (2) Rs. 16 (3) Rs17 (4) Rs. 23 Answer: For Solid DI SET 23 The cards are numbered 1,2,3…..9 There fore, the sum of numbers on all cards = 9 * 10 /2 = 45 If sum of numbers of cards in the 1st cage = X , then Sum of numbers of cards in the 2nd cage = X-2 Then , sum numbers of cards in the 3rd cage = X-4 X + X-2 + X-4 =45 or X =17 There fore the three cages would have cards totaling 17 , 15 and 13 respectively.So, each cage should have one card from each of the following three sets of cards . 1,2,3 4,5,6 7,8,9 The following combinations are possible if one has to satisfy the requirements.

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Case 1 : 17 = 9 + 6 +2 9 + 5 + 3 9 + 5 + 3 Case 2 : 15 = 8 + 4 +2 8 + 6 + 1 6 + 7 + 2 Case 3 : 13 = 7 + 5 + 1 7 + 4 + 2 8 + 4 +1 But combinations 2 and 3 are not possible because the only way a person can pay Rs 7 is if three cards are 4 , 2, 1 = 7 But in combination 2 and 3 , this is not possible. Therefore the only combination possible is 1. The lowest possible payment is 3 + 2 + 1 = 6 Ans 1 (3) Ans2 (3) The maximum possible payment is 9 + 8 + 7 = Rs 24. Ans3 (4) A customer cannot pay Rs 23 as 23 = 9 + 8 + 6 as 9 and 6 are in the same cage. Option (2) is possible as all three cards mentioned are in different cages. A customer can pay Rs 19 i.e 19 = 9 + 3 + 7. as all three cards are in different cages. Solid DI Set - 24 Question DIRECTIONS for the questions 1 to 5 Robert received a large order for stitching school uniforms for Pink Flower school.He has two cutters who will cut the fabric , five tailors who will do the stitching , and two assistants to stitch the buttons and button holes. Each of these 9 persons will work for exactly 10 hours a day.Each Pink Flower uniform requires 20 utes for cutting,1hour for stitching and 15 minutes for buttons and button holes. The Little Flower uniform requires 30 minutes , 1 hour and 30 minutes respectively. 1) Find the maximum number of Little Flower uniforms that Robert can complete in a day. (1)30 (2) 35 (3) 40 (4) 36 2) If on a day ,Robert decides to complete 20 Little Flower uniforms , then how many Pink Flower uniforms can he complete that day? (1) 30 (2) 35 (3) 40 (4) 36 3) If Robert decided to complete 30 Little Flower uniforms only and no other uniform on a particular day, then how many total man hours will go idle? (1) 30 (2) 60 (3) 45 (4) 36 4) If Robert hires one more assistant , then what is the maximum number of Pink Flower uniforms that he can complete in a day ? (1) 60 (2) 48 (3) 120 (4) 50 5) Robert has the option to hire one more employee of any category.Whom should he hire to get maximum increase in production capacity , assuming that he needs to stitch only Pink Flower uniforms on that day? (1) One cutter (2) One tailor (3) One assistant (4) Either a tailor or a cutter. Answer: For Solid DI SET 24 When he has to complete maximum number of Pink Flower uniforms in a day, he will not at al devote to the Little Flower uniforms .Now , to find the maximum number of Little Flower uniforms , we have to concentrate on the time resource .It will be the category with the least available time which will then decide the maximum no. of uniforms which can be prepared. Cutting :20hours available and30minutes required per uniform. Thus 20*60/30 = 40 uniforms can be cut. Stitching 50 hours available and 60 minutes required per uniform .Thus 50*60/60 = 50 uniforms can be stitched.

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Buttoning : 20 hours available and 30 minutes required per uniform. Thus ( 20 * 60)/30 = 40 uniforms can be buttoned .Obviously , the least number of the above three will determine the maximum number of uniforms that can be completed. Ans1 (3 ) 40 uniforms of Little Flower can be completed. Total uniforms of Little Flower to be completed = 20 Cutting time required = 20 * 30 = 600 minutes = 10 hours Stitching Time required = 20 * 60 = 1200 minutes = 20 hours Buttoning time required = 20 * 30 = 600 minutes = 10 hours Cutting time remaining = 20 –10 = 10 hours: Stitching time remaining = 50 –20 = 30 hours; Buttoning time remaining = 20 – 10 = 10 hours. Since the times for cutting , stitching and buttoning each Pink Flower uniform are 20 minutes , 60 minutes and 15 minutes respectively. We can cut ( 10 * 60) /20 = 30 Pink Flower uniforms , we can stitch ( 30 * 60)/ 60 = 30 Pink Flower uniforms and we can stitch ( 30 * 60 )/60 = 30 Pink flower uniforms , and we can button ( 10 * 60 )/60 = 30 Pink Flower uniforms, and we can button ( 10 * 60 )/ 15 = 40 Pink Flower uniforms 30 is the maximum number possible ( the bottleneck resource ) Ans2(1) Ans3(1) Total man- hours available = 20 + 50 + 20 = 90 per day. If Robert makes 30 Little Flower uniforms in a day , time utlised = (30 * 30) minutes + ( 30 * 1) hours + (30 * 30 ) minutes Total time utilized = 15 + 30 + 15 = 60 hours Man hours remaining = 90- 60 = 30 hours Again we have to basically find out the bottleneck resource Total cutting time available = 20 hours Number of uniforms that can be stitched = ( 50 * 60) / 60 = 50 Total stitching time available = 50 hours Number of uniforms that can be stitched = ( 50 * 60)/60 = 50 Total buttoning time available = 30 hours Number of uniforms that can be buttoned = 30 * 60 /15 = 120 The minimum hour = 50 = The maximum uniforms that can be completed Ans 4(4) When he makes only Pink Flower uniforms on a day , as per the current availability No. of uniforms that can be cut = 20 * 60 /20 Number of uniforms stitched = 50 * 60 / 60 = 50 , and the number of uniforms buttoned = ( 20 * 60 )/15=80. Thus maximum no. of uniforms completed = 50 and the bottle neck was time for tailoring ( stitching). Hence to get the maximum increase in the production capacity , he should employ one more tailor. Ans5 ( 2 ). Solid DI Set - 25 Question 1) A, B, C, D & E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 3. D is the greatest and A is the least. B is greater than E but less than C. The sum of the five integers is equal to E- 1. A + B is: A] 15 B] -8 C] -9 D] 16 2) Mark your answer as (1) If statement (A) alone is sufficient to solve the question but statement (B) alone is not; (2) If statement (B) alone is sufficient to solve the questions but statement (A) alone is not; (3) If neither (A) nor (B) is individually sufficient to solve the question but a combination of these is sufficient to solve the question; (4) If both the statements (A) & (B) are individually sufficient to solve the question and (5) If both the statements taken together are not sufficient and more information is required to solve the question Q. If the average height of three people if 68 inches, is the shortest person more than 60 inches tall ? (A) The height of the tallest person is 72 inches (B) One of the persons is 70 inches tall

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1] 1 2] 2 3] 3 4] 4 Answer: For Solid DI SET 25 1. Answer is B] We know that D>C>B>E>A and D+C+B+E+A=E-1. We also know that the numbers are E-3, E, E+3, E+6, E+9 or E = -4. B = -1, A = -7, A+B = -8 2. Answer is 1] Only the first statement is needed. If x, y and z are the heights, X + y + z = 68 x 3 = 204 If z = 72, x + y = 132 Since x and y are less than 72 (z is the tallest person), the shortest person has to be as tall as 132 – 72 = 60 inches. Solid DI Set - 26 Question In a one-day cricket international between India and Australia. Australia managed to score 329 runs in 50 overs. To win the match India was required to score 330 runs in 50 overs. Tendulkar and Seghwag opened the innings for India. The first wicket fell at the end of the 9th over when the score was 63. At the end of the 19th over the second wicket fell at 128. 3rd wicket fell at the score of 187 when Tendulkar was caught behind in the 32nd over. 4th & 5th wicket fell when score was 261 in 42nd over. Finally, India scored 333 with a four hit by Harbhajan of the first fall he faced in the 50th over. India won the match by 4 wickets with two balls to spare. Tendulkar scored approx 37% of the total runs scored by India, but man of the match was given to the player who scored curtail runs in the pressure situation at the end of the innings. Two more players scored more than 50 runs. Seghwag and Pathan scored in mid 20’s. Dhoni scored more than Pathan and Seghwag but still Seghwag was not the least scorer. Indian batting order – Tendulkar - Seghwag – Pathan – Dhoni – Yuvraj – Dravid – Kaif - Harbhajan – Zaheer – Balaji – kumble. Each team had 11 players 5 batsmen, 1 wicketkeeper and 5 bowlers, where only 10 wickets is to be taken of a team. The game was played in accordance with the rules laid down by the ICC. 1. What can be said about Sachin’s contribution in the three partnerships he was involved in assuming that there were no extras conceded by the Australian team? 1] 39, 40 & 44 2] 38, 39, 46 3] 40, 37 & 46 4] 41, 39, 44 2. What can be concluded from theanalysis of the paragraph given above inaccordance with the two statements give with this question: Statement 1: Dhoni scored second highest runs and was the 5th wicket to fall for India in the 42nd over. Statement 2: Dravid scored a duck in the match. 1] If statement 2 is true then statement 1 is necessarily false. 2] If statement 1 is false then statement 2 is necessarily true. 3] If statement 1 is true then statement 2 is necessarily true. 4] None of the above. 3. What can be said regarding the following two statements? Statement 1: Kaif was not out at the end of Indian innings with second highest score. Statement 2: Tendulkar was not involved in the highest partnership. 1] Both statements could be true. 2] At least one of the statements must be true. 3] At most one of the statement is true. 4] None of the above

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Answer: For Solid DI SET 26 1. 2 Sachin scored approximately 37% runs scored by India i.e. 333 *37% = 123 runs approx. He was involved in the partnerships of 63 (Seghwag), 65 (Pathan) and 59 (Dhoni). Seghwag and Pathan scored in mid 20’s (between 24 – 26) As Pathan scored more than Seghwag, so lets assume they score 25 and 24 respectively. In first partnership of 63 if Seghwag scored 24 so Sachin cannot score more than 39 runs. In second partnership of 65 if Pathan scored 26 so Sachin cannot score more than 39 runs. There in the first two partnerships Sachin cannot score more than 78 runs. So he must have score 45 runs in the third partnership with Dhoni to make 123 runs. So option 2. 2. 1 If statement 2 is true, than 1 cannot be true as if Dravid scored a duck than he must be the one to get out as the 5th wicket in the 42nd over for India. In such case either Dhoni or Yuvraj was the 4th wicket to fall for India as they were batting after the fall of 3rd wicket (Sachin). Dravid can only come to the crease after the fall of 4th wicket and he is the second batsman to get out in the 42nd over. So he can only be the 5th wicket to fall without scoring a run. See the batting order for India. So option 1. 3. 3 Statement 1: Kaif batted at no 7th, which means he came to crease after the fall of 5th wicket in 42nd over when score was 261. So Kaif was involved in a partnership of 72 runs for the 6th wicket, where as either or 5th or 6th (Rahul or Yuvraj) was involved in two partnerships of 74 and 72. So logically it could not be true. Statement 2: 1st wicket partnership was of 63, second wicket partnership was of 128 – 63 = 65, third wicket partnership was of 187- 128 = 61 when Tendulkar got out), 4th partnership was of 261- 187 = 74, 5th wicket fell at same over (given), 6th wicket partnership was of 333 – 261 = 72. So statement 2 is absolutely true. Solid DI Set - 27 Question A Quality Assurance inspector is planning to inspect certain vehicles on this Monday and Tuesday at Tata Motors. He has to inspect three vehicles on each of the two days. On these two days put together, he has to inspect at least three Indica’s, at least one Safari and at least one Ace. The registration numbers of a vehicle available for inspection are as follows: Indica : I 21, I 22, I 24, I 23 Safari : S 11, S 21, S 12, S 13 Ace : A 22 , A 11 , A 12 Each vehicle is given a registration number, which consists of a single – letter code (I, S or A) followed by a two – digit numerical code (21, 22, etc.) The following restrictions are placed in a selection of the vehicles to be inspected: (i) Not more than two vehicles of the same kind can be inspected on one day. (ii) Vehicles whose registration numbers have a numerical code of 21, 22 and 23 are available for inspection on Tuesday only. (iii) No vehicle inspected on Monday can be inspected on Tuesday. 1. Which of the following vehicles must be inspected by the vehicle inspector? 1] S 13 2] A 22 3] I 23 4] I 24 2. Which of the following is possible combination of vehicles that can be inspected on Tuesday? 1] I 21, S 21, I 14 2] S 11, A 12 , I 23 3] I 22, S 13, I 21 4] I 23, S 21, A 22 Answer: For Solid DI SET 27 1. 4 Among the Indica’s I 21, I 22 and I 23 can be inspected only on the second day. As three Indica’s have to be inspected in two days and at most two Indica’s can be inspected on Tuesday, I 24 must be inspected on Monday.

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2. 3 I 24 must be inspected on the first day. As only one Indica can be inspected on the first day, at least two Indica’s must be inspected on the second day. Hence option 2 and 4 are not possible combinations. Option 3 does not violate any condition. Solid DI Set - 28 Question There are six companies – Rediff, Bazee, Naukri, Contest 2 Win, Shaadi and MCX. In the dotcom companies market capitalization, four of these six companies have secured the first four positions. Three venture capitalists – Natwest, Chrysalis and General Atlantic – have invested in these companies their individual speculations regarding the companies that would top the market capitalization among the first four positions are given in the following tables. Venture Capitalists

Speculated Positions 1st 2nd 3rd 4th

Natwest Rediff Bazee Naukri MCX Chrysalis Bazee Shaadi Rediff Contest 2

Win General Atlantic MCX Naukri Bazee Contest 2

Win It is also known that, (i) No companies ranked in market capitalization in the same position as speculated by Natwest but exactly two of the four companies speculated by them finished the market capitalization within the first four positions. (ii) Exactly two companies ranked in market capitalization in the same positions as speculated by Chrysalis, while only one company speculated by them failed to finish the market capitalization within the first four positions. (iii) Exactly two companies speculated by General Atlantic ranked in the market capitalization within the first four positions while only one company ranked the market capitalization in the same position as they speculated. 1. Which company ranked third in market capitalization? 1] Naukri 2] Shaadi 3] Rediff 4] Contest 2 Win 2. Which of the following is the correct order of the companies, whichfinishedthemarket capitalization in the first four positions respectively? 1] Rediff, Bazee, Contest 2 Win, Shaadi. 2] Shaadi, MCX, Rediff, Contest 2 Win. 3] Shaadi, Naukri, Rediff, Contest 2 Win. 4] Cannot be determined. Answer: For Solid DI SET 28 1. 3 From (ii), three of the four companies speculated by Chrysalis finished in the first four positions. Hence, exactly one of the other two companies – Naukri and MCX – finished in the top four positions. From (i), Exactly one of Rediff and Bazee finished in first four positions. Hence, from (ii), Both Contest 2 Win and Shaadi must have finished in first four positions. From (iii), Bazee did not finish in the first four positions. Hence, Rediff finished in the first four positions. Now, the companies finished in the first four positions are Contest 2 Win, Rediff, Shaadi and MCX / Naukri. From (ii), Two of the companies as predicted by Chrysalis finished at the same positions. \ Rediff cannot finish at 2nd or 4th positions as in this case the above value for Chrysalis can be at most one. From (i), Rediff cannot finish at first position. \ It must have finished at third position.

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2. 2 If Contest 2 Win did not finish at the finish, then it should have finish at first position, in this case no company according to General Atlantic’s predictions could have finished at the correct position. Hence, Contest 2 Win finished at 4th position; Shaadi finished at first position and MCX finished at 2nd position. The correct order is Shaadi MCX Rediff Contest 2 Win Solid DI Set - 29 Question There are 11 players on each side in ODI cricket, and one team bats while the others bowl. Then the teams swap after 50 overs. Kraig Chapal, the coach of the Indian ODI cricket team is a master strategist when it comes to shuffling the batting order. In a match in which India scored 340 runs, 9 batsmen were out and the last unbeaten pair of batsmen together scored 40 runs before they ran out of overs. In the batting order the 4th and the 5th men each scored exactly a 100 runs, while the first two batsmen scored 50 between themselves. The ratio of the runs scored by the first three batsman, Ganguly, Sehwag and Pathan (though not necessarily) 1, 2 and 3 in the batting order) was 6 : 4 : 3. Two consecutive batsman scored 0, and the first 9 batsmen in the batting order scored either 0 or scores that were multiples of 5. Dhoni was the 8th batsmen in the batting order, and the next person after Dhoni scored a 5. The runs scored by Tendulkar if added to theextras (bonus runs not scored by any batsmen but given by the bowling team to the batting team) equaled Ganguly’s scores. Sehwag scored one-fifth of Yuvaraj and equal to Tendulkar. Srinath scored 5 times what Tendulkar scored. Munaf and Mohanty scored 18 and 22 respectively, while together they scored 25 more than Dhoni and Pathan together. Kumble was India’s most successful bowler of the match, and Harbhajan took 2 wickets less than Kumble. 1.What was the number of extras in the Indian score? (1) 0 (2) 10 (3) 20 (4) Indeterminate 2. Tendulkar’s number in the batting order was immediately after (1) Yuvaraj (2) Srinath (3) Yuvaraj or Srinath (4) Indeterminate 3. What is the total of the least 5 scores in the Indian Cricket team (excluding extras)? (1) 20 (2) 30 (3) 35 (4) 38 4. Who has scored 5 runs? (1) Kumble (2) Harbhajan (3) Tendulkar (4) Kumble or Harbhajan Answer: For Solid DI SET 29

• It is given that the first a batsmen scored multiples of 5.Also the first two scored a total of 50 and the ratio of scores of the first three batsmen Ganguly, Sehwag and Pathan was 6 : 4 : 3. i.e. either 6x + 4x = 50 or 6x + 3x = 50 or 4x + 3x = 50 As the only possibility is 6x + 4x = 50, Ganguly scored 30, Sehwag scored 20 and Pathan scored 15. Hence Pathan was 3rd in the batting order.

• Yuvraj scored 5 times that of sehwag, i.e. 100. • Tendulkar scored equal to sehwag, i.e. 20 • Srinath scored 5 times Tendulkar, i.e.100 • Hence Yuvaraj and Srinath occupy positives 4 and 5, not necessarily in that order • Ganguly = Tendulkar + Extras. \ Extras = 10 • Munaf and Mohanty are batsmen 10 and 11, though not necessarily in that order. • Together they score 40 which is equal to 25 + Dhoni + Pathan. Hence Dhoni = 0 • Batsmen 9 scored 5. As the two who score 0 are consecutive, batsmen 7 scores 0. Hence Tendulkar has

only one slot left, i.e. 6. Now all questions can be answered.

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Solid DI Set - 30 Question At 3:00 pm afternoon I’m 11th in a college fee payment counter queue. The queue increased at the rate of 1 person every minute the counter clerk takes 3 minutes to entertain a person. There is one girl after every 2 boys in the queue. The Tea break of 10 minute is at 3:35. The first person is a boy and the person behind me is a girl. The ratio of boy to girl gets interchanged after the 17th person. At 3:02 and 3:04 girls join the queue. 1. Assuming that there was delay of 5 minutes at 3:07 pm in the counter clerks working. At what time I’ll be free to catch up with my friends? 1. 3:43 2. 3:48 3. 3:45 4. 3:40 2. Where will I be at 3:18 hrs, i.e. my position? If the 3rd person in the queue decides to pay the fees of two persons (including herself) and a boy who was exactly after her, left the counter without paying his fees? position 1. 4th position 2. 5thposition 3. 6th position 4. None of these Answer: For Solid DI SET 30 1. 2 After 2 boys there is a lady. 1 st person is a boy, thus it can be BBG or BGBBGB. And so on, where B stands for boy and G stands for girl. The person behind me is a girl (12th in a row). There for it is BBGBBG i.e. 3rd 6th 9th 12th & 15th are girls. After 12th person girls ratio interchanges i.e. it becomes 2 girls to boys in a group … at 3:02 and 3:04. I am 11th in a queue, i.e. my number shall arrive after 10 people (3 minute per) 10X3 = 30 min. + 10 minutes tea break + 5 minutes interruption + 3 minute processing time. (30 + 10 + 5 + 3 = 48 min. So I’ll be free by 3:48 pm.. 2. 2 Counter clerk takes 3 minutes to entertain on person. So in 18 minutes 18/3 = 6 persons have paid their fees. I was 11th so now I am 5th Now one of the girls has paid 2 fees, so it is like being 6th in the queue, but a boy exactly after her, so we are back to being 5th position..

Solid DI Set - 31 Question The table below shows the sales and expenditure of three companies JAI foods, HAWAI foods and WAI foods for the financial year 2004-2005. These companies are located in the different parts of the world. Expenditure break ups are in percentage. Closely analyse the data and answer the questions. Particulars Jai foods (Sales Rs 7.5) Hawai foods (Sales Rs 1.9) Wai foods (Sales Rs 6.9)

Operating Profit 7 9 9 Interest paid 10 11 12 Rental 21 19 18 Taxes 8 8 11 Salaries 12 9 12 Raw material cost 25 18 19 Power and Electricity 5 10 7 Labour cost 5 6 4 Transportation 3 2 3 Maintenance 2 5 2 Miscellaneous 2 3 3 Total 100 100 100

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* Sales to be read as Rs. million / month * Sales break ups are in percentages (%) 1. What can be concluded about the expenditure in salaries, raw material, transportation and rental of all the three companies listed above in the table? 1. Percentage wise Wai food is spending more then the other two. 2. Revenue wise Jai food is spending more then Hawai and Wai together. 3. Revenue wise Hawai and Wai are spending less then Jai foods. 4. Percentage wise Hawai spends more than Jai, which in turn spends more than Wai. 2. If the interest paid by JAI FOODS is reduced by 1%, and everything else remains the same, its operating profit will: 1. Increase by 1% percent. 2. Not change. 3. Increase by 0.0075 million 4. Increase by 2% percent. 3. If the average monthly salary in WAI FOODS is Rs 9,500, then how many employees does WAI have? 1. Can’t say 2. 18 3. 81 4. 87 Answer: For Solid DI SET 31 1. 3 Option 1, 2 and 4 are not true, by visual observation and approximation. Revenue wise hawai and wai are spending less then Jai foods.. 2. 3 The reduction of 1% in the expenditure will result in increase of 10% x 1% in operating profit for Jai foods, so operating profit of Jai foods will increase 0.1% of 7.5 m. Increase of 0.0075 million.. 3. 4 Total salary paid by WAI foods = 6.9 x 0.12 x 1,000,000 = 828000. So number of employees = total salary paid/ average salary = 828000 / 9,500 = 87 employees.. Solid DI Set - 32 Question Between two persons, A and B, there is one apple and one banana. When I asked them as to who among them had the apple, they gave two statements each in reply : A: B has the apple. B has the banana. B: A doesn’t have the banana A has the apple. It is known that at least one of A and B tells a least one false statement.

1. Which of the following statements must be true? (1) Each of A and B tells at least one true statement. (2) At least one of A and B tells at least one true statement. (3) Neither A nor B tells at least one true statement. (4) Both A and B tell at least one true and at least one false statement. 2. If it is also known that each of A and B tells at least one true statement, then which of the following statements must be true? (1) All the four statements given by both A and B are true. (2) Both the statements given by exactly one person out of A and B must be true. (3) Each of A and B tells at least one false statement (4) B has the banana as well as the apple with him.

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Answer: For Solid DI SET 32 The given statements are : A : B has the apple. B has the banana. B : A doesn’t have the banana. A has the apple Let us study the choice and eliminate the incorrect choice: 1. (1) We can have an arrangement in which A’s statements are true and false in that order, and B’s statement are both false, which defers the statements given in choice (1) Bothe A and B cannot be liars as the first statement of A is the same as the second statement given by B, and one of them must have the banana. Hence, at least one of A and B tells at least one truth. (3) This means that both A and B are liars which is not possible. (4) This suggests that both A and B are altermators (i.e. one truth and one lie), which defies the arrangement mentioned in (1). Hence, only choice (2) is correct. Choice (2) 2. (1) Defies the initial condition. (2) Is correct as either A’s both statements are true and B’s statements, are true and false, in that order, or both of B’s statements are true and A’s statements are false and true, in that order. (3) Is incorrect as per the arrangement given above. (4) Is incorrect as in the second arrangement mentioned in (2) Choice ( 2) Solid DI Set - 33 Question From one sequence of digits another sequence of digits has to be formed as per the following rules: Single switch: Interchange of any two adjacent digits. Double switch: Interchange of any two digits with maximally one digit in between. Random switch: Interchange of any two digits. 1. Using only single switching what is the minimum number of steps required to change 42153 to 12345? a) 4 b) 5 c) 6 d) 7 2. Using only double switching what is the minimum number of steps required to change 53124 to 12345? a) 3 b) 4 c) 5 d) 6 3. Using only random switching what is the minimum number of steps required to change 312546 to 654321? a) 4 b) 5 c) 6 d) 7 4. Using only single switching for first two steps and then double switching what is the minimum number of steps required to change 54321 to 12345? a) 5 b) 6 c) 7 d) 8 5. Using only single switching for first three steps and then random switching what is the minimum number of steps required to change 621534 to 123456? a) 5 b) 6 c) 7 d) 8 Answer: For Solid DI SET 33 1. b Starting with 42153 interchange 3 and 5 to get 42135. Next, interchange 2 and 4 to get 24135. Next, interchange 4 and 1 to get 21435. Next, interchange 1-2 and 4-3 to get the required sequence 12345. Hence, the single switch operation has to be invoked 5 times. 2. b Starting with 53124, interchange 1-5, then 5-3, then 2-5, and then 4-5 to get 12345. 3. a Starting with 312546, first interchange 5-1, then 6-3, then 3-1, and 4-2 to get 654321. 4. b Starting with 54321, first interchange 2-3, then 4-5, then 2-5, then 1-5, then 1-4 and then 3-4 to get 12345. The first two operations being single switches and he rest double. 5. b Starting with 654321, first interchange 2-3, then 2-4, then 3-5, then 1-6 to get the required sequence 123456.

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Solid DI Set - 34 Question The following questions consist of a questions and two statements ,I and II. Choose (1) If one of the two statements (I or II) alone is sufficient but the other statement alone is not (2) If each statement alone is sufficient to answer the question asked. (3) If statements I and II together are sufficient to answer the question but neither statement alone is sufficient. (4) If even statements I and II together are not sufficient to answer the question 1) P, Q, R are three polygons of having different number of sides. Which has the largest area among them? I. Their perimeters are the same and Q is a square. II. R is a pentagon. 1.1 2.2 3.3 4.4 2) What is (ad – bc)? I. a, b, c, d are 4 consecutive terms of an A.P with common difference = 3. II. a, b, c, d are 4 consecutive positive even numbers. 1.1 2.2 3.3 4.4 Answer: For Solid DI SET 34 Ans 1) 4 We cannot find the polygon which is the largest area. Because we don’t have any information about P. Ans 2 ) 2 Each statement independently will give the answer. Assume in statement (I) the values of a, b, c, d as x, x + 3. x + 6, x + 9. Find ad – bc …it is equal to –18. Similarly for statement (II) we get the difference as –8. Solid DI Set - 35 Question Srinivas intends to draw one rectangle of integer sides with a pencil which can last for a maximum possible length of 100 units only. Let R denote the set of all possible distinct rectangles from which Srinivas can choose to draw one such rectangle. 1. The number of rectangles in set R is 1. 636 2. 601 3. 613 4. 625 2. All the rectangles in R are formed in to groups such that all the rectangles of same perimeter are in the same group. What is maximum number of groups that is possible? 1. 99 2. 96 3. 49 4. 51 Answer: For Solid DI SET 35 1. 4 Given 2(l + b) =100. But minimum 2(l + b) will be 4 units. i.e. 49 possible values that perimeter can assume for each possible l + b = n, we have different ways of choosing distinct pairs of l & b.

Value of (l+b) Number of Ways 2 1 3 1 4 2 5 2 6 3 49 24 50 25

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= 2(1 + 3 + ……… 25) – 25 = 625 2. 3 As explained above, 49 distinct parameters are possible or 49 groups are possible. Solid DI Set - 36 Question A student is allotted 1950 points to bid for courses totaling 16 credits in IIM. For every extra credit undertaken, he gets an additional 75 points. He is required to bid a minimum of 75 points per credit for all uncapped courses. However, in the case of capped courses, he can bid more than 75 points per credit. “A” decides to take 18 credits in which all courses, other than one course which is 3 credits, are uncapped. 1. What is the maximum number of points he can bid for the capped course? (1) 975 (2) 950 (3) 1125 (4) 1050 (5) None of the above 2. What would be the maximum number of points he could bid for the same course if he decides to take a total of 16 credits only? (1) 925 (2) 975 (3) 950 (4) 1125 (5) 1050 Answer: For Solid DI SET 36 Ans 1) 1 Minimum points to be allotted for uncapped course = 15 * 75 = 1125 Therefore Maximum points available for capped course = 2100 – 1125 = 975 Ans 2) 2 Round about method Total credits = 16, Total points allotted = 1950 Capped credits = 3, Uncapped credits = 13 Minimum points allotted for uncapped courses = 13 x 75 = 975 Maximum points available for capped course = 1950 – 975 = 975 Short cut method Maximum points available for capped course = 975 As 150 less points allotted and 150 (2 x 75) used up. Choice (2) Solid DI Set - 37 Question Each of the letters of the alphanumeric addition EAT + THAT = APPLE are distinctly different. The addition is done in the decimal system. 1). What is the sum of the digits of APPLE? a. 9 b. 10 c. 11 d. 12 e. 15 2). What is the value of L? a. 3 b. 4 c. 5 d. 6 e. 2 Answer: For Solid DI SET 37 A1) d A2) a The hints are: 1. A has to be 1. 2. T has to be 9. 3. So E is 8 4. If three digit number added to 4 digit number to get a 5 digit number then the second digit of APPLE has to be zero.

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Using all these we get (8 19) + (9 2 1 9) = (10 0 38) Solid DI Set - 38 Question The following questions consist of a questions and two statements ,I and II. Choose (1) If one of the two statements (I or II) alone is sufficient but the other statement alone is not (2) If each statement alone is sufficient to answer the question asked. (3) If statements I and II together are sufficient to answer the question but neither statement alone is sufficient. (4) If even statements I and II together are not sufficient to answer the question 1) A survey was conducted among 500 people and it was found that 58% preferred coffee, 47% liked tea and 9 % drank milk in the morning. How many people preferred nothing between coffee, milk and tea? I. 21% liked both coffee and tea. No person liked both milk and tea. II. 4 % liked both coffee and milk. 1.1 2.2 3.3 4.4 2) What is the value of x if it is a natural number? I. y is divisible by 3 and y – x = 720. II. y is divisible by 9 and y – x = 720. 1.1 2.2 3.3 4.4 Answer: For Solid DI SET 38 Ans 1.3 From statement I we know that the number of people drinking milk and tea is zero, so number of people drinking all 3 is also zero. From I and II we know that the number of people drinking exactly 1 drink or 2 drinks. So, we can find out the number of people not drinking any of the drinks. Ans 2.4 We cannot get the answer from statement II. Statement I is implied if statement II is true. Hence we cannot find the answer. Solid DI Set - 39 Question Rahul Sharma has a factory which manufactures Alpha I, Beta I and Gamma I. All these are manufactured by processing Omega 34. Alpha I requires 1 kg/unit, Beta I requires 2 kg/unit and Gamma I Gamma I requires 2.5 kg per unit of Omega 34, which costs Rs. 2 per kilogram. The total availability of Omega 34 is 350 kilogram. the processing is done on a machine having production hours of 160 hours in day shift and 182 hours in the night shift. The time required per unit production is as follows.

Product Day Shift

Night Shift

Alpha I 2 hours 2.5 hours

Beta I 3 hours 4.0 hours

Gamma I

1 hour 1.5 hours

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The machine costs Rs. 1 per hour. Selling price of Alpha I Beta I and Gamma I are Rs. 8 per Unit, Rs. 12 per Unit and Rs. 3.50 per Unit respectively. At least 5o units of Alpha I have to be produced and at the most 150 units of Gamma I can be produced. 1. Which of the following is possible? a) 75 units of Alpha 1, 4 units of Beta I in day shift, manufacture 40 units of Beta I and 40 units of Gamma I and 10 units of Alpha I in night shift. b) 75 units of Alpha I, 4 units of Beta I, in the day shit. Manufacture 40 units of Beta I and 40 units of Gamma I and 5 units of Alpha I in night shift. c) 74 units of Alpha I, 4 units of Beta I in day shift, 25 units of Beta I, and 10 units of Gamma I and 30 units of Alpha I in night shift. d) 74 units of Alpha I, 5 units of Beta I in day shift, 40 units of Beta I, 10 units of Gamma I and 30 units of Alpha I in night shift. 2. What percentage of the available raw material is utilised if 100 units of Alpha I, 40 units of Beta I, and 10 units of Gamma I are produced? a) 50% b) 58% c) 68% d) 78% 3. If Rahul Sharma spends initially 150 machine hours in day shift to manufacture Gamma I, 10 hours to manufacture Alpha I, and in the night shift manufactures 53 units of Gamma I and spends the rest of the night shift to manufacture Alpha 1. What will be his profit/loss? a) loss of Rs. 65 b) profit Rs. 65 c) No profit to loss d) This manufacturing pattern is not possible 4. If the minimum possible manufacturing requirement for Alpha I is met and the remaining raw material is utilised for the manufacture of the other 2 products then a) 10 units of Beta I can be manufactured b) 0 units of Beta I can be manufactured c) 5 units of Beta I can be manufactured d) Any of the above 5. If in the shift, 65 units of Alpha I, 4 units of Beta I, 15 units of Gamma I and in the night shift. 20 units of Beta 1,40 units of Gamma I and 20 units of Alpha I are manufactured then which of the following is true? I. 5 hours of machine time is unutilised II. Total cost of production is Rs. 54 III. More than 20% of the available raw material is unutilised a) I only b) II only c) I and III d) I and II

Answer: For Solid DI SET 39 1. c 74 units of Alpha I and 4 units of Beta I in day shift will require (74 x 2 + 4 x 3) = 160 hours of day shift which are available as per the condition given in the question. 25 units of Beta I, 10 units of Gama I and 30 units of Alpha in night shift will require (25 x 4 + 10 x 1.5 + 30 x 2.5) = 190 hours which again satisfies the condition given in the question. 2. b Amount of raw material i.e. Omega 34 utilised will be (100 x 1 + 40 x 2 + 10 x 2.5) = 205 kg. Total amount of Omega 34 available is 350 Kg. So % of total = 205/350 x 100 = 58%. 3. d Since in the question it is mentioned that the maximum no of units of Gamma I have to be 150 but according to the question total no of Gamma I units being manufactured are 203. 4. d Minimum possible manufacturing requirement of Alpha I is 50 units. So amount of raw material used will be 50 kg. Remaining raw material is 300 kg. so any of the first three options are possible. 5. c In the day shift time utlised (65 x 2 + 4 x 3 + 15 x 1) = 157 hours. So 3 hours unutilised in day shift. In the night shift time utilised (20 x 4 + 40 x 1.5 + 20 x 2.5) = 190 hours. So 2 hours unutilised in night shift. So total unutilised time is 5 hours. Total raw material consumed ((65 + 20) x 1 + (20 + 4) x 2 + (55 x 2.5)) =

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270.5 kg. So amount of raw material unutilised will be (350 - 270.5)/350 x 100 = 22.7% which is more than 20%. Hence c). Solid DI Set - 40 Question Toyota motor company’s teams A, B, C, D, E and F are racing new concept cars competing in a season of 6 races. Points awarded for rank 1, 2, 3, 4, 5 and 6 are 10, 8, 5, 3, 1 and 0 respectively. Points scored by five teams in the first 4 races are given in the table below.

Race Team A

Team B

Team C

Team D

Team E

1 1 10 0 3 8 2 0 1 3 10 8 3 10 3 5 0 1 4 10 5 8 1 0

The Championship is won by the team which scores the highest. Mark 1: If the question can be answered by using one of the statements alone, but cannot be answered using the other, statement alone. Mark 2: If the question can be answered by using other statements alone. Mark 3: If the question can be answered by using both statements together, but cannot be answered by using either statement alone. Mark 4: If the question cannot be answered. 1. If Team C wins the next two races, who wins the championship? I. Team F finishes second in the fifth race. II. Team F does not finish second in the sixth race. 1.1 2.2 3.3 4.4 2. If Team E wins the next race and finishes second in the last race, who wins the championship? I. Team D finishes second in one of the races. II. Team F does not win any race. 1.1 2.2 3.3 4.4

Answer: For Solid DI SET 40 1. 3 From the table, Team F scores 5, 5, 8 and 3 in the Race 1, 2, 3 and 4 respectively.Team C has 36 points after the 6 races: Statement I and II are individually insufficient as the positions of the other players in the last two races are not known. Combining I and II: Maximum number of points Team F can get = 8 + 5 = 13. His maximum possible score at the end of 6 races = 21 + 13 = 34. Team A cannot finish second in the fifth race as Team F is second. Maximum possible score of Team A is 21 + 13 = 34. No other player can score more than this, as their scores in the first four races are less than Team F and Team A. Therefore, Team C wins the championship with 36 points. 2. 4 End score of Team E = 17 + 10 + 8 = 35. From statement I, Team D’s maximum possible score = 14 + 8 + 10 = 32. Team F and Team A’s maximum possible score = 21 + 5 + 10 = 32. Team F and Team A’s maximum possible score = 21 + 5 + 10 = 36. Thus, nothing can be said about the winner. Therefore,Statement I is insufficient to answer the question.

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Statement II is insufficient to answer the question by itself. Considering both the statements together nothing can be said about the winner. Therefore, Question cannot be answered.

Solid DI Set -41 Question Twenty-one participants from four countries (Africa, America, Australia & Europe) attended a United Nations conference. Each participant was an expert in one of the four fields, labour, health, population studies& refugee relocation. The following five facts about the participants are given. (a) The number of labour experts in the camp was exactly half the number of experts in each of the three other categories. (b) Africa did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category. (c) None of the continents sent more than three experts in any category. (d) If there had been one less Australian expert, then the Americans wouls have had twice as many experts as each of the other continents. (e) Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australia.

1.Which of the following numbers cannot be determined from the information given? (1) Number of labour experts from America. (2) Number of health experts from Europe. (3) Number of health experts from Australia. (4) Number of experts in refugee relocation from Africa.

2. Which of the following combinations is NOT possible? (1) 2 experts in population studies from America & 2 health experts from Africa attended the conference. (2) 2 experts in population studies from America & 1 health expert from Africa attended the conference. (3) 3 experts in refugee relocation from America & 1 health expert from Africa attended the conference. (4) Africa & America each had 1 expert in population studies attending the conference.

3. If Ramos is the lone American expert in population studies, which one of the following is NOT true about the numbers of experts in the conference from the four continents. (1) There is one expert in health from Africa. (2) There is one expert in refugee relocation from Africa. (3) There are two experts in health from America. (4) There are three experts in refugee relocation from America.

4. Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex? (I) At least one (II) At most two (1) Only I and not II (2) Only II and not I (3) Both I and II (4) Neither I nor II

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Labour Health PS RR TOTAL Africa X B America 2B Australia Mike, Alfanso B + 1 Europe B Total A 2A 2A 2A 21 Now solving for A and B , we get 7A = 21 and 5B+1 = 21 => A = 3 and B= 4 => Now we will complete the table and get the answer

Labour Health PS RR TOTAL Africa X 4 America 1 8 Australia 1 1 Mike, Alfanso 1 5 Europe 1 1 1 1 4 Total 3 6 6 6 21 Ans1 (4 ) Ans2 ( 4 ) Ans3 ( 3 ) Ans4 ( 3 ) Solid DI Set - 42 Question Divide a circle into 8 equal parts; number them clockwise from 1 to 8. Assume that you are at 1 & your initial score is 1. If you move a step clockwise, you just add the number in the next slot to your current score. If you move a step anticlockwise, you add the number in that slot but subtract 2 from the total to get your new score. If you move to the number diagonally across, you add that number to your score but subtract 3 from the total. You can move to a slot only once. 1. Your maximum score after the second move can be (1) 12 (2) 11 (3) 10 (4) 8 2. Assuming you move a step clockwise in your first move, then the digit that you would have left untouched after the third move will be (1) 7 (2) 4 (3) 8 (4) 5 3. If you have made three moves, without seeking to maximize your score, then you most likely to get a score of (1) 12 (2) 9 (3) 8 (4) 10 Answer: For Solid DI SET 42 Ans1 (1) Moving in anticlockwise direction in 1st step will give the score 1 + 8 –2 = 7 . second step in anticlockwise direction will give the score = 7 + 7 –2 = 12 . Ans2 (3) Only digit 8 cannot be reached in the third move. Ans3(4). The most common score in the three moves is 10 irrespective of the direction of the moves.

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Solid DI Set - 43 Question Sally and Sue have a strong desire to date Sam, they all live on the same street yet neither Sally nor Sue knows where Sam lives. The houses on this street are numbered 1 to 99. Sally asks Sam. “Is your house number a perfect square?” He answers. Then Sally asks. “Is it greater than 50?” He answers again. Sally thinks she now knows the address of Sam’s house and decides to visit. When she gets there, she finds out she is wrong. This is not surprising, considering Sam answered only the second question truthfully. Sue, unaware of Sally’s conversation, asks Sam two questions. Sue asks, “Is your house number a perfect cube?” He answers. She then asks, “Is it greater than 25?” He answers again. Sue thinks she knows where Sam lives and decides to pay him a visit. She too is mistaken as Sam once again answered only the second question truthfully. Sam’s house number is less than the numbers of the houses where Sue and Sally live, and that the sum of all three of their numbers is a perfect square multiplied by two. 1) What is Sally’s house number? 1. 64 2. 81 3. 25 4. 24 5. Can’t say 2) What is Sue’s house number? 1. 64 2. 81 3. 55 4. 54 5. Can’t say 3) What is Sam’s house number? 1. 45 2. 55 3. 65 4. 72 5. 75 Answer: For Solid DI SET 43 1) 2 2) 1 3) 2 Since Sally thinks she has enough information, we deduce that Sam answered his house number was a perfect square greater than 50 (answering Yes to both). There are two of these {64, 81} and Sally must live in one of them in order to have decided she knew where Sam lives. Sam answered only the second question truthfully, so his house number is greater than 50, but not a perfect square. Since Sam answered Sue’s second question truthfully, he had to have answered yes to “Is it greater than 25?”. Sue was able to deduce Sam’s number, so he also must have said it was a perfect cube. Cubes greater than 25: {27,64}. Sue must live in one of these houses to deduce Sam’s number. Since Sam’s number is greater than 50 and is less than Sue’s number, she must live in 64. Since Sue and Sally are not roommates (we’re told there are three numbers), Sally must live in 81. Given fact: the sum of their numbers is a perfect square multiplied by two. Sue + Sally + Sam = 2p (for p an integer) Or, 64+81+Sam = 2p2 Applying the constraint that Sam’s number is greater than 50 and less than 64, it looks like Sam = 55 (p=10). In summary, Sam = 55 Sue = 64 Sally = 81 Solid DI Set - 44 Question Mr Odd collects all the even numbers between 1 and 100 (both included) and adds them up. Mr Even does the same for all odd numbers between 10 and 100 (both included). Mr. Prime collects all prime numbers between 50 and 65 (both included) and adds them up. Mr Square collects all the perfect squares of positive integers between 1 and 100 (both included) and adds them up.

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1. The final sum obtained is what percentage of the sum of first 100 positive integers? a) 90% b) 100% c) 110% d) 125% 2. The minimum value is obtained if we subtract the scores of: a) Mr Even and Mr Square b) Mr Odd and Mr Prime c) Mr Square and Mr Prime d) Mr Odd and Mr Even

Answer: For Solid DI SET 44 1. c Mr. Odd -> 2 + 4 + 6 +……..+ 100 = 50/2 [4 + (50 - 1) 2] = 25 x (4 + 98) = 2550 Mr Even -> 11 + 13 + 15 +…….. + 99 = 45/2 [22 + (45 - 1) 2] = 2475. Mr Prime -> 53 + 59 + 61 = 173 Mr Square -> 1 +4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385, Sum of 1 to 100 = 100/2 x (100 + 1)= 50 x 101 = 5050. Odd + Even + Prime + Square = 2550 + 2475 + 173 + 385 = 5583 Hence,Required Percentage = 5583/5050 x 100% = 110%. 2. d From the above.

Solid DI Set - 45 Question DIRECTIONS for questions 1 to 3: Among the marriages conducted for poor people by the “Association for Troubled Lowers” five grooms – Ranjha, Majnu, Romeo, Farhaad ;and Devdas – get married to the brides Heer, Laila, Juliet, Siri and Paaro, not necessarily in the same order. Each man marries exactly one woman and vice versa. Ten days after the marriages took place, the marriage registrar lost the records of these marriage, but remembered only the following information in connection with these five marriage.

(a) Either Laila married romeo or Ranjha marride Heer. (b) Farhaad married either Paaro or Heer. (c) Devdas marries Juliet only in case Paaro marries Farhaad. (d) Ranjha and Romeo married Laila and Siri, not necessarily in the same order. (e) Majnu does not marry Juliet. 1. Which of the following is a correct married couple? (1) Heer – Ranjha (2) Farhaad – Paaro (3) Romeo – Juliet (4) Paaro – Majnu

2. If the condition (a) is replaced by “Heer married Romeo only if Laila married Ranjha” than who married Siri? (1) Ranjha (2) Romeo (3) Majnu (4) Cannot be determined

3. Who among the following married Ranjha? (1) Heer (2) Parro (3) Siri (4) Cannot be determined

Answer: For Solid DI SET 45 For solving these questions, the symbol ‘_’ means ‘married’ and ‘x’ means ‘did not marry’. Let us take down the information as given below. Either Laila - Romeo or Ranjha - Heer Farhad - (Paaro or Heer) Devdas - Juliet, only if Parro - Farhad Manju X Juliet

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We get the following initial arrangements :

Heer Laila Juliet Siri PaaroRanjha X • (d) X •

(d) X

Manju - X X (e) X X Romeo X X •

(d) X

Farhad X•(d) X X X • (d) Devdas X X - X X

From the above, we conclude that Devdas marries Juliet, and hence Paaro marries Farhad ©. This means that Manju marries Heer. Now, Ranjha is not married to Heer. Hence Romeo must be married to Laila; hence, Ranjha must be married to Siri (d) We get the following pairs of married couples. Ranjha – Siri Manju – Heer Romeo – Laila Farhad – Paaro Devdas – Juliet

1. Choice (2)

2. Choice (4) We know that Ranjha and Romeo must marry Siri and Laila (not necessarily in that order). But now from the replaced condition we get only the following additional implication “if Laila did not marry Ranjha then Heer did not marry Romeo” which still is not enough to determine who among Romeo and Ranjha marries Siri. 3. Choice (3)

Solid DI Set - 46 Question DIRECTIONS for questions 1 and 2 : These questions are based on the data given below.

In order to save the world from the hand of evil forces, eight superheroes are sitting around a circular table to plan their strategy. It was known that Batman and Robin neither sat on adjacent seats nor directly opposite to each other. Superman sits besides Flash Gordon and opposite to Heman while Mandrake sat directly opposite to Phantom who sits adjacent to Superman.

1. The eighth hero, Spiderman, must be sitting next to (1) Batman (2) Robin (3) Phantom (4) Heman

2. Which of the following statements must be true? (1) Batman sits to the left of Heman. (2) Robin sits to the left of Flash Gordon (3) Spiderman sits to the right of Phantom (4) None of these

Answer: For Solid DI SET 46 It is known that :

(a) Batman neither sits adjacent nor sits opposite to Robin.

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(b) Superman sits between flash Gordon and Phantom (this will give rise to two arrangements)

(c) Heman sits opposite to superman and adjacent to Mandrake, who sat directly opposite to Phantom.

Hence, we get the following arrangements.

Case – I Flash sits to the left of Superman

Case – II Phantom sits to the left of Superman

1. Choice (3) As can be observed in the above possibilities, the Spiderman must be seated adjacent to the Phantom.

2. Choice (4) The Position of Batman and Robin are not fixed, hence choices (1) and (2) cannot be correct. As in case II, Spiderman sits to the left of the Phantom; hence even choice (3) is incorrect.

Solid DI Set - 47 Question There are five identical looking boxes having different objects in it and every box has a label indicating their contents. The following is the description of the contents and the label of each box: Contents Label Two Pins PP Two Balls BB Two Clips CC One Pin and One Clip PC One Ball and One Clip BC

Somebody has mischievously interchanged these labels in such a way that no box contains the label correctly explaining its contents.

1. If the first box opened contained label PP and the second box opened contained label PC and out of the combined four items, at least one item was a Ball, which of the following will be definitely true? 1. Other three items will not contain two Balls. 2. Other three items will not contain any Clip. 3. Other three items will contain at least one Clip. 4. None of the above.

2. If the box PP contained two Clips, the box CC contained two Pins and the box BB contained at least one Ball, which of the following will definitely not be true? 1. The box BC contains one Pin and one Clip. 2. The box BB contains one Ball and one Clip.

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3. The box BC contains two Balls. 4. The box PC contains two Balls.

3. If the information is available that box PC does not contain either any Pin or any Clip and box PP does not contain any Pin and box CC contains one Clip and one Ball, which of the following will definitely be true if only one of the remaining boxes is opened? 1. It will have one Pin and one Clip. 2. It will have at least one Clip. 3. It will have two Pins. 4. It will have at least one Pin.

4. If the first box, containing the label BC was opened and it was found that one item is a Ball, which of the following would be definitely true? 1. The other item may either be a Ball or a Clip. 2. The other box with BB label will contain a Ball and a Clip. 3. The other item will not be a Ball. 4. None of the above.

Answer: For Solid DI SET 47 1. 4 : If the first box label was PP then it could be any one of the other four and if the second box was PC, it could be any one of the other four. The union of the two indicates that the two boxes opened could be any two of the five and hence none of the statements can be DEFINITELY true. 2. 3 : From the given data, PP is CC, BB is BC and CC is PP. That leaves BB and PC to be allocated to PC and BC. Hence PC is BB and BC is PC. Thus the only statement that is DEFINITELY NOT true is that BC contains two balls. 3. 4 : From the given data, CC is BC, PC is BB and PP is CC. That leaves behind PC and PP, hence statement 3 is definitely true. 4. 4 : If one item is a Ball, the other one can be either a Ball or a Pin or a Clip. Hence none of the statements are true.

Solid DI Set - 48 Question The table shown below is a board on which a counter is moving from cell to cell. Initially, the value of the counter is the value of the cell it is in. Follow the rules given below to answer the questions.

Cell No. 1 2 3 4 5 A 2 6 7 3 1 B 3 -3 -2 2 1 C -4 -2 -1 6 7 D 5 -5 3 1 2 E -3 -4 -5 -2 1 Rule 1: If the counter moves from cell 1 to cell 2, its value will be the value of cell 1 multiplied by the value of cell 2. For example, if the counter is moving from cell (A, 1) to cell (D, 5), its value will be 2 x 2 = 4. Next time if it moves from (D, 5) to (D, 3), its value will be 4 x 3 = 12. Rule 2: If the counter moves from cell 1 to cell 2 and the value of cell 1 is greater than that of cell 2, then the counter value is the value of cell 2, else the counter value will be the value of cell 1.

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1. Rule 1: If the counter moves from (B, 3) to (D, 4) to (A, 1), its value will be: a) 4 b) 8 c) –2 d) –4 2. Rule 1: If the counter moves from (A, 2), to (B, 2) to (C, 2) to (D, 3) to (E, 4), its value will be a) 1 b) – 226 c) 0 d) -216 3. If the counter moves from (A, 1) to (C, 3) to (E, 5) to (D, 4), its value according to rule 2 is a) 1 b) – 4 c) 2 d) – 1 4. If rule 1 supersedes rule 2 for the value of counter > 0, but not for the value of the counter < 0, and the counter moves from (B, 3) to (D, 1) to (C, 3) to (B, 4), what will be its value? a) 2 b) – 1 c) – 2 d) 1

Answer: For Solid DI SET 48 1. d Value of counter = (-2) x (1) x (2) = -4 2. d Value of counter = (6) x (-3) x (-2) x (3) x (-2) = -216 220. 3. a Value of counter = Value (4, 4) = 1 4. a (B, 3) to (D, 1) = 5, (D, 1) to (C, 3) = -5, (C, 3) to (B< 4) = 2

Solid DI Set - 49 Question There exists a 10 digit number such that the 1st digit from left represents the number of 0's in the number, the 2nd digit from left represents the number of 1's occurring in the number and so on until the 10th digit represents the number of 9's in the number. 1. The sum of the digits of the number is: 1. 8 2. 9 3. 10 4. 19 2. The number of 0s in the number is: 1. 9 2. 8 3. 7 4. 6 3. The number of 1s occurring in the number is: 1. 0 2. 1 3. 2 4. 3

Answer: For Solid DI SET 49 Since each digit represents the number of that particular digits representing in that number, the total sum is 10, as only 10 digits exist in the number. That is the sum of digits is equal to the total digits by the property given. All the counting is done from the left side of the number. To find the number of 0's note that you cannot have 9, 8 or 7. For the place which gives the number of 7 clearly it can at maximum be one since the sum of digits is equal to 10, suppose the value is 1 then clearly the 7 which occurs can only be in the first digit otherwise again the sum will exceed 10. Suppose 7 is the first digit and 1 is the 8th digit then the ones digit must have at least 2 since there is already one 1 occuring in 8th digit, suppose the second digit is 2, then the 3rd digit has to be 1, since we have one 2 occuring in the number.

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But if this happens then the sum of digit exceeds 10 thus there can be no 0 in 8th, 9th or 10th digit. Suppose the 7th digit is 1, i.e. there is one 6 in the number, then the 6 can only be in the 1st digit otherwise the sum of the digits will exceed 10, so if the 6 is in 1st digit, then, at least one 1 is present, (because the 7th digit already has 1), now the number of 1 has to be greater than 1 as you cannot have the second digit as 1 (then two 1's will be present in the number).

Thus the 2nd digit is 2 and the third digit which represents the number of 2's has to be 1 as the second digit is 2, thus the number is 6210001000. And the remaining solutions follow. 1. Choice 3 2. Choice 4 3. Choice 3

Solid DI Set - 50 Question Subhart, a mathematics wizard, develops a coded language. He converts all words in some number series in the following manner:

All vowels (and no other consonant) are represented by prime numbers. For all consonants, whose positions in the alphabet series are prime numbers, they are represented by a number which is twice the number giving their positions in the alphabet series. For example: The letter “C” being the 3rd alphabet. Will be denoted by 3 ´ 2 = 6. If the position of any consonant in the alphabet series is a number, half of which is a prime number, it is represented by adding a 5 at the end of that number. For example, The letter “Z” being the 26th alphabet, will be represented by 265. All remaining consonants will be represented by a number giving their position in the alphabet series. 1. The word coded as “22 17 12 17 38 8 145 11 22 23 225” is- a) PATAMXNEPUR b) FEGTSHNJKID c) KALASHNIKOV d) TUTUPHENKO

2. The word coded as “38 145 11 16 7 18” is: a) WEAKER b) STRIKE c) SNIPER d) TAURUS

3. The world “CALCUTTA” will be coded as: a) 6 29 8 9 16 18 18 29 b) 20 17 10 20 295 4 4 12 c) 6 17 12 6 29 20 20 17 d) 12 11 15 12 29 20 20 31

Answer: For Solid DI SET 50 Write down all the letters as per the given rules.

1. c We get K = 22, L = 17, S = 38, hence (c).

2. c S = 38, N = 145, P = 16, hence SNIPER.

3. c C = 6, L = 12, C = 6, hence (c). Solid DI Set - 51 Question These questions are based on the following pie chart and the table, which gives the details of expenses of an Excellent Management Training Institute in India (EMTI)

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EXPENSES OF EMTI FOR 1995 – 96

Table shows INCREASE IN EXPENSES FROM 1994–95 TO 1995-96

1. If it cost EMTI Rs.4.4 lakhs for printing in 1995-96, salaries in 1994-95 are closest to (in Rs.lakhs)

(1) 6.0 (2) 4.8 (3) 3.0 (4) Insufficient data

2. If a pie-chart were to be drawn for the expenses in 1994-95 also, which expense would show the maximum drop in the angle from

1994-95 to 1995-96?

(1) Others (2) Administrative expenses (3) Salaries (4) Insufficient data

3. If the profits were 20% of total turnover in 1995-96, and total expenses in 1995-96 are the same as the turnover of 1994-95, profit as a percentage of turnover in 1994-95 is how many percentage points less than that in 1995-96?

(1) 6.4 (2) 7.6 (3) 12.6 (4) Insufficient data

4. If the total expenses of EMTI in 1995-96 are Rs.16 lakhs, the total expenses in 1994-95 are closest to (in Rs. lacs).

(1) 12 (2) 13 (3) 14 (4) 15

5. If the total expenses of EMTI in 1995-96 was Rs.22 lacs and the profit that year stood at 10% of the total expenses, the turnover of EMTI in 1994-95 was closest to which of the following?

(1) Rs.19 lacs (2) Rs.20 lacs (3) Rs.21 lacs (4) Insufficient data

Faculty 25% Advertising 20% Material Preparation 10% Printing 25% Administrative expenses 7.5% Salaries 5% Others 7.5%

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