TCS Xtra Aptitude Questions 3/3
51) Franchois Pachet, a researcher at Sony Computer Science Laboratories is also a jazz musician. He decided to build a robot able to improvise like a pro. Named Continuator, the robot duet can with alive musician in real- time. It listens to a musical phrase and then computes a complementary phrase with the same playing style. If the cost of making the robot is divided between materials, labour and overheads is the ratio of 4:5:2. If the materials cost $ 84.0, the cost of the robot is
(a) 184.80 $ (b) 189.00 $ (c) 231.00 $ (d) 462.00 $
Soln:
x*4/11 = 84
x = 231
Ans: c
52) The great Indian mathematician Bhaskaracharya formulated this problem in the twelfth century for his teenaged prime number aged daughter Lilavati. He also authored the eponymous Lilavati, a compendium of mathematical puzzles, in which the number of problems that use this formula is the sum of two prime numbers. The product of the two prime numbers is smaller than the total number of problems in the Lilavati. Now, if the difference of any two numbers is 4 and their product is 18, what is the sum of their squares?
(a) 34 (b) 40 (c) 52 (d) 42
Soln:
x-y = 4
x*y = 18
x^2 + y^2 = (x-y)^2 + 2*x*y
= 16+36
= 52
Ans: c
53) A taxi driver commenced his journey from a point, and drove 10 km towards north, and turned to his left and drove another 20 km. After waiting to meet a friend here he turned to his right and continued to drive another 50 km. In which direction is he now?
(a) North (b) South (c) West (d) East
Soln: North
Ans: a
54) A result of global warming is that the ice of some glaciers is melting. Twelve years after the ice disappears tiny plants, called lichens, start to grow on the rocks. Each lichens 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 = 13 * (t-11) for t > 11 where d represents the diameter of the lichen in millimetres, and t represents the number of years after the ice disappeared. Using the above formula, calculate the diameter of the lichen, 36 years after the ice has disappeared.
(a) 468 mm (b) 457 mm (c) 325 mm (d) 11 mm
Soln:
d = 13 * 25
= 325
Ans: c
55) The British mathematician Lewis Caroll also loved to make up fantastic stories in which he embedded a number of clever puzzles and curious riddles. For example, his popular story, Alice in Wonderland, is about young girl called Alice who dreams of a strange world where she meets several unusual characters including the Red Queen and the March hare. In our story, after 2 years of time, Paul will be twice as old as Alice. Presently he is 6 times as old. How old is Paul now?
(a) 2 (b) 4 (c) 3 (d) 6
Soln:
x y be ages,
x = 6y
x+2 = 2(y+2)
-2 = 4y - 4
y = 1/2
x =3
Ans: c
56) A long, thin strip of width 10cm is kept on a flat surface. Another identical strip is kept on it as an overlapping manner such that the combined width of the two is 15cm.What is the width if 22 such strips kept like this?
(a) 115 cm (b) 110 cm (c) 200 cm (d) 95 cm
Soln:
total width = 10+ 21*5
= 115
Ans: a
57) 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 produces3music tunes of the same type (1 in _____ ) ?
(a) 3 (b) 9 (c) 8 (d) 4
Soln:
prob= 1/2*1/2*1/2
= 1/ 8
Ans: c
58) Fill dirt or fill soil is usually the sub-soil removed from an excavation side and is used to level a place or create artificial mounds. If the average density of sub—soil removed from a site is 3gm/cu cm and it weight 400 kg. How many hemispherical pits each of volume 240 cubic cm, can this sub-soil fill?
(a) 555 (b) 277 (c) 556 (d) 554
Soln:
d = 3gm/cu cm = m/v
mass of pit = v*d
= 240*3
= 720
no of pits = 400*1000 / 720
= 555.556
Ans: a
59) The New York Public library is one of the world’s greatest repositories of books and journals. It has a beautiful reading room facing Manhattan’s famous Fifth Avenue. In the reading rooms are 10 reading spots. Each reading spot consists of a round table with 4 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 10 readers, how many reading spots are empty?
(a)None (b)6 (c)5 (d)4
Soln: see TCS Aptitude Questions: Pattern2
Ans: b
60) A group of friends Tom, Tim, Dick, Diana, Harry, and Harriet go out to a fair three hundred meters from the Mc.Donalds which is five KMs away. They see a weighing machine and decide to have some fun. However the girls refuse to step on the weighting machine. So Tom,Dick and Harry, weigh themselves in a particular order. First Tom, Dick, and Harry weigh themselves individually and then tom and Dick, Dick and Harry, Tom and Harry and then Tom, Dick and harry together respectively. The recorded weight for the last measure is 158 kgs. The average of all the 7 measures is
(a) 112.86 (b)52.67 (c)90.29 (d)67.71
Soln:
T+D+H = 158
T+D+H+(T+D)+(D+H)+(H+T)+(T+D+H) = 4*(T+D+H)
= 632
AVG = 632 /7
= 90.29
Ans: c
61) In the year 2002, Britain was reported to have had 4.3m closed-circuit televisions (CCTV) cameras–one for every 14 people in the country. This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogates two suspects. The ratio between the ages of the suspects is 6:5 and the sum of their ages is 66 years. After how many years will the ratio be 8:7?
(a) 11 years (b) 12 years (c) 6 years (d) 7 years
Soln:
x, y be ages,
x + y = 66
x/y = 6/5
x = (6/5)y
--> y (1+6/5) = 66
y = 66 * 5 / 11
= 30
x = 36
After 12 years , x =48, y=42
--> x/y = 8/7
Ans: b
62) A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?
a) All statements are false
b) The odd numbered statements are true the even numbered are false
c) All statements are true
d) The even numbered statements are true and the odd numbered are false
Soln:
Ans: a
63) 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) A only
(b) B only
(c) Both A and B
(d) Neither A nor B
Soln: see TCS Sample Aptitude Questions 4
Ans: a
64. The pace length 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 = pace length in meters. Bernard knows his pace length is 164cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed kmph.
(a) 236.16 (b) 11.39 (c) 8.78 (d) 23.62
Soln:
TCS Sample Aptitude Questions 4 - Recruitment 2011
Ans: d
65. Alice and Bob play the following coins-on-a-stack game. 20 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 (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 0-move.
(b) In order to win, Alice’s first move should be a 1-move.
(c) Alice has no winning strategy.
Soln:
Ans: b
66) Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals (after which the winner is decided by knockout). However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup?
(a) (2/3)^10 (b) (2/3)^9 + 8/3 * (2/3)^9
(c) 8/3 * (2/3)^9 (d) (2/3)^10 + 8/3*(2/3)^9
Soln:
Case 1:
win all 10, probability = (2/3)^10.
Case 2:
win 7 out of 8, prob = (2/3)^7
los 1 prob = 1/3
this can occur in 8 ways = 8 * (2/3)^7 * 1/ 3
win semi & final = (2/3)^2
--> prob = (2/3)^9 + (8/3)*(2/3)^9
Ans: b
67) A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?
a) The first 26 statements are false and the rest are true.
b) The odd numbered statements are true the even numbered are false
c) The first 13 statements are true and the rest are false.
d) The even numbered statements are true and the odd numbered are false
Soln:
n are true else false
Ans: c
68) There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one 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, and so on). If tank B is 1/32 filled after 11 hours, what is the total durations required to fill it completely?
(a)5 Hours (b) 15 Hours (c) 17 Hours (d)16 Hours
Soln:
Ans: d
69) A sheet of paper has statements numbered from 1 to 10. For all values of n from 1 to 10, statement n says At most n of the statement on this sheet is false. Which statements are true and which is false?
(a) All the statements are FALSE
(b) The odd numbered statements are true and the even numbered are false.
(c) The first half statements are true and the rest are false.
(d) The even numbered statements are true and the odd numbered are false.
Soln:
Ans: a
70) A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 90. What could be possible number of bicycles?
(a)12 (b) 14 (c) 10 (d)11
Soln:
2x+4y = 90
x=11 -->
4y = 90 -22
y = 68/4
= 17
Ans: d
71.Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling as to who gets to first cut and has a piece of the cake. One friend suggests that they blindfold a friend and then choose from a well shuffled set of cards numbered from one to six. You check and find that this method works as it should be simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfolding and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums up to a number between 2 and 12. Which total would be likely to appear more often – 8, 9 or 10?
(a) 8 (b) 9 (c) 10 (d) All are equally likely.
Soln:
8 = 2+6 = 3+5 = 4+4
9 = 3+6 = 5 + 4
10 = 4 + 6 = 5 + 5
Ans: a
72. 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 and after which you take one spoon of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statements holds true?
(a) There is less coffee in the first tumbler than water in the second tumbler.
(b) There is more coffee in the first tumbler than water in the second tumbler
(c) There is as much coffee in the first tumbler as there is water in the second tumbler
(d) None of the statements holds true.
Soln:
Suppose spoon can contains 5 drops. tumbler can contain 100 drops.
1 --> 2 (spoon contains 5w drops)
tumb 1: 95w
tumb 2: 100c + 5w
2 --> 1 (spoon contains 4c+1w drops)
tumb 1 : 96w
tumb 2 : 96c
Ans: c
73. A lady has fine gloves and hats of different colours in her closet- 18 blue, 32 red and 25 yellow. 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 an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure that she has a pair of each colour?
(a) 6 (b) 8 (c) 60 (d) 59
Soln:
ans = 32+25+2
Ans: d
74. It was the semester exam day, Vidhya caught the college bus. She enjoyed travelling by bus. Moving at 6 mph, the bus took Vidhya to college at the right time. She finished her exam and had a chit chat with her friends and suddenly she realized that it was 6 pm and she had missed the college bus. She decided to walk back home at 4 mph. What is her average speed for the day?
(a) 4 mph (b) ) 5 mph (c) 2.4 mph (d) 4.8 mph
Soln:
Avrg speed = 2*6*4/10
Ans: d
75. Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19 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) $27 (b) $ 18 (c) $45 (d) $ 486
Soln:
more to pay = 27 * (45-27)
= 486
Ans: d
76. 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 a time?
(a) 1 in 16 (b) 1 in 125 (c) 1 in 32 (d) 1 in 25
Soln:
Ans:
77.Given a collection of 36 points in the plane P and a point “X” equidistant from all points in P, which of the following are necessarily true?
A. The points in P lie on a circle.
B. The distance between any pair of points in P is larger than the distance between X and a point in P
(a) A only (b) B only (c) Both A and B (d) Neither A nor B
Soln:
Ans:
78.Susan made a block with small cubes of 8 cubic cm volume. To make the block she used 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
Soln:
Ans: a
79.A seamstress buys a certain amount of Gingham cloth which comes in rolls that are exactly 56 inches wide. She has also bought a certain length of Seek sucker cloth and 35 inches wide. The seamstress first focuses on the Gingham roll ad discovers that she has 116 yards of Gingham and she wants to divide the gingham into 116 lengths of 1 yard each. She wants to have twice as many pieces of seek sucker as she does of the Gingham. It takes 4 seconds to cut each length of Gingham. Working non-stop, how long (in seconds) will it take her to cut all 116 pieces?
(a) 464 (b) 460 (c) 463 (d) 465
Soln:
time = 4 *115
= 460
Ans: b
80.A man goes north 37km,turns left goes 2km,turns right goes 17 km again turns right goes another 2km. Find distance between the starting & the ending point.
(a) 56 (b) 52 (c) 58 (d) 54
Soln:
distance between the starting & the ending point = 37+17
= 54
Ans: d
81.A research lab in Chennai requires 100 mice and 75 sterilized cages for a certain set of laboratory experiments. To identify the mice, the lab has prepared labels with numbers 1 to 100, by combining tags numbered 0 to 9. The SPCA requires that the tags be made of toxin-free material and that the temperature of the cages be maintained at 27 degree Celsius. Also, not more than 2 mice can be caged together and each cage must be at least 2 sq.ft in area. The 5 experiments to be conducted by lab are to be thoroughly documented and performed only after a round of approval by authorities. The approval procedure takes around 48 hours. How many times is, the tag numbered '4' used by the lab in numbering these mice?
(a) 9 (b) 19 (c) 20 (d) 21
Soln:
no of 4s between 1 & 100 = 20
Ans: c
82. A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What will be the area of the square made from the same rope?
(a) 280.561 (b) 280.563 (c) 280.564 (d) 280.562
soln:
Perimeter = 25+11+31
side of square = 67/4
Area = 16.75^2
= 280.562
Ans: d
83. Mr. Alex is the father of children Jane, Joe, and Jill. He goes to a nearby park twice a week. He loves his children very much. On a certain day, on his way to the park he finds fruit vendors selling different fruits. Watermelon is one penny each, dates at 2 for a penny and plums at 3 for a penny. Mr.Alex spent 7 pennies and got the same amount of each type of fruit for each of his three children. What did each child get?
(a) 1 Watermelon, 2 Dates, 1 plum (b) 1 Watermelon, 1 Date, 1 plum
(c) 1 Watermelon, 3 Dates, 2 plums (d) 1 Watermelon, 2 Dates, 2 plums
Soln:
Ans: a
84.An athlete decides to run the same distance in 1/4th less time that she usually took. By how much percent will she have to increase her average speed?
(a) 25% (b) 50% (c) 33.33% (d) 20%
Soln:
S --- T
S --- 3T/4
Increase in speed = 4S/3T - S/T
Ans: c
85. 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 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?
(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.
Soln:
Ans:
86. A racehorse starts chasing a wild pony 3 hours after the pony bolts the stable. The pony runs through the entire country of Alb. Texas jumping 3 streams and crossing four 10 meter roads. The racehorse finally catches up with the pony after four hours by the time the sun had set and the moon was up in the sky for 4 hours. If the average speed of the racehorse is 73kmph then average speed of the wild pony is?
(a) 54.75 kmph (b) 42.71 kmph (c) 31.29 kmph (d) 41.71 kmph
87.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*v (t-9) for t = 9 , where d represents the diameter in mm and t, the number of years since the solar blast. Anubhav recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?
(a) 17 (b) 21.25 (c) 12.25 (d) 12.06
88.How many 13 digit numbers are possible by using the digits 1, 2, 3, 4, 5 which are divisible by 4 if repetition of digits is allowed?
(a) 4*5 (b) 5 12 (c) 5*12! (d) 5
89.In a family there are some boys and girls. All boys told that they are having equal number of brothers and sisters and girls told that they are having twice the number of brothers than sisters. How many boys and girls are present in a family?
(a) 5 boys & 3 girls (b) 7 boys & 2 girls (c) 4 boys & 3 girls (d) 6 boys & 2 girls
90.Mr Behera wants to build a house for his wife. In his dream house there are 5 rooms each having equal area. The length of each room is 4 m, breadth is 5 m and the height is 2m. For every single unit of area, he requires 17 bricks, how many bricks are required to make the floor of a particular room?
(a) 340 (b) 420 (c) 280 (d) 400
91. The Mehta’s have decided to launch their perfumes and have narrowed down to five ingredients for the perfume: Lilac, Balsamic, Lemon, Woody and Mimosaic. The customer can order for specific variety of perfume. To make a perfume that is in demand the Mehta’s adhered to the following conditions: Lilac and Balsamic go together. Woody and Mimosaic go together; Woody and Balsamic never go together. Lemon can be added with any material. All of the following combinations are possible to make a perfume except___.
(a) Balsamic and Lilac (c) Mimosaic and Woody
(b) Woody and Lemon (d) Mimosaic and Lilac
92.If ‘a’ and ‘b’ are mixed in 3:5 ratio and b, c are mixed in 8:5 ratio and if the final mixture is 35 litres. Find the amount of b in the mixture.
(a) 15.73 (b) 14.73 (c) 15.24 (d) 14.24
93. The Chennai corporation has a particular strategy for assigning numbers for buildings. The Corporation had strict rules that every building should have a number. In T Nagar, a place in Chennai there many buildings were under residential category. For buildings, the Corporation numbered from 1 to 100. For shops, corporation numbered between 150 and 200 only in prime numbers. How many times does the number “6” appear in the building numbers?
(a) 20 (b) 19 (c) 10 (d) 13
94.A Person buys a horse for 15 pounds, after one year he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the profit for that person?
(a) 20 pounds (b) 15 pounds (c) 25 pounds (d) 10 pounds
95.A scientist was researching on animal behaviour in his lab. He was very interested in analyzing the behaviour of bear. For some reason he travelled 1 mile in the north direction & reached the North Pole. There he saw a bear and then followed the bear around 1 hr with a speed of 2km/hr in east direction. After that he travelled in south direction & reached at his lab in 2 hrs. Then what colour is the bear?
(a) White (b) black (c) brown (d) grey
96. Three boys Bob, Pete and Oliver and two girls Samantha and Kristie are to be seated in a row. Samantha always sits to the left of Bob. No girl sits at the extreme positions and at the middle positions. Peter always sits at the extreme positions. Who sits to the right of Kristie?
(a)Peter or Oliver (b) Bob (c) Peter (d)Oliver
97.If x/2y =2a, then 2x/x-2ay=?
(a) 4 (b) ay (c) 2 (d) 2a
98.A man looks at a painting and tells “Neither have I any brother nor any sister, but the person in the painting is my father’s son”. Then who is in the painting?
(a) Father (b) Daughter (c) Son (d) Himself
99.Inspired by Fibonacci series, Sanket decided to create his own series which is 1,2,3,7,7,22,15,67,..... What number comes immediately before 63?
(a) 31 (b) 61 (c) 57 (d) 202
100) Determine the distance between the x-intercept and the z-intercept of the plane whose equation is 2x+9y-3z=18
(a) 6.32 (b)10.82 (c)3.00 (d)5.00
101.A game is played between 2 players and one player is declared as winner. All the winners from first round, played in the second round. All the winners from second round played in third round and so on. If 8 rounds were played to declare only one player as winner, how many players played in first round?
(a) 256 (b) 128 (c) 255 (d) 127
102.1/3 rd of a number is more 3 than the 1/6 of the same number, then find the number?
(a) 24 (b) 12 (c) 18 (d) 20
Soln:
x/3 = x/6 + 3
x = 18
Ans: c
103.It is the class with the seating arrangement in 4 rows and 8 columns. When the teacher says 'start' the girl who is sitting in first row and first column will say 1, then the next girl sitting behind her will say 4, the next girl sitting behind that girl will say 7, in a particular order each girl is telling a number, the following girls told 10, 13 next turn is yours what you will say?
(a) 14 (b) 16 (c) 20 (d) 17
Soln:
1,4,7,10,13,...
Ans: b
104. If Valentine’s day of 2005 was celebrated on a Monday. What day is Feb 14 ,2010 ?
(a)Monday (b) Sunday (c) Tuesday (d) Wednesday
Soln:
Ans: b
105.If a pipe can fill the tank in 6 hrs but unfortunately there was a leak in the tank due to which it took 30 more minutes .Now if the tank was full how much time will it take to get emptied through the leak?
(a) 39 hrs (b) 78 hrs (c) 72 hrs (d) 70 hrs
Soln:
Without leak tank fill 1/6 in 1 hour
With leak tank fill 1/6.5 in 1 hour
leak in 1 hour = 1/6 - 1/6.5
= 1/78
Time taken to empty = 78
Ans: b
