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TCS Previous Years Aptitude Questions 2012 Written Test Questions
1. Alok and Bhanu play the following min-max game. Given the expression N = 19 + X * (Y - 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
O 100
O 019
O -62
O 37
2. The number of bacteria in a colony was growing exponentially. At 4 pm yesterday the number of bacteria was 400 and at 6 pm yesterday it was 3600. How many bacteria were there in the colony at 7 pm yesterday?
O 3600
O 10800
O 32400
O 14400
3. A multiple choice question has 4 options. Choosing the correct option earns the student 3 marks. However choosing the wrong option incurs negative marks so that if a student chooses an option randomly, his expected score is 0. Suppose a student has successfully eliminated 2 incorrect options. His expected score if he chooses randomly among the remaining options is.
O 1.00
O 1.50
O 00
O 3
4. 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 minutes while each minute has 60 seconds. 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 12:40 am.
O 111 degrees
O 251 degrees
O 71 degrees
O 89 degrees
5. You're going to get grounded for a week if you don't get at least 80% in your science class. So far you have 237 of the total 300 points. The final test is worth 100 points. What is the minimum score you need to get on the final test? Assume the teacher rounds properly.
O 93
O 80
O 83
O 100
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 tournoi 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 tournoi how many matches were played?
O 257
O 72
O 255
O 256
7. 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. 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
O In order to win, Alice's first move can be a 0-move or a 1-move.
O In order to win, Alice's first move should be a 1-move.
O In order to win, Alice's first move should be a 0-move.
O Alice has no winning strategy.
8. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of S7 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 some rate. Suppose 20 such programmers take 20 minutes to write 20 lines of code in total. How long will it take 5 programmers to write 5 lines of code in total?
O 25
O 20
O 100
O 5
9. Achilles was the son of the nymph Thetis and Peleus, the king of the Myrmidons. Zeus and Poseidon had been rivals for the hand of Thetis until Prometheus, the fire-bringer, warned Zeus of a prophecy that Thetis would bear a son greater than his father. For this reason, the two gods withdrew their pursuit, and had her wed Peleus. The following statement is another interesting prophecy about the ages of two childen of Zeus that would hold true at some time during the lifetime of the children. 4 years ago, Athena's age was twice Helen's age. 4 years hence, Athena's age will be 4/3 times the age of Helen. Find Athena's present age in binary numbers during the time that the statement holds true.
O 100
O 1001
O 101
O 1100
10. 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 the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
O 11
O 18
O 12
O 13
11. Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n = ………………?
O 25
O 10
O 2
O 5
12. There are two boxes, one containing 32 red balls and the other containing 31 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 is
O .25
O .51
O .75
O .50
13. A man has some socks in his drawer - 18 identical blue, 24 identical red, and 22 identical black. The lights are out and it is totally dark. How many socks must he take out to make sure he has a pair of each colour?
O 32
O 48
O 42
O 34
14. A cyclist buys a cycle for 29 pounds paying with a 50 pound cheque. The seller changes the cheque next door and gives the cyclist change. The cheque bounces so the seller paid his neighbour back. The cycle cost the seller 12 pounds. How much did the seller lose?
O 33 pounds
O 12 pounds
O 50 pounds
O 41 pounds
15. The original price of a car was $23600. Because the car owner thought he could get more money for the car, he increased the price of the car to 160% of its original price. After a week, the car had not sold, so the owner then discounted the price by 20%, the car was finally sold. What price was the car sold for?
O 30208 $
O 37760 $
O 23600 $
O 7552 $
16. The chairman of Tata Motors, Ratan Tata, had 300 engineers work for 5 years designing the world's lowest-cost car, convinced that cost-conscious Indian drivers could live without air-conditioning and cup holders. However, after the booking started they found that only 23 percent of initial 253850 orders for the car - the Nano - were for the no frills $2600 model. How much time (in days) would it have taken if there were 500 employees working for double the time?
O 547.50
O 3041.67
O 1095.00
O 450.00
17. Earl can stuff advertising circulars into envelops at the rate of 36 envelopes per minute and Ellen requires a minute and a half to stuff the same number of envelopes. Working together, how long will it take Earl and Ellen to stuff 360 envelopes?
O 6 minutes
O 5 minutes
O 7 minutes
O 3 minutes
18. In 1911, a French physicist Paul Langevin, devised a thought experiment based on Einstien's Special Relativity. In the experiment, a person makes a journey into space at nearly the speed of light and comes back to earth. He finds that he has aged five times less than his twin who stayed back on earth for 40 years. This is popularly known as the Twin Paradox. Now, consider the case of Hansel and Gretel, who are not twins. 9 years ago, Hansel was twice as old as Gretel. If they journey into space, an atomic clock assists in logging the start time of their journey accurately. If they do not journey into space, 9 years hence, Hansel's age will be 413 times the age of Greters. Find Hansel's age today in binary numbers.
O 11000
O 11011
O 1010
O 1001
19. Recent reports have suggested that sportsmen with decreased metabolic rates perform better in certain sports. After reading one such report, Jordan, a sportsperson from Arlington decides to undergo a rigorous physical training program for 3 months, where he performs Yoga for 3 hours, walks for 2 hours and swims for 1 hour each day. He says: I began my training on a Wednesday in a prime number month of 2008. I lost 1% of my original weight within the first 30 days. In the next two months combined, I lost 1 Kg. If he walks at 6 mph over a certain journey and walks back over the same route at 8 mph at an altitude of 200 meters, what is his average speed for the journey?
O 48.00
O 6.86
O 3.43
O 7.00
20. Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P) over all configurations P of 11 points in the plane is
O 11
O 5
O 12
O 10
21. Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 31, the number of points equidistant from all the 3 lines is
O 3
O 4
O 0
O 1
22. 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 11/12 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
O .01
O .85
O .15
O .92
23. A result of global warming is that the ice of some glaciers is melting. 12 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 =5* (t -12) for t >12, where d represents the 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, 49 years after the ice has disappeared.
O 185
O 12
O 245
O 233
24. 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 5 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?
O 625
O 250
O 781
O 782
25. Elephant competitions are of great entertainment value in south India. In one such competition held in Cochin, 200 elephants participated. Each elephants was given equal amount of milk to drink for a certain time period. Whichever elephant could drink the maximum would be the winner. One of the elephants named Garru could drink 1/3 of the amount of milk offered. Another elephant named Marta could drink only 1/20 of the amount of milk offered, but it was better than Thorny which could drink 2/45 of the amount of milk offered. Amazingly Darru could drink 6 litres more than 1/4 of the amount of milk offered, where as Malar could drink 2/15 of the amount of milk offered. If the amount of milk left over by the elephants Garru and Darru were same, then calculate the total amount of milk offered to each elephant.
O 73.00 litres
O 71.00 litres
O 12.00 litres
O 72.00 litres
26. Planet Fourfe resides in 4-dimensional space and thus the currency used by its residents are 3-dimensional objects. The rupee notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins. A. The diameter of the coins should be at least 4mm and not exceed 8mm.B. Given a coin, the diameter of the next larger coin is at least 50% greater.C.The diameter of the coin must always be an integer. You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design?
O 3
O 0
O 1
O 2
27. The citizens of planet Oz are 4 fingered and thus have developed a number system in base 4. A certain street in Oz contains 100 buildings numbered from 1 to 100. How many 1's are used in numbering these buildings? Express your answer in base 10.
O 5
O 8
O 4
O 12
28. 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 13 such programmers take 13 minutes to write 13 lines of code in total. How many programmers would it take to write 91 lines of code in 91 minutes?
O 13
O 7
O 91
O 20
29. A sheet of paper has statements numbered from 1 to 16. For all values of n from 1 to 16, statement n says 'At least n of the statements on this sheet are false.' Which statements are true and which are false?
O The even numbered statements are true and the odd numbered are false.
O The odd numbered statements are true and the even numbered are false.
O The first half of the statements are true and the last half statements are false.
O The first half of the statements are false and the last half statements are true.
30. For the King's revelry 254 barrels of beer have been ordered. However, it was found that one of them is poisoned. The poison takes effect even if consumed in the tiniest amount after 14 hours. You 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
O 9
O 8
O 254
O 7
31. Dollar stores, the stores which sell all of their merchandise for $1, have long had a reputation for being down-at-the-heels places to buy cheap, generic goods. While keeping their low prices, they are revamping their image and climbing the respectability ladder, in some cases to the Fortune 500. One such dollar store which recently made an entry in the Fortune list which has 3800 stores all over the United States, said that they had a 4 percent increase in the number of transactions in 2008 compared with the previous year to 32 million. The company made a profit of $22 million this year. What is the average profit per store?
O 5.79 thousand $
O .58 thousand $
O 17.37 thousand $
O 8.42 thousand $
32. Mr. Bean visited a magic shop and bought some magical marbles of different colours along with other magical items.While returning home whenever he saw a coloured light, he took out marbles of similar colours and counted them. So he counted the pink coloured marbles and found that he has bought 25 of them. Then he counted 18 green marbles and then 46 yellow marbles. He later counted 30 purple coloured marbles with him. But when he reached a crossing , he looked at a red light and started counting red marbles and found that he had bought 45 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 colours and became white, while other marbles were unchanged. It will take 1 day to regain its colours, but he needs to give atleast one pair of marbles to his wife now. So how many white marbles must he choose and give to his wife so as to ensure that there is atleast one pair of red , yellow and green marbles?
O 54
O 95
O 93
O 64
33. A police car starts chasing a fugitive in a BMW 3 hours after the BMW escapes from the scene of crime at 10 AM. The BMW drives for 10 Km through the crowded roads of Shanghai and then drives into a highway, where the traffic allows vehicles to move twice as fast. After a while, the police car finally catches up with the BMW after a chase that lasted 4 hours. By this time the moon was up in the sky for 4 hours. If the average speed of the police car is 83 kmph, then the average speed of the BMW is …………….. kmph.
O 35.57
O 47.43
O 48.43
O 11.86
34. 19 people (a1, a2, ….. , a19) are invited to a party. The host and the hostess shake hands with each invitee and also with each other. The invitees shake hands in a circular fashion, i.e. the pairs (a1, a2),(a2, a3),……..,(a18, a19),(a19, a1) shake hands. So, in all there are 58 handshakes. Let S be a set of people such that every pair in S shake hands. The size of S is at most
O 2
O 3
O 1
O 4
35. 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?
O 500
O 488
O 900
O 800
