Arithmetic(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 6 of 15 pages

Question 51. In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.
Determine the minimum number of people who could have name exactly two places as their favourite.

Discuss Question

Answer: Option B. -> 0
:
B
B
For II to be the minimum, III has to be the maximum. The maximum value of III can be 75. So, minimum value of II = 0

Question 52. In a survey among 70 people, 50 like Vanila and 40 like Chocolate. What is the minimum and maximum number of people who like exactly 2 flavours respectively?

50, 50
20, 40
20, 20
30, 20

Discuss Question

Answer: Option C. -> 20, 20
:
C
X = I + II = 70
S = I + 2II = 50 + 40 = 90
S – X = II = 90 – 70 = 20 = x
So, minimum and maximum value of x = 20.

Question 53. In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.
Determine the maximum number of people who could have name exactly two places as their favourite.

Discuss Question

Answer: Option B. -> 50
:
B
For II to be maximum, III has to minimum i.e. 0. In this case, II = 150. But, II can’t be 150 as the maximum possible value in only 100.
Also,
We have II +2III = 150
Also I + II + III = 100.
So when III=50 and II =50 then all the equations are getting satisfied, hence II=50 is the minimum and maximum value for II
So, maximum value of II = 50

Question 54. What is the total number of students who opted for hockey?

100
60
50
Cannot be determined

Discuss Question

Answer: Option B. -> 60
:
B
B

Question 55. In a class of 200 students who play cricket and hockey, the number of students who play neither of the games is 16 less than those who play both. The number of students who do not play cricket is 24 more than those who do not play hockey.
The number of students who play hockey is ___.

Discuss Question

:

Consider 2 complement sets. So if the no of students not playing hockey =x. number of students not playing cricket = x+24
Students playing both =y. Students playing neither = y-16
x+ (x+24) -(y-16)+y=200
2x+40=200
x=80
x+24=104
Those who play hockey 200-80=120

Question 56. A group of 80 People play atleast one of the games- carrom, snooker and TT. 40 play carrom, 50 play snooker and 35 play TT. If 14 people play both Carrom and Snooker, 20 people play both Snooker and TT and 12 people play both TT and carrom, find the ratio of the number of people who play carrom only to the number who play only TT?

17:4
13:1
15:4
10:1

Discuss Question

Answer: Option C. -> 15:4
:
C
Answer Option - C
x- number who play all 3 games
80= 125 –(14+12+20) +x
x= 1, the venn diagram can be represented as

A Group Of 80 People Play Atleast One Of The Games- Carrom,...

Thus ratio=15:4

Question 57. In a class there are 200 students, at least 140 of students like Maths, at least 150 like Science and at least 160 like English. What is the minimum number of students who like all three subjects?

Discuss Question

Answer: Option A. -> 50
:
A
A
X = I + II + III = 200
S = I + 2II + 3III = 140 + 150 + 160 = 450
S – X = II + 2III = 450 – 200 = 250
For III to be the minimum, II has to be the maximum. Now, II can take the maximum value of 200.
So, minimum value of III = 250 – 200= 50.

Question 58. What is the number of people who opt for both Football and cricket?

15
30
45
Cannot be determined

Discuss Question

Answer: Option D. -> Cannot be determined
:
D
D

Question 59. In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.
Determine the minimum number of people who could have named all three places as their favourite.

Discuss Question

Answer: Option B. -> 50
:
B
For III to be the minimum, II has to be the maximum.
also, all the equations will have to be satisfied.
We have II +2III = 150
Also I + II + III = 100.
II can take a maximum value of 50. So, III = 50, at this point all the equations are consistent, hence 50 is the minimum number of people.

Question 60. In Little flowers school, for a school drill, the students are divided into 2 groups of lilies and daisies.The ratio of lilies: daisies = 8:3. The ratio of boys: girls is 7:4.

60 %

of the daisy group is boys.
What is the difference in the number of boys who are in the lily group and the number of girls in the daisy group, given that there are 48 girls in the daisy group?