Gradient TCS Questions Explanation

8/13/2019 Gradient TCS Questions Explanation

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A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise

goes in one direction and the hare in the other. The hare starts after the tortoise

has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet

when the hare has covered only 1/8 of the distance. By what factor should the

hare increase its speed so as to tie the race?

a) 37.80 b)8 c) 40 d) 5

Answer: 37.8

Explanation: (H-1) (H1 - H/T)where T = 5 as tortoise has covered 1/5, so take

value of T as denominator of the fraction.

And H = 8 as Hare has covered 1/8, of the distance before meeting the tortoise, so

take value of H as denominator of the fraction.

By Substituting the values one can get the answer quite easily.

Note:The value of the fraction keeps on changing but only consider the integer in

the denominator of each fraction as explained above.

The question also comes with data such that H = 4 and T = 3. In that case, answer

is 5 times.

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3/46

Alok and Bhanu play the following min-max game. Given the expression

N = 40 + X + YZWhere X, Y and Z are variables representing single digits (0 to 9), Alok would like to

maximize N while Bhanu

would like to minimize it. Towards this end, Alok chooses a single digit number and

Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next

value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for

the remaining variable. Assuming both play to their optimal strategies, the value of N at

the end of the game would be

a) 31 b) 50 c) 51 d) 58Answer: 51

Explanation :

Optimal Values in Min-Max game of different expressions are:

X+Y-Z= 11; X-Y-Z= 2; X(Y-Z) = 18



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5/46

After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters

randomly into the envelopes (1 letter per envelope). What is the probability that

exactly 1 letter is inserted in an improper envelope?

a)1/12 b)0 c)12/212 d)11/12

Ans: 0Explanation: Impossible Event of exactly one letter going into wrong envelope.

Minimum 2 letters are required such that both can go into wrong envelopes.

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Given 3 lines in the plane such that the points of intersection form a triangle with

sides of length 20, 20 and 30, the number of points equidistant from all the 3

lines is

Ans: 4

Explanation: There are three Ex-Centres and one in-centre of any triangle, whichare all equidistant from the sides of the triangle



6/46

There are two boxes, one containing 10 red balls and the other containing 10 green

balls. You are allowed to move the balls between the boxes so that when you

choose a box at random and a ball at random from the chosen box, the probability

of getting a red ball is maximized. This maximum probability isa)1/2 b)14/19 c)37/38 d)3/4

Ans: 14/19

Explanation: Put all red balls except one from the 1stto the 2ndbox. So, the

probability of drawing a red ball becomes

*1 + *(9/19) = 14/19

is probability of bag selection and 1 & 9/19 are red ball selection probabilities from

2 boxes

NOTE: Minimum probability of drawing a red ball is when all the red and green balls

are put into the same box. So, the probability will be *0 + *(10/20) =

Also, this question comes with the data 39 Red and 26 Green balls. In that case the

answer is *1 + * {38/(38+26)} = 0.8



7/46

A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a

dart at it and it hits the dartboard at some point Q in the circle. What is the

probability that Q is closer to the center of the circle than the periphery?

a) 0.75 b) 1 c) 0.5 d) 0.25

Ans: 0.25

Explanation:

Probability =favorable area / Total Area

= (0.5)2/ (1)2

= 0.25-----------------------------------------------------------------------------

14 people meet and shake hands. The maximum number of handshakes possible if there

is to be no cycle of handshakes is (A cycle of handshakes is a sequence of peoplea1, a2,ak, k>2 such that the pairs {a1,a2}, {a2,a3},, {a(k-1), ak}, {ak, a1} shakehands).

a) 11 b) 12 c) 10 d) 13

Answer: 13

Explanation: if n members are there, maximum number of handshakes would be n-1 if

the cycle of handshakes is not to be completed. So, for 14 people above, answer is

14-1=13.



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A and B play a game of dice between them. The dice consist of colors on their faces

(instead of numbers). When the dice are thrown, A wins if both show the same

color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red

and blue faces should the other die have if the both players have the same chances

of winning?a) 3 red and 3 blue faces b) 2 red and remaining blue

c) 6 red and 0 blue d) 4 red and remaining blue

Ans: 3 red and 3 blue faces

Explanation: Let there be m red and 6-m blue faces on the 2nddie. The probability ofA winning should be as both A & B have equal probability of winning.

Prob (A wins) = (4/6) * (m/6) + (2/6) * (6-m)/6 = ; So, m= 3

{both red} {both Blue}

So, 3 red faces and 3 blue faces must be there.

NOTE: whatever be the number of red and blue faces on the 1stdie, the 2nddie will

always have 3 red and 3 blue faces for A and B to have equal probability of

winning.



9/46

Alice starts and the two players take turns. A turn consists of moving the coin on the top to a position i

below the top coin (0 = i = 20). We will call this an i-move (thus a 0-move implies doing nothing).

The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on

subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a

player's turn then the player wins the game. Initially, the gold coin is the third coin from the top.

Then

a) In order to win, Alice's first move should be a 1-move.

b) In order to win, Alice's first move should be a 0-move.

c) In order to win, Alice's first move can be a 0-move or a 1-move.

d) Alice has no winning strategy.

Answer: In order to win, Alice's first move should be a 1-move.

Explanation: In this case, bringing the golden coin to the top results in loosing the game. i= 0 or 1 willkeep the golden coin at the 3rdplace and i2 will take it to the 2ndplace. Consider the followingmoves by A & B in the same sequence.

A0;B - 2 (Golden coin now comes at the 2ndplace)---A looses whatever he does

A -1; B - 2; A-0 and then B looses whatever he does

A -1; B - 0; A- 2 again B looses whatever he does

So, Picking a 1-move ensures As win

Sometimes, instead of 20, there are different no. of coins but the answer wont change.

NOTE:If, however, bringing the golden coin to the top results in winning, A has no winning

strategy



10/46

Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above

the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is

to bring the gold coin to the top by repeatedly moving the topmost coin to another

position in the stack. Alice starts and the players take turns. A turn consists of moving the

coin on the top to a position i below the top coin (for some i between 0 and 100). We will

call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move

cannot be repeated; for example once a player makes a 2-move, on subsequent turns

neither player can make a 2-move. Initially, the gold coin is the third coin from the top.

Then

a) In order to win, Alices first move should be a 1-move.

b) In order to win, Alices first move should be a 0-move.c) Alice has no winning strategy.

d) In order to win, Alices first move can be a 0-move or a 1-move.

Answer: Alice has no winning strategy.

Explanation: In this case Alice has no winning strategy. Consider the moves below

A0;B-1; A-2 ; B-bringing the coin on top and winningA-1; B-0; A2 ; B-bringing the coin on top and winning

A2; B-bringing the coin on top and winning

So in all cases B wins and A looses. So, A has no winning strategy.



11/46

Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle

with each coin touching two other coins. Two of the coins are special and the rest are

ordinary. Alok starts and the players take turns removing an ordinary coin of their choice

from the circle and bringing the other coins closer until they again form a (smaller)

circle. The goal is to bring the special coins adjacent to each other and the first player todo so wins the game. Initially the special coins are separated by two ordinary coins O1

and O2. Which of the following is true?

a) In order to win, Alok should remove O1 on his first turn.

b) In order to win, Alok should remove one of the coins different from O1 and O2 on his

first turn.

c) In order to win, Alok should remove O2 on his first turn.d) Alok has no winning strategy.

Answer: In order to win, Alok should remove one of the coins different from O1 and

O2 on his first turn.

Explanation: The 1stperson to move is always the winner if he is presented with a set up

such that there are even number of ordinary coins on one side and odd number of

ordinary coins on the other side of the special coins. In order to win, 1stplayer should

always remove the coins from the odd side.



12/46

The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7

billion. As one of the forerunners in the technology front, Tirnop continues to lead

the way in products and services in India. At Tirnop, all programmers are equal in

every respect. They receive identical salaries and also write code at the same rate.

Suppose 14 such programmers take 14 minutes to write 14 lines of code in total.How long will in take 5 programmers to write 5 lines of code in total ?

a)19 b) 5 c) 14 d) 70

Answer: 14minutes

Explanation: P1T1/L1= P2T2/L2

P---Number of Programmers

T---Time taken in Minutes

L--- Lines of codes to be written



13/46

45 suspects are rounded by the police and questioned about a bank robbery. Only

one of them is guilty. The suspects are made to stand in a line and each

person declares that the person next to him on his right is guilty. The

rightmost person is not questioned. Which of the following possibilities aretrue? A. All the suspects are lying. B. The leftmost suspect is guilty. C. The

rightmost suspect is guilty. Which is the logical combination of statements

a) A only b) A and C c) B only d) A and B

Answer: A and B

Explanation: Each of the suspects is blaming the person on the right (except therightmost one). The only person who is not blamed by anyone is the leftmost

person. So, if we assume that everyone is lying (Statement A) that will lead us

to the conclusion that the leftmost person is guilty (Statement B)



14/46

The dynamics of crowd behavior are hard to study because usually people are not

reliable witnesses of their own behavior. Now consider 4 people standing in the

queue of a supermarket. You want to predict their behavior based on their age

group. You get to know from the supermarket records that their average age 4

years ago was 43 years. After a while, another person joins the queue and thepresent average of all the 5 is 40 years. The present age of the last person in the

queue is :

a) 28 years b) 12 years c) 32 years d) 24 years

Answer: 12 years

Explanation: Average age of 4 person in the queue four years ago was 43 years.

Present average age of 4 of them = 47 years

So, sum of the ages of 4 of them = 47*4 = 188 years

Average Age of all 5 of them = 40 years

So, sum of the ages of all 5 of them = 40*5 = 200 yearsHence the age of the 5thperson is 200188 = 12 years



15/46

One day Snow-white meets Pal and Unicorn in the Fairyland. She knows the Pal

lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other

days of the week. Unicorn, on the other hand, lies on Thursdays, Fridays and

Saturdays, but tells the truth on the other days of the week. Now they make the

following statements to Snow-whitePal: Yesterday was one of those dayswhen I lie. Unicorn: Yesterday was one of those days when I lie too. What day

is it?

a) Tuesday b) Monday c) Thursday d) Sunday

Answer: Thursday

Explanation: Go Through Options. If you check for Thursday,

It is a TRUTH DAY for Pal and a LIE DAY for Unicorn.So, pal should tell the truth and Unicorn should lie on Thursday, which they are

doing when they mention that statement.



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The Barnes Foundation in Philadelphia has one of the most extra-ordinary and

idiosyncratic collections in French impressionist art. Dr. Barnes who put together this

collection has insisted that the paintings be hung in a particular manner specified by

him at a museum designed by the French architect Paul Philippe Cret who also

designed the Rodin Museum. The museum has, say, seven galleriesEugeneBoudin, Cassatt, Boudin, Forain, Gonzales, Manet and Monet. Visitors reach themain Eugene Boudin by an elevator, and they can enter and leave the exhibition only

through Eugene Boudin gallery. Once inside, visitors are free to move as they

choose. The following list includes all of the doorways that connect the seven

galleries: There is a doorway between Eugene Boudin and Cassatt, a doorway

between Eugene Boudinand Boudin, and a doorway between Eugene Boudin and

Gonzales galleries. There is a doorway between Cassatt and Boudin galleries. There

is a doorway between Gonzales and Forain and a doorway between Gonzales and

Manet galleries. There is a doorway between Manet and Monet galleries. Which of

the following rooms CANNOT be the third gallery that any visitor enters ?

a)Monet b) Boudin c) Forain d) Cassatt

Answer: MonetExplanation : Make a rough diagram and check.



17/46

Mr. Beans visited a magic shop and bought some magical marbles of different colors

along with other magical items. While returning home whenever he saw a colored light,

he took out marbles of similar colors and counted them. So he counted the pink colored

marbles and found that he has bought 25 of them. Then he counted 14 green marbles and

then 21 yellow marbles. He later counted 30 purple colored marbles with him. But when

he reached a crossing, he looked at a red light and started counting red marbles andfound that he had bought 23 Red marbles. As soon as he finished counting, it started

raining heavily and by the time he reached home he was drenched. After reaching home

he found that the red, green and yellow marbles had magically changed colors and

became white, while other marbles were unchanged. It will take 1 day to regain its

colors, but he needs to give at least one pair of marbles to his wife now. So how many

white marbles must be choose and give to his wife so as to ensure that there is at leastone pair of red, yellow and green marbles?

a) 46 b) 35 c) 29 d) 48

Answer: 46

Explanation: There are 23 red, 21 yellow and 14 green marbles. These are marbles which

are changing colors to white. We will take the worst case scenario, i.e. despite pickinga certain number of marbles, Mr Beans is not sure of picking at least 2 of each color.So, for that we add the two bigger numbers 23 and 21 and then add 2 more to it. So

worst case scenario is

23 red + 21 yellow + 2 Green = 46 marbles. Minimum that is the number which he has to

pick in order to be sure of having at least one of each color



18/46

In the reading room of a library, there are 23 reading spots. Each reading spot consists of a

round table with 9 chairs placed around it. There are some readers such that in each

occupied reading spot there are different numbers of readers. If in all there are 36 readers,

how many reading spots do not have even a single reader?

a)8 b) none c) 16 d) 15Answer: 15

Explanation: start with 1 reader on 1streading spot

2 readers on 2ndreading spot

3 readers on 3rdreading spot and so on

36 readers in this manner will occupy 8 reading spot as1+2+38 = 36. So, 23-8=15 reading spots would be vacant

NOTE:Sometime this question comes with 10 reading spots and 4 chairs on each spot.

Answer in that case is 6 spots would remain vacant.



19/46

Susan made a block with small cubes of 8 cubic cm volume to make a block, 3 small cubes

long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more

small cubes than she really needed. She realized that she could have glued a fewer

number of cubes together to lock like a block with same dimensions, if it were made

hollow. What is the minimum number of cubes that she needs to make the block?a)114 b) 135 c) 21 d) 71

Answer: 114

Explanation: Total number of small cubes = 3X9X5 = 135

Total number of small cubes to be removed to make a hollow block = 1X7X3 = 21

So, number of small cubes required would be 135-21 = 114 cubes

NOTE: If there are is a cuboid of p X q X r small cubes, number of small cubes in the core

(beneath the outer surface) would be (p-2) X (q-2) X (r-2).



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21/46

A car manufacturer produces only red and blue models which come out of the final testingarea completely at random. What are the odds that 5 consecutive cars of the same colorwill come through the test area at any one time?

a) 1 in 16 b) 1 in 12 c) 1 in 32 d)1 in 25

Answer: 1 in 16Explanation: for five consecutive times the probability of a particular color car coming out

is ()5. But there are 2 colors, so either of them coming out 5 consecutive times wouldbe

2 X ()5 = ()4= 1/16

Note: If there are n cars of the same color, answer would be 1/2n-1or 1 in 2n-1.

-------------------------------------------------------------------------------------

A scientist was researching on animal behavior in his lab. He was very interested inanalyzing the behavior of bear. For some reason he travelled 1mile in north direction &reached at North Pole. There he saw a bear. He then followed the bear around 1 hr with aspeed of 2km/hr in east direction. After that he travelled in south direction & reached at

his lab in2 hrs. Then what is the color of the bear?a) White b) Black c) Gray d) Brown

Answer: White

Explanation: Polar bears come only in one color i.e. white, unless they are wearing blackjackets due to the cold weather!



22/46

A person has to make 146 pieces of a long bar. He takes 4 seconds to cut a piece.

What is the total time taken by him in seconds to make 146 pieces?

a) 584 b) 580 c) 730 d) 725

Answer: 580

Explanation:146 pieces would require 145 cuts. So total time would be 145* 4 = 580

seconds

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A Person buys a horse for 15 pounds, after one year he sells it for 20 pounds. Afterone year, again he buys the same horse at 30 pounds and sells it for 40 pounds.

What is the profit for that person?

Answer: 15 pounds

Explanation: In the 1sttransaction there is a profit of 5 pounds and in the 2ndone, 10

pounds. Total profit = 15 pounds



23/46

A lady has fine gloves and hats in her closet- 13 blue, 27 red, and 40 yellow gloves

are there. The lights are out and it is totally dark. In spite of the darkness, she can

make out the difference between a hat and a glove. She takes out an item out of the

closet only if she is sure that if it is a glove. How many gloves must she take out to

make sure she has a pair of each color?Answer: 69 gloves

Explanation: Two largest values + 2 more.

40+ 27 + 2 = 69

NOTE: Just like Mr. beans this problem would be solved by the same logic



24/46

If there are 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find

the possible number of 2 wheelers parked there if there were 58 wheels parked there.

a)10 b) 23 c) 22 d) none

Answer: 23

Explanation: 2a + 4 b = 58. a and b are no. of 2 & 4 wheelers respectively

So, a + 2b = 29 or 2b = 29a.

In the above equation, a has to be odd for b to be an integer.

NOTE:the above question comes with numerous variations and data. In all the cases choose

the odd value from the options.

------------------------------------------------------------------------------------One grandfather has three grandchildren, two of their age difference is 3, eldest child age is 3

times the 2ndchilds age and eldest childs age is two times of sum of other two children.What is the age of eldest child?

Answer: 18

Explanation: Take the ages of 3 grandchildren as a, a+3 and 3(a + 3)It is given that eldest childs age is twice the sum of other two children. So,

3(a+3) = 2 (2a + 3). From here a = 3 and eldest childs age is 18 years.



25/46

Consider two vessels, the first containing one liter of water and the second containing one

liter of Pepsi. Suppose you take one glass of water out of the first vessel and pour it into

the second vessel. After mixing you take one glass of the mixture from the second vessel

and pour it back into the first vessel. Which one of the following statements holds now?

None of the statements holds true.

There is less Pepsi in the first vessel than water in the second vessel.

There is more Pepsi in the first vessel than water in the second vessel.

There is as much Pepsi in the 1stvessel as there is water in the 2ndone

Answer: There is as much Pepsi in the 1stvessel as there is water in the 2ndone

Explanation: The process explained above will always lead to the same ratio of Pepsi and

water in the 1stas that of water and Pepsi in the 2ndvessel. In other words,

Vessel 1Water : Pepsi = a:b Vessel 2Pepsi : Water = a:b

NOTE: Even if the above process is repeated several times, the result explained above will

not change i.e. there will be as much Pepsi in the 1stvessel as there is water in the 2ndone

and vice-versa.



26/46

33 people {a1, a2,,a33} meet and shake hands in a circular fashion. In other words,there are totally 33 handshakes involving the pairs, {a1,a2}, {a2,a3},,{a32, a33},{a33, a1}. Then the size of the smallest set of people such that the rest have shaken

hands with at least one person in the set is

a)10 b)11 c)16 d)12

Answer: 11

Explanation: Always 1/3rdof the persons present will be taken out. Consider the set

{a2, a5, a8,..a32}. If we separate out these people from the original group,people who would be left in that group would have shaken hands with at least one

person in the new set. a2 with a1 and a3; a5 with a4 and a6 and so on. So the

smallest set possible is n/3 whereas n is the total number of people present.

NOTE: If n is not divisible by 3 then go to the next number which is divisible by 3and find 1/3rdof that number. For ex- if n=80, answer is 27 (81/3).



27/46

A greengrocer was selling watermelon at a penny each, chickoos at 2 for a penny and

peanuts at 3 for a penny. A father spent 7p and got the same amount of each type of

fruit for each of his three children, Jane, Joe and Jill. Jane is three years older than

Jill and Joe is exactly half the age of Jane and Jill together. What did each child

get?

a) 1 watermelon, 3 chickoos, 2 peanuts

b) 1 watermelon, 1 chickoo, 1 peanuts

c) 1 watermelon, 2 chickoos, 2 peanuts

d) 1 watermelon, 2 chickoos, 1 peanut

Answer: 1 watermelon, 2 chickoos, 1 peanut

Explanation: The share of each of the children would be 7/3 p. The only option

which would ensure 7/3 p for each child is option (d).

1 watermelon----1p

2 chickoos ------1p

1 Peanut---------1/3 p

7/3 P



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32/46

The question is followed by two statements, A and B. Answer the question using the

following instructions: Choose1: if the question can be answered by using one of the

statements alone but not by using the other statement alone. Choose2: if the question can

be answered by using either of the statements alone. Choose3: if the question can be

answered by using both statements together but not by either statement alone. Choose4:

if the question cannot be answered on the basis of two statements. Tarun is standing 2

steps to the left of a green mark and 3 steps to the right of a black mark. He tosses a coin.

If it comes up heads, he moved 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 stops? A: he stops at 21 coin tosses. B: he obtains three more tails

than heads.a) 1 b) 3 c) 4 d) 2

Answer: 2 i.e. the question can be answered by using either of the statements alone

Explanation: If HT =2, then Tarun will stop at Black mark.

If TH = 3, then Tarun will stop at Green mark.

Statement A: He stops at 21 tosses=>

H + T = 21. It means, out of H & T, one is even andthe other one is an odd number. In that case their difference would also be odd. The only

possible case of an odd difference is TH = 3, in which case he stops at Green mark.

Statement B: Here it is directly given that TH = 3, which again takes us to the conclusionthat Tarun stops at Green mark



33/46

There are two water tanks A and B, A is much smaller than B. While water fills at the

rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B.

(At the end of first hour, B has 10 litres, second hour it has 20, and so on). If tank B

is 1/8 filled after 5 hours, what is the total duration required to fill it completely?

(a)9 hours (b)7 hours (c)3 hours (d)8 hours

Answer: 8 hours

Explanation: If 1/8this filled in 5 hours, then the volume filled in 5 hours = 310 Ltrs.

So, total volume of the tank = 310 X 8 = 2480 Ltrs.

In the 6th, 7th& 8thhour volumes filled would be 320, 640 & 1280 Ltrs.

So, total volume filled at the end of 8thhour = 2550 Ltrs.

Hence It will take 8 hours to fill the tank.

NOTE: Consider the statement, If tank B is 1/8 filled after 5 hours, given in the question.In that 1/8 = 1/23. Take the exponent of 2 in the denominator i.e. 3 and add it to 5 hours. The

answer will be the sum i.e. 8 hours

So, if 1/2nof B is filled after thours, total time taken would be n+t hours


A l f l b l i i h h i f l i i l i 13


34/46

A result of global warming is that the ice of some glaciers is melting. 13 years

after the ice disappears, tiny plants, called lichens, start to grow on the rocks.

Each lichen grows approximately in the shape of a circle. The relationship

between the diameter of this circle and the age of the lichen can be

approximated with the formula: d=10*(t13) for t > 13, where d representsthe diameter of the lichen in millimeters, and t represents the number of years

after the ice has disappeared. Using the above formula, calculate the diameter

of the lichen, 45 years after the ice has disappeared.

(a) 450 (b)437 (c)13 (d)320

Answer: 320

Explanation: Just substitute 45 in place of t in the formula given.NOTE: Sometimes the expression for d = 4 (t 8) for t > 8 and value to t is given as

24. The answer is 16 mm

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Rearrange the following letters to make a word and choose the category in which it

fits RAPETEKAa) Bird b) Vegetable c) City d) Fruit

Answer: Bird

Explanation: Re-arranging the above letters results in PARAKEET which is a Bird.



35/46

Ferrari S.P.A. is an Italian sports car manufacturer base in Maranello , Italy. Founded

by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored driver and

manufactured race cars before moving into production of streetlegal vehicles in1947 as Ferrari S.p.A. Throughout its history, the company has bee noted for its

continued participation in racing, especially in Formula One, where it has enjoyed

great success. Rohit once brought a Ferrari.It could go 2 times as fast asMohits

old Mercedes. If the speed ofMohitsMercedes is 40 Km/hr and the distance

traveled by the Ferrari is 913 Km, find the total time taken for Rohit to drive the

distance.

(a) 12 Hours (b)22 Hours (c)456 Hours (d)11.41 Hours

Answer: 11.41 HoursExplanation: Read the italics part of the question. Ferrari is twice the speed of

Mercedes.

Speed of Mercedes is 40 km/hr so, speed of Ferrari would be 80 Km/hr. So time taken

to cover 913 Km would be

Time = distance /speed

Time = 913Km / 80Kmph = 11.41 Hours



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37/46

A sheet of paper has statements numbered from 1 to 20. For all values of n from 1 to

20, statement n says: Exactly n of the statements on this sheet are false. Which

statements are true and which are false?

a) The even numbered statements are true and the odd numbered statements are false.

b) All the statements are false.c) The odd numbered statements are true and the even numbered statements are false.

d) The second last statement is true and the rest are false.

Answer: The second last statement is true and the rest are false.

Explanation: In case of Exactly.Falsecombination, 2ndlast statement is the only

statement to be true, rest are false.



38/46

A sheet of paper has statements numbered from 1 to 20. For each value of n from 1 to

20, statements n says At least n of the statements on this sheet are true. Which

statements are true and which are false?

a) The odd numbered statements are true and the even numbered are false.

b) The first 13 statements are false and the rest are true.c) The first 6 statements are true and the rest are false.

d) The even numbered statements are true and the odd numbered are false.

Answer: The first 6 statements are true and the rest are false.

Explanation: In case of At Least.True combination, 1stany number of statementscan be true and the rest would be false.

NOTE: Instead of 1st6 statements, there can be other answers like 1st8, 1st15, or all

20 statements are true. Look for the answer which is of the form 1stm statements

are true and rest are false. 0mn



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70. Statement n says ' At least n of the statements on this sheet are false . Whichstatements are true and which are false?

a) The even numbered statements are true and the odd numbered are false.

b) The odd numbered statements are true and the even numbered are false.

c) The first 35 statements are true and the last 35 are false.

d) The first 35 statements are false and the last 35 are false.

Answer: The first 35 statements are true and the last 35 are false.

Explanation: In case of At Least.Falsecombination, 1stn/2 statements are true restare false.

NOTE: At Least.False combination is only valid for even number of statements.



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55. Statement n says At most n of the statements on this sheet are True Whichstatements are true and which are false?

a) All the statements on the sheet are true

b) All the statements on the sheet are falsec) The first 27 statements are true and the rest are false.

d) The first 27 statements are false and the rest are true.

Answer: The first 27 statements are false and the rest are true

Explanation: In case of At Most.True combination, 1st(n-1)/2 statements are false

rest are true. For n = 55, (n-1)/2 = 27

NOTE:At Most.True combination is only valid for odd number of statements.



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40. Statement n says At most n of the statements on this sheet are False Whichstatements are true and which are false?

a) All the statements on the sheet are true

b) All the statements on the sheet are falsec) The first 20 statements are true and the rest are false.

d) The first 20 statements are false and the rest are true.

Answer: All the statements on the sheet are true

Explanation: In case of At Most.False combination, all statements are true is the

only valid logic



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A i l i d f Th id f h i l 21 24 d 28


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A triangle is made from a rope. The sides of the triangle are 21 cm, 24 cm and 28 cm.

What will be the area of the square made from the same rope?

a) 280.5625 b) 333.0625 c) 245.0125 d) 400

Answer: 245.0125

Explanation: Use Heros formula s(s-a)(s-b)(s-c)S = (a+b+c)/2 = 73/2 = 36.5. So, the value is 245.1

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a, b & c measured their weights in the following manner. 1sta, b, c weighed

themselves separately then a& b, b & c and c & a weighed themselves in pairs. At

last a, b & c weighed themselves together. The last weight was 167,then what willbe the average weight of the 7 reading?

Answer: 95.2

Explanation: There are 7 weighing in total.

Sum of 1stthree is a+b+c; Sum of next three is 2(a+b+c)

Last one is a+b+cSo, Sum of all 7 weighing is 4(a+b+c) and average = 4(a+b+c)/7

Substitute a+b+c = 167

NOTE: Instead of 167 there can be other data. Just multiply that with 4/7 in order ot

get the average.



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Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were

responsible for the Irish potato famine of the mid-19th century. These seem to have attacked the

tomato crops in England this year. The tomato crops have reduced and the price of the crop has

risen up. The price has already gone up to $45 a box from $27 a box a month ago. How much more

would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid

last month?

a) $276 b) $418 c) $456 d) $486

Answer: $486

Explanation:Difference between old and new price is $45 - $27 = $18

Total difference in payment is $18/box X 27 boxes = $486

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What is the distance between the z-intercept from the x-intercept in the equation ax+by+cz+d=0

Answer: d (1/a2+ 1/c2)1/2

Explanation: For finding the X intercept, put y=z=0. x= -d/a. Similarly, for Z intercept , put x=y=0.

So z=-d/c.

Now by using distance formula, find the distance between (-d/a,0,0) and (0,0,-d/c)

The distance is d (1/a2+ 1/c2)1/2

NOTE: In test, there would be constant values used instead of a, b, c & d. Use the above result

accordingly.



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Gradient TCS Questions Explanation

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