TCS Sample Aptitude Questions 5 - Recruitment 2011
Q1. 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?
(a) 5/9
(b) 1/9
(c) 2/3
(d) 1/3
Soln:
Prob of Ghana=2/3
Prob of Bolivia=1/3
"Paul picks A with the same probability as A’schances of winning."
→ probability that Paul will correctly pick the winner = 2/3*2/3+1/3*1/3
= 5/9
Ans: a
2. One 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 clock on Oz when the time is 12.40 am.
(a) 89
(b) 251
(c) 111
(d) 79
Soln:
Hour hand :
18 hour = 360 deg
1 hour = 20 deg
90 min = 20
1 min = 2/9
→ Angle at 12:40 = 12*20+ (2/9)*40
= 248.88
Minute hand :
90 min = 360
1 min = 4
→ 40 min = 160
→ Angle b/w the hands = 248.8 - 160
= 88.88 =89
Ans: a
Q3. 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 the 4 faces of the outer surface of the cube are painted totally, how many faces of the smaller cubes remain unpainted?
(a) 900
(b) 488
(c) 500
(d) 800
Soln:
Total volume of the big cube= 5*5*5 = 125
Volume of the hollow space = 3*3*3 = 27
→ Volume occupied by small cubes(1 cm) = 125-27 = 98
Volume of small cube = 1
→ Number of small cubes occupied in big cube = 98
Total number of faces of small cubes = 98*6 = 588
After painting 4 faces, Total number of painted faces of small cubes = 25*4 =100
→ number of unpainted faces = 588-100 = 488.
Ans: b
4. Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3- dimensional objects. The 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.
- The diameter of the coins should be at least 64mm and not exceed 512mm.
- Given a coin, the diameter of the next larger coin is at least 50% greater.
- 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?
(a) 5
(b) 8
(c) 9
(d) 6
Soln:
As next larger coin is 50% greater, the diameters of the coins can be 64, 64+32=96, 96+48=144, 144+72=216, 216+108=324, 324+162=486.
Ans: d
Q5. A hare and a tortoise race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after 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) 8
(b) 37.80
(c) 40
(d) 5
Soln:
Hare starts after tortoise covered 1/5 of distance.
Hare covered 1/8 when tortoise covered 7/8 of distance. (meet)
time taken to cover 1/8 by hare = time taken to cover 7/8-1/5 = 27/40) by tortoise.
let speed of hare & tortoise be H & T respectively.
→ 1/8H = 27/40T
H = (5/27) T
for the rest of the journey, hare has to cover 7/8 where tortoise has to cover 1/8.
7/8Hh = 1/8T
Hh = 7T
→ So speed of hare should be increased by = 7T/(5/27)T
= 37.8
Ans: b
Q6. Anoop managed to draw 7 circles 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 radius of the circles to the side of the square.
(a) 1:(2 + 72)
(b) 1:(4 + 73)
(c) (2 + 72):1
(d) 1:(2 + 62)
Soln:
Let side of square be a & radius of circles be r,
diagonal = a2
Also diagonal = 12r + 2r 2
→ r(12+22) = a2
r (6 2 + 2) = a
r / a = 1 / ( 2 + 62 )
Ans: d
Q7. 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 is maximized. This maximum probability is
(a) 37/38
(b) 1 / 2
(c) 14/19
(d) 3 / 4
Soln:
The probability of getting a red is maximized by moving 9 red balls to other box.
probability of choosing one box = 1/2
probability of choosing red ball from box1 = 1
probability of choosing red ball from box2 = 9/19
→ maximum probability = 1/2+1/2*9/19 = 14/19
Ans: c
Q8. Pizza shops make pizzas of same thickness but different diameter. Cost of pizza A with diameter 8 cm is 80 $, cost of the pizza B with diameter 12 cm is 240 $, cost of the pizza B with diameter 24 cm is 720 $. Which of the above mentioned pizzas gives the best value for money?
(a) A
(b) B
(c) C
(d) Cannot say
Soln:
Value of money for 8cm & 24cm pizzas are same.
Ans: d
Q9. Lucy finds around 25 groups of stars that appear to her as constellations. She draws 7 patterns of the constellations in her notebook and notes down the number of stars in each of them. She counts 5 stars in first constellation and 15 on next. She counts a number the third time and forgets to note it down. The next four constellations she counts 51, 53, 159, 161. Next day her father looks at the notebook and wants to know the number of stars in the third constellation. Lucy only remembers that number of stars counted in each of the constellation followed a pattern 5, 15, x, 51, 53, 159, 161. What is the value of x?
(a) 19
(b) 17
(c) 47
(d) 31
Soln:
As the difference between the successive numbers = 2
So, 15+2 = 17
Ans: b
Q10. X is 6 years younger to Y. X's father is a businessman who invested 10000 at 8% rate of interest and obtained his amount after 10 years. Y's father is a job holder who invested around 20000 at 2% rate and obtained his amount after 20 years. Now compounding, both of them get around Rs. A. After 5 years, the ratio of ages of X and Y is 1:2. Now X's father is 20 years older to Y and Y's father is 30 years more than X. After 20 years, again X's mother asks X's father to purchase a LCD TV which costs around 45000. What is the age of X and Y together?
(a) 12
(b) 8
(c) 18
(d) 6
Soln:
Y-X = 6
Y = X+6
X+5 / Y+5 = 1/2
X+5/X+11 = 1/2
→ X=1, Y=7
X+Y=8
Ans: b
Q1. 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?
(a) 5/9
(b) 1/9
(c) 2/3
(d) 1/3
Soln:
Prob of Ghana=2/3
Prob of Bolivia=1/3
"Paul picks A with the same probability as A’schances of winning."
→ probability that Paul will correctly pick the winner = 2/3*2/3+1/3*1/3
= 5/9
Ans: a
2. One 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 clock on Oz when the time is 12.40 am.
(a) 89
(b) 251
(c) 111
(d) 79
Soln:
Hour hand :
18 hour = 360 deg
1 hour = 20 deg
90 min = 20
1 min = 2/9
→ Angle at 12:40 = 12*20+ (2/9)*40
= 248.88
Minute hand :
90 min = 360
1 min = 4
→ 40 min = 160
→ Angle b/w the hands = 248.8 - 160
= 88.88 =89
Ans: a
Q3. 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 the 4 faces of the outer surface of the cube are painted totally, how many faces of the smaller cubes remain unpainted?
(a) 900
(b) 488
(c) 500
(d) 800
Soln:
Total volume of the big cube= 5*5*5 = 125
Volume of the hollow space = 3*3*3 = 27
→ Volume occupied by small cubes(1 cm) = 125-27 = 98
Volume of small cube = 1
→ Number of small cubes occupied in big cube = 98
Total number of faces of small cubes = 98*6 = 588
After painting 4 faces, Total number of painted faces of small cubes = 25*4 =100
→ number of unpainted faces = 588-100 = 488.
Ans: b
4. Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3- dimensional objects. The 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.
- The diameter of the coins should be at least 64mm and not exceed 512mm.
- Given a coin, the diameter of the next larger coin is at least 50% greater.
- 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?
(a) 5
(b) 8
(c) 9
(d) 6
Soln:
As next larger coin is 50% greater, the diameters of the coins can be 64, 64+32=96, 96+48=144, 144+72=216, 216+108=324, 324+162=486.
Ans: d
Q5. A hare and a tortoise race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after 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) 8
(b) 37.80
(c) 40
(d) 5
Soln:
Hare starts after tortoise covered 1/5 of distance.
Hare covered 1/8 when tortoise covered 7/8 of distance. (meet)
time taken to cover 1/8 by hare = time taken to cover 7/8-1/5 = 27/40) by tortoise.
let speed of hare & tortoise be H & T respectively.
→ 1/8H = 27/40T
H = (5/27) T
for the rest of the journey, hare has to cover 7/8 where tortoise has to cover 1/8.
7/8Hh = 1/8T
Hh = 7T
→ So speed of hare should be increased by = 7T/(5/27)T
= 37.8
Ans: b
Q6. Anoop managed to draw 7 circles 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 radius of the circles to the side of the square.
(a) 1:(2 + 72)
(b) 1:(4 + 73)
(c) (2 + 72):1
(d) 1:(2 + 62)
Soln:
Let side of square be a & radius of circles be r,
diagonal = a2
Also diagonal = 12r + 2r 2
→ r(12+22) = a2
r (6 2 + 2) = a
r / a = 1 / ( 2 + 62 )
Ans: d
Q7. 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 is maximized. This maximum probability is
(a) 37/38
(b) 1 / 2
(c) 14/19
(d) 3 / 4
Soln:
The probability of getting a red is maximized by moving 9 red balls to other box.
probability of choosing one box = 1/2
probability of choosing red ball from box1 = 1
probability of choosing red ball from box2 = 9/19
→ maximum probability = 1/2+1/2*9/19 = 14/19
Ans: c
Q8. Pizza shops make pizzas of same thickness but different diameter. Cost of pizza A with diameter 8 cm is 80 $, cost of the pizza B with diameter 12 cm is 240 $, cost of the pizza B with diameter 24 cm is 720 $. Which of the above mentioned pizzas gives the best value for money?
(a) A
(b) B
(c) C
(d) Cannot say
Soln:
Value of money for 8cm & 24cm pizzas are same.
Ans: d
Q9. Lucy finds around 25 groups of stars that appear to her as constellations. She draws 7 patterns of the constellations in her notebook and notes down the number of stars in each of them. She counts 5 stars in first constellation and 15 on next. She counts a number the third time and forgets to note it down. The next four constellations she counts 51, 53, 159, 161. Next day her father looks at the notebook and wants to know the number of stars in the third constellation. Lucy only remembers that number of stars counted in each of the constellation followed a pattern 5, 15, x, 51, 53, 159, 161. What is the value of x?
(a) 19
(b) 17
(c) 47
(d) 31
Soln:
As the difference between the successive numbers = 2
So, 15+2 = 17
Ans: b
Q10. X is 6 years younger to Y. X's father is a businessman who invested 10000 at 8% rate of interest and obtained his amount after 10 years. Y's father is a job holder who invested around 20000 at 2% rate and obtained his amount after 20 years. Now compounding, both of them get around Rs. A. After 5 years, the ratio of ages of X and Y is 1:2. Now X's father is 20 years older to Y and Y's father is 30 years more than X. After 20 years, again X's mother asks X's father to purchase a LCD TV which costs around 45000. What is the age of X and Y together?
(a) 12
(b) 8
(c) 18
(d) 6
Soln:
Y-X = 6
Y = X+6
X+5 / Y+5 = 1/2
X+5/X+11 = 1/2
→ X=1, Y=7
X+Y=8
Ans: b
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