Sets Questions

The sets questions are an important part in the quant for CAT section as a good number of questions are asked from the “Sets” topic. So, here are some practice questions for sets which can help the candidates to strengthen their CAT preparation.

Venn Diagrams and Sets Questions

1. In a class,110 students like physics, 80 like chemistry, 120 like mathematics and 70 like English. 20 students like only physics, 15 like only chemistry, 30 like only mathematics and 15 like only English.

What can be the maximum possible number of students in the class?

a) 155

b) 210

c) 380

d) 230

2. Of the 200 candidates who were interviewed for an admin position at Noesis, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

a) 0

b) 20

c) 10

d) 18

3. If one out of every four in 100 students had a car and three out of five students had a bike and half the students had a cycle and not more than 20 out of 100 had exactly two of the three above mentioned vehicles, then the maximum number of students having all three modes of transport is?

a) 20

b) 25

c) 17

d) cannot be determined

4. At a cricket match, out of the 2 lakh spectators, 90% were fans of team A, 85% of Team B, 70% of Team C, 75% of Team D and 80% of Team E. What is the minimum number of spectators who were fans of all five teams if it is given that each of these spectators supports at least one team?

a) 5

b) 100 

c) 1000 

d) none of these

5. A group of 100 people plays carom, snooker and chess. 90 people play chess, 80 people play snooker and 80 people play carom. Find the maximum number of people who play all three games, if each person plays at least one game.

a) 70

b) 75

c) 65

d) none of these

6. In a college, 35% of the students play at least two out of three games- Cricket, Hockey and Football. Football is played by 45% of the students. 15% of the people play both Cricket and Hockey, while 10% of the people play all the three games. If 7% of the students do not play any game, what percentage of the students play only Football?



b) 15%

c) 25%

d) 30%

Directions for questions 7-8:

In a group of 500 people, 350 are Engineers, 250 are MBAs. Determine:

7. How many are both Engineers and MBAs?

a) 100

b) 75

c) 50

d) 150

8. How many are either only MBA or only Engineer?

a) 250

b) 300

c) 350

d) 400

9. 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?

a) 50

b) 83

c) 100

d) 150

Directions for questions 10-11:

In an examination, it was found that every student has failed in at least one subject out of the three subjects: English, Maths and Science.

28 students failed in English, 30 students failed in Maths and 32 students failed in Science. 6 students failed in English and Maths, 8 students failed in Maths and Science and 10 students failed in English and Science. The number of students who failed in only one subject is 54. Also, 20 students failed only in Maths.

10. Determine the number of students who appeared in the examination.

a) 50

b) 20

c) 40

d) 70

11. Determine the number of students who failed in English and Science but not Maths.

a) 4

b) 7

c) 5

d) 6

Directions for questions 12-14:

In a music school, three instruments are taught: Tabla, Violin and Guitar. Out of 278 students in the school, 20 learn Tabla and Violin, 23 learn Violin and Guitar and 21 learn Tabla and Guitar. 9 students learn all three instruments.

It is known that equal number of seats in all three instruments classes. (If a student is learning Guitar as well Tabla, then he occupies two seats: one in Tabla Class and one in Guitar Class)

12. Determine the number of students who have occupied only one seat.

a) 232

b) 200

c) 197

d) 234

13. Determine the number of students who have occupied seats in Violin or Guitar class but not in Tabla Class.

a) 160

b) 153

c) 175

d) 167

14. Determine the number of students who have occupied seats in Tabla and Violin Class but not in Guitar Class.

a) 9

b) 11

c) 13

d) 7

Directions for questions 15-17:

There are 70 workers in a company out of which 40 are men. Also,

i) 35 are married

ii) 35 are engineers

iii) 18 married workers are engineers of which 9 are men

iv) 12 men are engineers & not married

v) 12 men are married& not engineers

15. How many unmarried engineers are working in the company?

a) 16

b) 18

c) 15

d) 17

16. How many unmarried women work in the company?

a) 4

b) 5

c) 6

d) none of these

17. How many graduate men are not married?

a) 12

b) 14

c) 13

d) can’t be determined

Directions for questions 18-20:

In a class of 150 students, none of the students opted for only cricket. None of the students opted for only Hockey and Football. 60 students opted for cricket or hockey or both. Also, all 150 students opted for at least one of these 3 games

18. What is the total number of students who opted for only football?

a) 40

b) 80

c) 90

d) Cannot be determined

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

a) 100

b) 60

c) 50

d) cannot be determined

20. What is the number of people who opted for only cricket and only Football?

a) 15

b) 30

c) 90

d) cannot be determined

21. 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?

a) 17:4

b) 13:1 

c) 15:4 

d) 10:1

22. In an examination, 38% of students failed in Science and 33% failed in Maths while 19% failed in both the subjects. If the number of students who passed in only Science is 700, then determine the total number of students who appeared in the examination.

a) 500 

b) 350

c) 5000 

d) 3500

23. In a class 40 people are interested in Music alone and 21 are interested in Dance alone. If the number of students who are interested in neither are equal to the number who like both, what is the likely strength of the class?

a) 65

b) 57 

c) 70 

d) 62

24. A,B,C and D are contesting for the district elections. Of the total population, 50% like A, 25% like B, 30% like C. All of those who don’t like any of these like D. All those who like B, like both A and C.All those who like C, like A as well. Number of people who like C and not B is what percent of those who like D?

a) 0

b) 10 

c) 15

d) 25

25. In a study XYZ on the effect of sleep on call center workers, following were the observations made on a certain number of volunteers in the study. 75% of the volunteers receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the volunteers who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the volunteers receive fewer than 6 hours of sleep, what percent of the volunteers report no feelings of tiredness during their shifts?

a) 24 

b) 21

c) 42 

d) 19

Visit Sets Solutions to know the detailed explanation of the aforementioned questions on sets. Also, get numerous questions and solutions on other important topics for CAT exam at BYJU’S.