TCS Sample Aptitude Questions 4 - Recruitment 2011
Q1. 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 164 cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed in kmph.
(A) 236.16
(B) 11.39
(C) 8.78
(D) 23.24
Soln:
n/p=144 p=164cm=1.64m
→ number of steps per minute, n = 144*1.64
distance traveled in 1 minute = n*p
= 144*1.64*1.64
distance traveled in 1 hour (km) = 144*1.64*1.64*60/1000
= 23.238144
Ans: D
Q2. 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.
(C) Both A and B
(D) Neither A nor B
Soln:
Possiblities,
1. Leftmost is guilty --> All suspects are lying. (Leftmost suspect is not innocent)
2. Leftmost is not guilty and other person is guilty --> Leftmost suspect is innocent (All suspects are not lying.)
Ans: A
Q3. 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
(A) 1
(B) 0
(C) 4
(D) 2
Soln:
There are four such points.1 incentre and 3 exacentres.
Ans: C
Q4. 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 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
(A) 192
(B) 64
(C) 54
(D) 102
Soln:
The number of times 3 used from 1 - 100 (i.e 64 numbers in decimal) is 16.In the 300 series 64 3's used in the hundreds place of each number.
--> 16*8+64=192
Ans: A
Q5. 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?
(A) 375
(B) 625
(C) 500
(D) 3125
Soln:
A no divisible by 4 means it contain ending two digits as 12,24,32,44,52.
ie, The five digit number can be in the form XXX12,XXX24,XXX32,XXX44,XXX52.
--> No of five digit numbers divisible by 4= 5*5*5*5
=625
Ans: B
Q6. 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) 11/12
(B) 0
(C) 1/12
(D) 1/6
Soln:
It can not be exactly 1.If one letter is placed wrong envelop then there should be another letter placed in the wrong envelope.
Ans:B
Q7. 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) 1/4
(B) 1/2
(C)3/4
(D) 1/3
Soln:
The point Q is closer to the center than the periphery if it falls within an inner circle with radius 1/2.we will compare the areas of the inner circle to the area of the entire circle, to determine the probability that the point falls within this inner circle.
--> probability = pi*(1/2) / pi * 1
=1/4
Ans: A
Q8 On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. Echina grows in the form of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4 * √ (t - 8) for t ≥ 8 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 8mm. How many years back did the solar blast occur?
(A) 8
(B) 12
(C) 16
(D) 24
Soln:
16 = 4 * √ (t - 8)
√ (t - 8)=4
t=24
Ans: D
Q9 Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. Oneof 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.
(d) In order to win, Alice’s first move can be a 0-move or a 1-move
Soln:
Alice's first move should be 1,
If Alice moves 0, Bob moves 2.
whatever Alice moves it will lose.
But Alice never loses if it starts with 1.
Ans: B
Q10. 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
(A) 18
(B) 13
(C) 34
(D) 12
Ans: D
Q1. 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 164 cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed in kmph.
(A) 236.16
(B) 11.39
(C) 8.78
(D) 23.24
Soln:
n/p=144 p=164cm=1.64m
→ number of steps per minute, n = 144*1.64
distance traveled in 1 minute = n*p
= 144*1.64*1.64
distance traveled in 1 hour (km) = 144*1.64*1.64*60/1000
= 23.238144
Ans: D
Q2. 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.
(C) Both A and B
(D) Neither A nor B
Soln:
Possiblities,
1. Leftmost is guilty --> All suspects are lying. (Leftmost suspect is not innocent)
2. Leftmost is not guilty and other person is guilty --> Leftmost suspect is innocent (All suspects are not lying.)
Ans: A
Q3. 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
(A) 1
(B) 0
(C) 4
(D) 2
Soln:
There are four such points.1 incentre and 3 exacentres.
Ans: C
Q4. 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 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
(A) 192
(B) 64
(C) 54
(D) 102
Soln:
The number of times 3 used from 1 - 100 (i.e 64 numbers in decimal) is 16.In the 300 series 64 3's used in the hundreds place of each number.
--> 16*8+64=192
Ans: A
Q5. 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?
(A) 375
(B) 625
(C) 500
(D) 3125
Soln:
A no divisible by 4 means it contain ending two digits as 12,24,32,44,52.
ie, The five digit number can be in the form XXX12,XXX24,XXX32,XXX44,XXX52.
--> No of five digit numbers divisible by 4= 5*5*5*5
=625
Ans: B
Q6. 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) 11/12
(B) 0
(C) 1/12
(D) 1/6
Soln:
It can not be exactly 1.If one letter is placed wrong envelop then there should be another letter placed in the wrong envelope.
Ans:B
Q7. 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) 1/4
(B) 1/2
(C)3/4
(D) 1/3
Soln:
The point Q is closer to the center than the periphery if it falls within an inner circle with radius 1/2.we will compare the areas of the inner circle to the area of the entire circle, to determine the probability that the point falls within this inner circle.
--> probability = pi*(1/2) / pi * 1
=1/4
Ans: A
Q8 On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. Echina grows in the form of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4 * √ (t - 8) for t ≥ 8 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 8mm. How many years back did the solar blast occur?
(A) 8
(B) 12
(C) 16
(D) 24
Soln:
16 = 4 * √ (t - 8)
√ (t - 8)=4
t=24
Ans: D
Q9 Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. Oneof 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.
(d) In order to win, Alice’s first move can be a 0-move or a 1-move
Soln:
Alice's first move should be 1,
If Alice moves 0, Bob moves 2.
whatever Alice moves it will lose.
But Alice never loses if it starts with 1.
Ans: B
Q10. 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
(A) 18
(B) 13
(C) 34
(D) 12
Ans: D
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