Set Theory Questions for CAT with Answers PDF

From the diagram,
Number of people who do not eat vegetarian food, but eat non-vegetarian food = 450

Since the dailies are sold in equal number, the total sale of each may be taken as x.
Hence, from the diagram, if we add up all the ''only'' regions, we get:
(x - 54) + (x - 48) + (x - 39) + 9 + 27 + 18 + 12 = 906
⇒ x = 327

Percentage of people buying Hindu or Express but not Mail = 

Number of students in the group = 45
Number of students who speak Hindi only = 22
Number of students who speak English only = 12
Let 'x' be the number of students who speak both Hindi and English.
22 + x + 12 = 45
x = 11

T = Tea
C = Coffee
Let the number of people who like coffee but not tea be x.
Number of people in the group = 26
From the Venn diagram:
8 + 8 + x = 26
x = 10

Out of 100, 23 are Indian men and 29 are Indian women.
So, the remaining 48 are foreigners.

N6 contains all multipliers of 6 and N₈, those of 8. So, N₆ ∩ N₈ contains all those numbers which are common multiples of 6 and 8 both, i.e. multiples of 24 (LCM of 6 and 8 = 24).
So, N₆ ∩ N₈ = N₂₄

A ∪ B will contain minimum number of elements if A ⊂ B; and in that case, n(A ∪ B) = n(B) = 6.

Total number of people = 65
Number of people who like cricket = 40
Number of people both cricket and tennis = 10
From the Venn diagram,
40 - 10 + 10 + x = 65
x = 25
Thus, number of people who like only tennis and not cricket = 25

Number of people who speak French = 50
Number of people who speak Spanish = 20
Number of people who speak both Spanish and French = 10
Number of people who speak at least one of the two languages = Number of people speaking only French + Number of people speaking only Spanish +
Number of people speaking both French and Spanish = (50 - 10) + 10 + (20 - 10) = 60

n(M) + n(A) - n(M ∩ A) = n(M ∪ A)
n(M ∩ A) = 168 + 198 - 300 = 366 - 300 = 66
Number of families using air conditioners only = 198 - 66 = 132

Assuming 100 students:
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
⇒100 – 20 = 75 + 55 – n(A ∩ B)
⇒ n(A ∩ B) = 50
Hence, 50% of the students answered both questions correctly.

Number of students in the school = 800
Number of students who are enrolled in Chemistry = 480
Number of students who are enrolled in both Chemistry and Physics = 160
∴ From the diagram,
480 + P + x = 800
[According to the question, 7x = P + 160 because x = (1/7)th of the total number of students enrolled in Physics]
Or, P = 7x - 160
⇒ 480 + 7x -160 + x = 800
⇒ 320 + 8x = 800
⇒ 8x = 480
⇒ x = 60
Hence, total number of students enrolled in neither Physics nor Chemistry = 60

Number of families who buy none of A, B and C = N - n(A ∪ B ∪ C),
where N = Total number of families.
n(A): Number of Newspaper A readers.
n(B): Number of Newspaper B readers.
n(C): Number of Newspaper C readers.
Number of families who buy none of A, B and C = 10000 - {n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C)}
= 10000 - 4000 - 2000 - 1000 + 500 + 300 + 400 - 200
= 4000
Number of families who buy none of A, B and C = 4000

A = 130 and B = 90
Option (2):
A only = 90 and B only = 50
Option (3):
'Both A and C, but not B' = 25 and 'Both B and C, but not A' = 25
Option (4):
'Both A and B' = 15 and 'Both B and C' = 40
So, option 3 is correct.

Since there are 14 players who are in triathlon and pentathlon, and there are 8 who take part in all three games, there will be 6 who take part in only triathlon and pentathlon. Similarly,
Only triathlon and marathon = 12 – 8=4 & Only Pentathlon and Marathon = 15 – 8 = 7.

The figure above can be completed with values for each sport (only) plugged in:
The answers would be: 3 + 6 + 8 + 4 + 5 + 7 + 10 = 43.
Option (b) is correct.