Below are some of the TCS Sample Aptitude Questions Solved

1. A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters at 10 meters per minute. However, the toy train is defective and it now produces only two different tunes at random. What are the odds that the toy train produces 4 consecutive music tunes of the same type?

Ans 1 in 8

2. A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21. What is the remainder left, when twice the number is divided by 3D?

Ans 3

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

c) 1 in 16

ci) 1 in 125

cii) 1 in 32

ciii) 1 in 25

4. Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari , the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Feraari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success .Rohit once bought a Ferrari . It could go 4 times as fast as Mohan’s old Mercedes. If the speed of Mohan’s Mercedes is 46 km/hr and the distance traveled by the Ferrari is 953 km, find the total time taken for Rohit to drive that distance.

20.72

5.18

238.25

d) 6.18 (solution:b)

5. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ‘ At least n of the statements on this sheet are false. ‘Which statements are true and which are false?

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

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

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

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

(solution:d)

6. Middle – earth is a fictional land inhabited by Hobbits, Elves, dwarves and men. The Hobbits and the Elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows . A tournol is one where out of the two teams that play a match, the one that loses get eliminated. The matches are played in different rounds where in every round , half of the teams get eliminated from the tournament. If there are 8 rounds played in a knock-out tournol how many matches were played?

257

256

72

d) 255 (solution:d)

7. Consider two tumblers, the first containing one litre of coffee. Suppose you take one spoon of water out of the first tumbler and pour it into the second tumbler. After moving you take one spoon of the mixture from the second tumbler and pour it back into the first tumbler . Which one of the following statement holds now?

There is less coffee in the first tumbler than water in the second tumbler.

There is more coffee in the firs tumbler than water in the second tumbler

There is as much coffee in the first tumbler as there is water in the second tumbler

None of the statements holds true.

8. a circular dashboard of radius 2.0 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 perphery?

.75

.25

1.00

.50

9. A horse chases a pony 2 hours after the pony runs.Horse takes 3 hours to reach the pony.If the average speed of the horse is 81Kmph.Then what is the average speed of the pony?

Ans 48.6

10. Alok is attending a workshop “How to do more with less” and today’s theme is Working with fewer digits. The speakers discuss how a lot of miraculous mathematics can be achieved if mankind(as well as womankind) had only worked with fewer digits.

The problem posed at the end of the workshop is

How many four digit numbers can be formed using the digits 1, 2,3,4 ,5 ( but with repetition) that are divisible by 4?

Can you help Alok find the answer?

a) 100 b) 125 c) 75 d) 85

11. Rearrange the following letters to make a word and choose the category in which it Ms RAPETEKA

Bird

Vegetable

City

Fruit

12. On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula

d = 4*√ (t-9) for t ≥ 9

where d represents the diameter in mm and t the number of years since the solar blast.

Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?

17

21.25

12.25

d) 12.06 (solution:b)

13. A lady has fine gloves and hats in her closet- 18 blue- 32 red and 25 yellow. The lights are out and it is totally dark inspite 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 colour?

50

8

60

42

14. Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. 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 to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of the following is true ?

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

In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.

In order to win, Alok should remove O2 on his first turn.

Alok has no winning strategy.

15. The pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed in kmph.

Ans 23.62

16. In a shopping mall with a staff of 5 members the average age is 45 years. After 5 years a person joined them and the average age is again 45 years. What’s the age of 6th person?

Ans 20

17. Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter?

Ans 20 years

18. Alok and Bhanu play the following min-max game. Given the expression N = 15 + X+(Y â€“ Z) Where 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?

Ans 24

19. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter 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 liters, second hour it has 20 liters and so on). If tank B is 1/32 filled of the 21 hours, what is total duration of hours required to fill it completely?

a) 26 B)25 c)5 d)27

20. For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A,s chances of winning.

Let,s assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?

4/9

2/3

1/9

5/9

Solution:(1/3*1/3)+(2/3*2/3)=5/9

21. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base

buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?

256

54

192

64

Solution:From 1 to 1000 number of 3’s are 300.

Since they mentioned 8 fingered we have to take base 8.

i.e., (3*(8^2))+(0*(8^1))+(0*(8^0))=192

answer is 192

22. 36 people {a1, a2, ., a36} meet and shake hands in a circular fashion. In

other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3},…., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

12

13

18

11

Solution: for at least one person & for exactly one person =36/3

for at least two person & for exactly two person =36/2

23. 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

4

3

1

Solution: For 3 lines of intersection the answer is 4

For 3 linesegments of intersection the answer is 1

24. 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?

12/212

11/12

1/12

25. 10 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 are true?

A. All suspects are lying or the leftmost suspect is innocent.

B. All suspects are lying and the leftmost suspect is innocent .

A only

Neither A nor B

Both A and B

B only

Answer:

All suspects are lying or the leftmost suspect is innocent.

All suspects are lying and the leftmost suspect is innocent .

Both can satisfy the situation so answer is “Both A and B”

26. There is 7 friends (A1, A2, A3….A7).If A1 have to have shake with all without repeat. How many handshakes possible?

a) 6

b) 21

c) 28

d) 7

Solution:6

27. On the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 9:40 am.

a. 251

b.111

c.29

d.89

Ans.: c

For 12:40 am Ans.. z 89

Formule: 20H-(34/9)M

28. A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

800

500

488

900

Ans.:side of cube = 5 cm

its thichness = 1 cm

so volume of outer cube = 5*5*5

volume of inner cube = 3*3*3

volume of the hollow cube = 5*5*5 â€“ 3*3*3 = 98

so total no of small cubes of the size 1 cm = 98/1*1*1 = 98

we know a cube has 6 faces so total no of face = 98*6 = 588

one surface of outer cube contains a total of 25 surface of smaller cube , so when 4 surface of outer cube is painted total no of surface of small cubes i.e supposed to be painted is 4*25 = 100

so the total no of surfaces of small cube that will be remained unpainted is 588-100 = 488

no of faces remain unpainted: 588-( 25* no faces painted)

29. 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 Ans. also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?

Ans. 12 min

prgrmr*min/ loc= prgmr *min/ loc

a) no of Programmer

b) no lines of codes

c) how much time they will take

30. There are 1000 pillars for a temple. 3 friends Linda, Chelsea, Juli visited that temple. (Som unrelated stuff) Linda is taller than Chelsea and taller than 2 of 1000 pillars. Juli is shorter than Linda. Find the correct sentence?

a) Linda is shorter among them

b) Chelsea is taller than Juli

c) Chelsea is shorter than Juli

d) Cannot determine who is taller among Chelsea and Juli

Ans: Cannot determine who is taller among Chelsea and Juli

31.A scientist was researching on animal behavior in his lab. He was very interested in analyzing the behavior of bear. For some reason he traveled 1mile in north direction and reached at North Pole. There he saw a bear he then followed the bear around 1hr with a speed of 2km/hr in east direction. After that he traveled in south direction and reached at his lab in 2 hrs. Then what is the colour of the bear?

Ans white

32. Anoop managed to draw 5 cricle of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the ratio of the side of the square to radius of the circles. you may assume that square root of 2 is 1.4

7.60:1

12.50:1

10.50:1

9.00:1

33. For the king’s revelry 30 barrels of beer have b een ordered . howerver, it was found that one of them is poisoned. The poison takes effect even if consumed in the tiniest amount after 14 hours. Yhou need to find within 24 hours the poisoned barrel and have at your disposal some beer guzzling mice. The smallest number of mice required to find the poisoned barrel is

1) 2

2) 1

3) 4

4) 3

hint: 2^n> no of barrels ans:4

34.A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare I the other. The hare starts after the tortoise had coveredc 1/7 of its distance and that tooo leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor shoul the hare increase its speed so as to ties the reace?

8

41.00

56

7

Ans: 1/7, 1/8

7*8=56

56-7=49

49-8=41

49*41/7^2=41.00

35. John buys a cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper exchanged the cheque with his neighbor and gave change to John. After 2 days, it is known that cheque is bounced. Shop keeper paid the amount to his neighbor. The cost price of cycle is 19 dollars. What is the profit/loss for shop keeper?

a)loss 23 b)gain 23 c)gain 54 d)Loss 54

Ans: a hint: 19+4=23