TCS Xtra Aptitude Questions 2/3
26 .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 be determined
Soln:
TCS Sample Aptitude Questions 5 - Recruitment
Ans: d
27. Determine the distance between x-intercept and z-intercept of the plane whose equation is 6x+8y-3z=72.
(a) 31.92 (b)26.83 (c) 32.66 (d) 25.63
Soln:
For the plane ax+by+cz+d=0,
distance between x-intercept and z-intercept = √((d/a)^2+(d/c)^2(
Here d=-72,a=6,c=-3
--> = √(144+576)
= 26.83
Ans: b
28. 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 starts counted in each of the constellation followed a pattern 5,15, x, 51, 53, 159, 161.
(a) 19 (b) 17 (c) 47 (d) 31
Soln:
Two patterns
5,x,53,161,... & 15,51,159,...
x=51/3 = 17
Ans: b
29. 6 persons standing in the queue for ROBERT movie, are wearing different colour shirts. All of them belong to different age group, after two years their average age will be 43 and seventh person joined with them, hence the current average age has become 45. Find the age of seventh person?
(a) 67 (b) 69 (c) 72 (d) 74
Soln:
Current average age of 6 persons = 41.
Age of 7th person = 45+6*4
= 69
Ans: b
30. 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 Compounded both of them get around Rs. ABC .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' 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:
x= y-6
(x+5)/(y+5) = 1/2
On solving-->
2(y-1) = y+5
y = 7
x = 1
--> x+y = 8
Ans: b
31. The great musician Rahman has organized a live concert. The concert is organized in a big auditorium. Rahman plays both English and Tamil songs on his Yamaha Casio. The audience in the Eastern part of the auditorium love listening to Tamil Songs and those in the western part of the auditorium. He plays songs in random. The probability that he plays English songs for 6 consecutive times is 1 in
(a) 32 (b) 16 (c) 64 (d) 128
Soln:
probability = 1/2^6 =1/64
Ans: c
32. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same colour?
(a) 3 (b) 25 (c) 48 (d) 26
Soln:
1st - red/blue
2nd - blue/red
3rd - red/blue
It is clear that atleast two socks of the same colour will be obtained in 3rd attempt.
Ans: a
33. A person was fined for exceeding the speed limit by 10mph. Another person was also fined for exceeding the same speed limit by twice the same. If the second person was traveling at a speed of 35 mph, find the speed limit.
(a) 35mph (b) 15 mph (c) 20 mph (d) 30 mph
Soln:
let x be the speedlimit,
speed of second person x+20 = 35
x = 15
Ans: b
34. A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hour and sees the same 2 digits in reverse order. 1 hour later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
(a) 54 (b) 45 (c) 27 (d) 36
Soln:
Let x, y be the digits
Since speed = v
then
d = v*1 d = v*1
10x+y------------------------10y+x---------------------100x+y
--> 10x+y + v = 10y+x
9x-9y+v=0
10y+x + v = 100x+y
-99x+9y+v=0
--> -90x+2v=0
v = 45x
x=1,y=6
--> v=45
Ans:b
35. With four fifths of then tank full, a vehicle travels 12 miles. How much distance will the vehicle travel with one third tank full?
a)8.05 km (b) 6.05 km (c) 12km (d) 5 km
Soln:
4/5 full --> 12
1/5 -- 12/4
5/5 -- 15
3/3 -- 15
1/3 -- 5
1 mile=1.609 km
5 miles = 8.05
Ans: a
36. Peter is twice as old as Paul was when Peter was as old as Paul is now. The combined age of Peter and Paul is 42 years. How old is peter now?
(a) 21 (b) 18 (c) 24 (d)26
Soln:
For this kind of problems we have,
7x/4 =sum of ages, where x is the age of elder.
7x/4 = 42
x = 24
Ans: c
37. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre 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 litres, second hour it has 20, and so on) If tank B is 1/16 filled after 17 hours, what is the total durations required to fill it completely?
(a) 4 hours (b) 21hours (c) 22 hours (d) 24 hours
Soln:
See TCS Sample Aptitude Questions - Recruitment 2011
Ans: b
38. 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 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 10rounds played in a knock-out tournoi how many matches were played?
(a)1024 (b) 1023 (c)1026 (d)1011
Soln:
1+2+4+8+16+32+64+128+256+512 = 1023 or 2^10-1 = 1023
Ans: b
39. 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 Ferrari S.p.A. Throughout its history, the company has been noted for its continued participations in racing, especially in Formula One, where it has enjoyed great success Rohit once bought a Ferraris. It could go 4 times as fast Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 35 km/hr and the distance travelledby the Ferrari is 968km, find the total time taken for Rohit to drive that distance.
(a) 242 hours (b) 27 hours (c) 7 hours (d) 6.91 hours
Soln:
speed m =35
speed r = 4*35
time = 968/140 = 6.91
Ans: d
40. Two blocks of copper with density of 100 kg/m^3 are twisted into wires of length 100 km and thickness 0.1mm. Copper is a very ductile material. Its ductility is measured in terms of percentage elongation upon application of tensile forces. The conductivity of the copper wire is extremely high rendering it useful in the construction of many electronic circuits. If the voltage through one such circuit is 18 V and the current flowing in the circuit is 190 ma. What is the resistance of the wire?
(a) 208.00 K Ohms (b) 3420.00 K Ohms (c) 0.09 k Ohms (d) 10.56 KOhms
Son:
R = V / I
= 18/190
Ans: c
41. 5 men and 5 women meet and men dance with women. Which of the following are always true?
A. There are 2 men who have danced with same number of women.
B. There are 2 women who have danced with same number of men.
(a) Both A and B (b) A only
(c) B only (d) Neither A nor B
Soln:
Ans:d
42. Three boys John, Tom and Oliver and two girls Rachel and Kim are to be seated in a row. Rachel always sits to the left of John. No girl sits at the extreme positions and at the middle positions. Tom always sits at the extreme positions. Who sits to the right of Kim?
(a) Oliver (b) Tom (c) Tom or Oliver (d) John
Soln:
Ans: c
43. The thank giving banquet at No.2, Ritcher Street, had 49 guests which consisted of 6 statesmen, 26 relatives and their families. At the end of a banquet 19 people shake hands with other , some of which were between the statesmen alone, some between relatives alone and some between the statesmen and relatives. How many handshakes will there be in total?
(a) 342 (b) 171 (c) 180 (d) 162
Soln:
19c2 = 171
Ans: b
44. There are 7 children. You are told that the youngest child is a boy. The probability that all of them are boys is 1 in
(a) 64 (b) 21 (c) 2 (d) 128
Soln:
prob = 1/2^6*1
= 64
Ans: a
45. 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 minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e. no three points in P lie on a line) is
(a) 3 (b) 5 (c) 2 (d)7
Soln:
For minimum value = 3
Ans: a
46. 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 5 points in the plane in general position (.i.e. no three points in P lie on a line) is
(a) 3 (b) 5 (c) 2 (d)7
Soln:
For maximum value = ans is no of pints.
Ans: b
47. There is a pie to be divided among 20 people. A man eats3 pizza, a women eats two pieces and a child eats half a piece of pie. Find the number of men, women and children so that they are 20 people in total and everyone gets some pie. There are 20 pieces of pie in all.
(a) 7 women, 1 men and 12 children
(b) 5 women, 1 men and 14 children
(c) 6women, 2 men and 12 children
(d) 4women, 2 men and 14 children
Soln:
Suppose for men x, women y & childrem z,
-->
3x+2y+0.5z=20
x=1,y=5,z=14
Ans:b
48. 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?
(a) 13 (b) 42 (c) 3 (d) cannot be determined
Soln:
x = aD+8
x = b3D+21
-->
D(a-3b)=13
Since 13 is prime & D leaves a remainder of 8,
D=13,
a-3b = 1
a=4, b=1
x = 60
120%39 = 3
Ans: c
49. In a pizza restaurant, you get a basic pizza with two toppings, cheese and tomato. You can also make up your own pizza with extra toppings. You can also choose from 10 different toppings, e.g. olives, ham, mushroom, salami etc. Ross wants to order a pizza with 2 different extra toppings. How many different combinations are possible?
(a) 100 (b) 1024 (c) 90 (d) 45
Soln:
10C2 = 45
Ans: d
50. The Thousand Pillar Temple of Hyderabad was built by the Kakatiyans of Chalukyan dynasty in the 12th century. Each pillar has carvings made of block monolithic rocks of basalt which are polished to give it a brilliant look. One sunny morning, three tourists visit the temple. Samantha is taller than Lily and taller than two of the thousand pillars and Kelly is shorter than Samantha and the pillars. Which of the following statements would be more accurate?
(a) Its impossible to tell (b) Kelly is as tall as Lily
(c) Lily is shorter than Kelly (d) Lily is taller than Kelly
Soln:
Incomplete data.
Ans: a
26 .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 be determined
Soln:
TCS Sample Aptitude Questions 5 - Recruitment
Ans: d
27. Determine the distance between x-intercept and z-intercept of the plane whose equation is 6x+8y-3z=72.
(a) 31.92 (b)26.83 (c) 32.66 (d) 25.63
Soln:
For the plane ax+by+cz+d=0,
distance between x-intercept and z-intercept = √((d/a)^2+(d/c)^2(
Here d=-72,a=6,c=-3
--> = √(144+576)
= 26.83
Ans: b
28. 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 starts counted in each of the constellation followed a pattern 5,15, x, 51, 53, 159, 161.
(a) 19 (b) 17 (c) 47 (d) 31
Soln:
Two patterns
5,x,53,161,... & 15,51,159,...
x=51/3 = 17
Ans: b
29. 6 persons standing in the queue for ROBERT movie, are wearing different colour shirts. All of them belong to different age group, after two years their average age will be 43 and seventh person joined with them, hence the current average age has become 45. Find the age of seventh person?
(a) 67 (b) 69 (c) 72 (d) 74
Soln:
Current average age of 6 persons = 41.
Age of 7th person = 45+6*4
= 69
Ans: b
30. 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 Compounded both of them get around Rs. ABC .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' 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:
x= y-6
(x+5)/(y+5) = 1/2
On solving-->
2(y-1) = y+5
y = 7
x = 1
--> x+y = 8
Ans: b
31. The great musician Rahman has organized a live concert. The concert is organized in a big auditorium. Rahman plays both English and Tamil songs on his Yamaha Casio. The audience in the Eastern part of the auditorium love listening to Tamil Songs and those in the western part of the auditorium. He plays songs in random. The probability that he plays English songs for 6 consecutive times is 1 in
(a) 32 (b) 16 (c) 64 (d) 128
Soln:
probability = 1/2^6 =1/64
Ans: c
32. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same colour?
(a) 3 (b) 25 (c) 48 (d) 26
Soln:
1st - red/blue
2nd - blue/red
3rd - red/blue
It is clear that atleast two socks of the same colour will be obtained in 3rd attempt.
Ans: a
33. A person was fined for exceeding the speed limit by 10mph. Another person was also fined for exceeding the same speed limit by twice the same. If the second person was traveling at a speed of 35 mph, find the speed limit.
(a) 35mph (b) 15 mph (c) 20 mph (d) 30 mph
Soln:
let x be the speedlimit,
speed of second person x+20 = 35
x = 15
Ans: b
34. A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hour and sees the same 2 digits in reverse order. 1 hour later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
(a) 54 (b) 45 (c) 27 (d) 36
Soln:
Let x, y be the digits
Since speed = v
then
d = v*1 d = v*1
10x+y------------------------10y+x---------------------100x+y
--> 10x+y + v = 10y+x
9x-9y+v=0
10y+x + v = 100x+y
-99x+9y+v=0
--> -90x+2v=0
v = 45x
x=1,y=6
--> v=45
Ans:b
35. With four fifths of then tank full, a vehicle travels 12 miles. How much distance will the vehicle travel with one third tank full?
a)8.05 km (b) 6.05 km (c) 12km (d) 5 km
Soln:
4/5 full --> 12
1/5 -- 12/4
5/5 -- 15
3/3 -- 15
1/3 -- 5
1 mile=1.609 km
5 miles = 8.05
Ans: a
36. Peter is twice as old as Paul was when Peter was as old as Paul is now. The combined age of Peter and Paul is 42 years. How old is peter now?
(a) 21 (b) 18 (c) 24 (d)26
Soln:
For this kind of problems we have,
7x/4 =sum of ages, where x is the age of elder.
7x/4 = 42
x = 24
Ans: c
37. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre 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 litres, second hour it has 20, and so on) If tank B is 1/16 filled after 17 hours, what is the total durations required to fill it completely?
(a) 4 hours (b) 21hours (c) 22 hours (d) 24 hours
Soln:
See TCS Sample Aptitude Questions - Recruitment 2011
Ans: b
38. 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 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 10rounds played in a knock-out tournoi how many matches were played?
(a)1024 (b) 1023 (c)1026 (d)1011
Soln:
1+2+4+8+16+32+64+128+256+512 = 1023 or 2^10-1 = 1023
Ans: b
39. 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 Ferrari S.p.A. Throughout its history, the company has been noted for its continued participations in racing, especially in Formula One, where it has enjoyed great success Rohit once bought a Ferraris. It could go 4 times as fast Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 35 km/hr and the distance travelledby the Ferrari is 968km, find the total time taken for Rohit to drive that distance.
(a) 242 hours (b) 27 hours (c) 7 hours (d) 6.91 hours
Soln:
speed m =35
speed r = 4*35
time = 968/140 = 6.91
Ans: d
40. Two blocks of copper with density of 100 kg/m^3 are twisted into wires of length 100 km and thickness 0.1mm. Copper is a very ductile material. Its ductility is measured in terms of percentage elongation upon application of tensile forces. The conductivity of the copper wire is extremely high rendering it useful in the construction of many electronic circuits. If the voltage through one such circuit is 18 V and the current flowing in the circuit is 190 ma. What is the resistance of the wire?
(a) 208.00 K Ohms (b) 3420.00 K Ohms (c) 0.09 k Ohms (d) 10.56 KOhms
Son:
R = V / I
= 18/190
Ans: c
41. 5 men and 5 women meet and men dance with women. Which of the following are always true?
A. There are 2 men who have danced with same number of women.
B. There are 2 women who have danced with same number of men.
(a) Both A and B (b) A only
(c) B only (d) Neither A nor B
Soln:
Ans:d
42. Three boys John, Tom and Oliver and two girls Rachel and Kim are to be seated in a row. Rachel always sits to the left of John. No girl sits at the extreme positions and at the middle positions. Tom always sits at the extreme positions. Who sits to the right of Kim?
(a) Oliver (b) Tom (c) Tom or Oliver (d) John
Soln:
Ans: c
43. The thank giving banquet at No.2, Ritcher Street, had 49 guests which consisted of 6 statesmen, 26 relatives and their families. At the end of a banquet 19 people shake hands with other , some of which were between the statesmen alone, some between relatives alone and some between the statesmen and relatives. How many handshakes will there be in total?
(a) 342 (b) 171 (c) 180 (d) 162
Soln:
19c2 = 171
Ans: b
44. There are 7 children. You are told that the youngest child is a boy. The probability that all of them are boys is 1 in
(a) 64 (b) 21 (c) 2 (d) 128
Soln:
prob = 1/2^6*1
= 64
Ans: a
45. 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 minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e. no three points in P lie on a line) is
(a) 3 (b) 5 (c) 2 (d)7
Soln:
For minimum value = 3
Ans: a
46. 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 5 points in the plane in general position (.i.e. no three points in P lie on a line) is
(a) 3 (b) 5 (c) 2 (d)7
Soln:
For maximum value = ans is no of pints.
Ans: b
47. There is a pie to be divided among 20 people. A man eats3 pizza, a women eats two pieces and a child eats half a piece of pie. Find the number of men, women and children so that they are 20 people in total and everyone gets some pie. There are 20 pieces of pie in all.
(a) 7 women, 1 men and 12 children
(b) 5 women, 1 men and 14 children
(c) 6women, 2 men and 12 children
(d) 4women, 2 men and 14 children
Soln:
Suppose for men x, women y & childrem z,
-->
3x+2y+0.5z=20
x=1,y=5,z=14
Ans:b
48. 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?
(a) 13 (b) 42 (c) 3 (d) cannot be determined
Soln:
x = aD+8
x = b3D+21
-->
D(a-3b)=13
Since 13 is prime & D leaves a remainder of 8,
D=13,
a-3b = 1
a=4, b=1
x = 60
120%39 = 3
Ans: c
49. In a pizza restaurant, you get a basic pizza with two toppings, cheese and tomato. You can also make up your own pizza with extra toppings. You can also choose from 10 different toppings, e.g. olives, ham, mushroom, salami etc. Ross wants to order a pizza with 2 different extra toppings. How many different combinations are possible?
(a) 100 (b) 1024 (c) 90 (d) 45
Soln:
10C2 = 45
Ans: d
50. The Thousand Pillar Temple of Hyderabad was built by the Kakatiyans of Chalukyan dynasty in the 12th century. Each pillar has carvings made of block monolithic rocks of basalt which are polished to give it a brilliant look. One sunny morning, three tourists visit the temple. Samantha is taller than Lily and taller than two of the thousand pillars and Kelly is shorter than Samantha and the pillars. Which of the following statements would be more accurate?
(a) Its impossible to tell (b) Kelly is as tall as Lily
(c) Lily is shorter than Kelly (d) Lily is taller than Kelly
Soln:
Incomplete data.
Ans: a
