Logical Reasoning

1.[(x)power1/3]+[(x)power1/9]=60 3 marks

ans take .[(x)power1/3]=a then form the eqation a+a(power2)=60

2.a cube is painted in 27 cubes. Find the number of cubes with 8marks

a.3 sides painted

b.2 sides painted

c.1 sides painted

d. no sides painted

3.i participated in a race 1/5th of those who are before me and 5/6th are behind me. Find the total number of participants. 3 marks

Ans : 31

Approach:

Let the total number of participants be X

So, [(x-1)/5 + 5(x-1)/6] = X on solving we get the total no. as 31

4.A & B are two friends. Together they go from shopping .A buys a hat and a suit.all together A spends 15 rupees. B buys a hat which costs same as the suit bought buy A. B says to a that”if at all i had bought my hat by spending 1.5 times u spent on buyingh ur hat, we both would have spent the same amount on buying our items(together ie 15 rs)

a.what is cost of hat bought by A

b. the money A & B spent all together. 6marks

Ans (a) 6.4rs

(b)rs 29

Ans 4 a. lets sayA spent x & y on hat and suit resp.

From the condition we can say B spent y and x-1 rs on hat and dress resp.

From what B told to A we can write

x+y=15

=1.5x+(x-1)=15

=2.5x-1=15

=x=16/2.5=6.4rs

b. total A alone spent =x+y=15.

B spent =y+(x-1)=14

=x+y-1

=15-1=14

so together they spent 15+14=29 rs

5. There was a long question in which different relations were given like A is younger than B but older than C Some names were assigened toA,B,C..The question was to find the youngest of all. This was very simple. 6marksAns: E(Edward)

6.A man was travelling in a car he saw a milestone with 2 digits after 1 hour he saw another milestone with 2 digits reversed...then he saw another milestone with 2 digits separated by 0.what is the numbers(repeated) 4 marks

ans. 45km/hr miles stones were 16,61 & 106

7.There are A, B, C, D, E, F students they speak one are more than one of english, itali,

french, Spanish, portueges; B, C speak English. But after D joins they have Spanish as

the common language

Spanish is most common language

A, B, E have French as common language

C, E has Italian as common language

3 speak portueges

Out of all 1=all speaks 5 Langs, 1= speaks 4 Langs, 1= speaks 3

Langs, 1= speaks 2 Langs,1= speaks 1 language?

then 4 questions were asked based on above data like

1) A knows which languages? 4 options were given (one can easily get the answer from

the above data and given options)

2) B knows how many languages

a) English, French b)English, French Spanish c)English, French, Spanish Italian

d)English, French, Spanish, Italian,Portugese

3)and 4) I am sorry i forgot 8 Marks

8. A five digit no. whose third digit is one greater than the sum of two digits and the third is double the forth and forth is double of the fifth digit and second is greater than first digit by 5. if we multiply forth and fifth digits we get the third digit. 4marks

Ans.16842

9.in a town there are 100 persons. Out of those 70 are bachelor,80 has house, 90 has cars. how many people are bachelor, have car and house . 4 marks

10. 4 maks

Q1). x^1/3 - x^1/9 = 60 . find the value of X. (3 marks)

Ans : write x^1/3 as x^1/9. x^1/9. x^1/9

Now x^1/9(x^2/9 - 1) =60

Now use trial and error method. Then x= 4^9

Q2). There are A, B, C, D, E, F students they speak one are more than one of english, itali, french, Spanish, portueges;

B, C speak English. But after D joins they have Spanish as the common languageSpanish is most common languageA, B, E have French as common languageC, E has Italian as common language3 speak portuegesOut of all 1=all speaks 5 Langs, 1= speaks 4 Langs, 1= speaks 3Langs, 1= speaks 2 Langs,1= speaks 1 language? (8 marks)

then 4 questions were asked based on above data like1) A knows which languages? 4 options were given (one can easily get the answer from the above data and given options)

2) B knows how many languagesa) English, French

b)English, French Spanish

c)English, French, Spanish Italiand)English, French, Spanish, Italian,Portugese

3) C can’t speak which language (4 options were given)4) E can speak which languages (4 options were given)

Q3) same old cubes problem (8 marks)

A cube has its 6 faces painted red. It is cut by 6 straight lines into 27 smaller cubes. Find how many smaller cubes are there having:(i) 3 faces painted red. (ans : 8 )(ii) 2faces painted red. (ans : 12 )

(iii) 1 face painted red. (ans : 6 )(iv) 0 faces painted red (ans :1 )

Q4) There was a cycle race going on. 1/5th of the those in front of a person and 5/6th of those behind him gives the total number of participants. How many people took part in the race? (3 marks) Ans : 31 (5 marks)

Approach:Let the total number of participants be XSo, [(x-1)/5 + 5(x-1)/6] = X

Q5) A man starts from XYZ city and drives a constant speed. After some time he sees a milestone with two digits written on it. after he drives for an hour, he sees another milestone with the same digits, but in reversed order. After another hour of journey, he sees another milestone with original digits but with a zero between them.

What was the speed of his car if milestones show kilometers? ( 6 marks)

Ans ) 45 kmph

Let speed of car be x kmph

Let at first he sees digits as ‘ab’…that is the value of number is: 10a+b

After traveling for one hour, he sees the number as ‘ba’…thus its value is 10b+a

After traveling another hour,he sees the number as ‘a0b’…thus value is 100a+b

Now,

10a+b+x=10b+a..which gives x=9b-9a

10b+a+x=100a+b..which gives x=99a-9b

Equating we get,

b=6a

since ‘a’ and ‘b’ are digits, a=1 and b=6 and thus x=45

Q6). Uncle Reuben and Aunt Cynthia came to town for shopping. Reuben bought a suit and hat for $15. Cynthia paid as much as for her hat as Reuben did for his suit then she spent the rest of their money for a new dress.

On the way home Cynthia called Reuben’s attention to the fact that his hat cost $1 more than her dress, then she added “if we had divided our hat money differently so that we bought different hats mine costing 1 and 1/2 time cost of yours” then we each would have spent the same amount of money.

In that case Uncle Reuben asked "how much would my hat have cost" (6 marks)

Ans). Uncles hat costs $9 (total money was $29)(not sure)check it

Q7). A five digit no whose third digit is one greater than the sum of the first two digits, and the third digit is double the fourth digit ,and fourth digit is double the fifth digit, and second digit is greater than first digit by 5. and if we multiply fourth and fifth digit we get third digit.

(5 marks)

Ans) 16842 take the no as “abcde” work it out using the given conditions (very easy)

Q8)ferie younger than jack and older than louise, louise older than edward and younger than jim (some names r given in that order) Who is youngest person?

U can easily solve this one by examining the conditions (3 marks)

Ans ) EDWARD very simple we have 2 club all conditions around 6, then we will get youngest person

Q9) ona sacle of 100: (3 marks)85 are married, 80 have cars, 75 have phones, and 70 have houses. How many minimum persons are married, have phone, car and houses on a scale of 100.

Ans) 15 (not sure check it out)

Q10) There are 100 teams for a cricket tournament. It’s a knockout tournament .The team which

looses once will be out. How many matches are required to choose the winner?

Ans) 99

Infosys Talent Test

1. There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary.

2. If 5/2 artists make 5/2 paintings using 5/2 canvases in 5/2 days then how many artists r required to make 25 paintings using 25 canvases in 25 days?

3. If the digits of my present age are reversed then i get the age of my son.If 1 year ago my age was twice as that of my son.Find my present age.ans. father-73, son-37

4. There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be weighed for finding out the haevy ball.ans. 8

5. If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks.ans. 120miles and 24 miles/hr

6. There r four face cards (J,Q,K,A) all of different types(diamond,club,spade,heart) and some conditions r given.find the order of cardsans. king -> jack -> queen -> aceheart diamond spade club

7. If A,B,C,D,E r 5 members of a family.4 of them give true statements : 1. E is my mother in law2. C is my son in law's brother3. B is my father's brother4. A is my brother's wife

Who made the stmt. and what r the realtions among themans. E| A<-->B--C

|D<--> denotes husband-wife-- denotes brothers

8. The product of 5 different temperatures is 12.If all of then r integers then find all the temperaturesans. -2,-1,1,2,3

9. If a flight travels between India(IST) and Toronto(TST).There r 2 types of flights slow and fast.

IST TSTSLOW - - FAST - -

TST ISTSLOW - -FAST - ?

These are the departure times and arrival times for slow and fast flights in IST and TST. then find the time in ?ans. 22:40

10.There r 9 cities numbered 1 to 9.From how many cities the flight can start so as to reach the city 8 either directly or indirectly such the path formed is divisible by 3.eg. 1368-Flights goes through 1-3-6-8.

11. If i do this puzzle i find it to be hard than the last puzzle that i did before that after that..............very complex stmt.Is that puzzle difficult,easy,can't say or depends on the no. of puzzles

1.Solve for X, (3 marks)

(X) 1/3 –(X) 1/9=60

2.A person took part in a cycling race with many others. After pedaling for several minutes, he found that 1/5 th of the racers ahead of him and 5/6 th of the cyclist behind him together formed the total number of participants. How many people participated in the race?

Solution:

Let X be the total number of racers.

Then,

(X-1)/5 – 5(X-1)/6=X

X=31(Sure)

3.A big cube painted red on all the sides. It was cut into 27 smaller cubes by 6 straight lines. How many of the smaller cubes painted on all 3 sides, on 2 sides, on 1 side and no faces painted? (8 marks)

Solution:

Let n be the side of cube.

Sides of cube = 3 X 3 X 3

No faces painted=(n-2) X (n-2) X (n-2)

=(3-2) X (3-2) X (3-2) = 1(Sure)

1 side painted = 6 X (n-2) X (n-2)

=6(Sure)

2 sides painted = 12 X (n-2)

= 12(Sure)

All the 3 sides painted = 8(Sure)

4.There is a five-digit number. The fifth digit is one fourth of the third digit and one half of the fourth digit. Third digit is one half of the first digit. Second digit is 5 more than the fifth digit. What is that 5-digit number? (6 marks)

Solution:

Let the fifth digit be X, then fourth digit =2X and third digit = 4X.

And also Second digit is 5 more than the last digit.

Therefore 2nd digit = X + 5

Also first digit = 4X * 2

It is clear from the above statements that the fifth digit must be 1.

Therefore the number is 86421. (Sure)

5.A car is traveling in a uniform speed. The driver sees a milestone, which is a 2-digit number. After traveling for an

Hour the driver sees another milestone with the same digit in reverse order. After another hour the driver sees another milestone containing the same two-digit number with 0 in between them. What is the average speed of the car?

Solution:

Let the milestone be XY.

After an hour he saw a milestone numbered YX.

After another hour he saw a milestone numbered X0Y

The number is 16,61,106

(61-16) = (106-61) = 45

And the average speed is 45 km/hr. (Sure)

6.B and C initially speak English but when D joined Spanish they too took up Spanish. The only common language between A, B and E is French. The only common language between C and E is Italian. Three people speak Portuguese. Most common language is Spanish. One person knows all the 5 language, one person knows 4 languages, one person knows 3 languages, one person knows 2 languages and one person knows only one language. (8 marks)

Solution:

A ->French, Spanish, Portuguese (Sure)

B ->English, Spanish, French, Portuguese, Italian (Sure)

C -> English, Spanish, Italian, Portuguese (Sure)

D ->Spanish (Sure)

E ->French, Italian (Sure)

7.Uncle Reuben and aunt Cynthia came to town to shop.Reuben bought a suit and hat for $15.Cynthia paid as much as for her hat as Reuben did for his suit.Then she spent the rest of her money for her dress.On the way to home Cynthia called Reubens attention to the fact that his hat cost $1 more than her dress.Then uncle said if we had divided our hat money differently such that we bought a different hats mine costing 1 and ½ times cost of yours then we would have spent the equal amount of money.

(i)How much the hat would cost in that case?

(ii)What is the total amount spent?

Solution:

3,31(not sure)

8.There was a match to be held.And 100 nations were to participate in that match.It was totally an elimination match,that is if a team loses a match it must be eliminated.Find out the total number of matches played to find out the grand winner?

Solution:

99

9.There were totally 100 men.85 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?