Question 1
Out of total 150 students, 45 passed in Accounts, 30 in Economics and 50 in Maths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 in both Accounts and Economics, 25 students passed in all the three subjects. Find the number who passed at least in any one of the subjects:
A
63✓✗
B
53✓✗
C
73✓✗
D
None✓✗
Explanation
By the inclusion-exclusion principle:
|A ∪ E ∪ M| = |A| + |E| + |M| - |A ∩ M| - |M ∩ E| - |A ∩ E| + |A ∩ E ∩ M|
= 45 + 30 + 50 - 30 - 32 - 35 + 25
= 125 - 97 + 25 = 53
Question 2
In a town of 20,000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only is:
A
6600✓✗
B
6300✓✗
C
5600✓✗
D
600✓✗
Explanation
|A| = 8000, |A∩B| = 1000, |A∩C| = 800, |A∩B∩C| = 400 (all out of 20,000 families)
A only = |A| - |A∩B| - |A∩C| + |A∩B∩C|
= 8000 - 1000 - 800 + 400 = 6600
Question 3
In a survey of 300 companies, the number of companies using different media -- Newspapers (N), Radio (R) and Television (T) -- are as follows:
n(N) = 200, n(R) = 100, n(T) = 40, n(N∩R) = 50, n(R∩T) = 20, n(N∩T) = 25, and n(N∩R∩T) = 5.
Find the number of companies using none of these media.
A
20 companies✓✗
B
250 companies✓✗
C
30 companies✓✗
D
50 companies✓✗
Explanation
|N∪R∪T| = |N| + |R| + |T| - |N∩R| - |R∩T| - |N∩T| + |N∩R∩T|
= 200 + 100 + 40 - 50 - 20 - 25 + 5 = 340 - 95 + 5 = 250
Companies using none = 300 - 250 = 50
Question 4
There are 40 students; 30 of them passed in English, 25 of them passed in Maths and 15 of them passed in both. Assuming that every student passed at least in one subject, how many students passed in English only but not in Maths?
A
15✓✗
B
20✓✗
C
10✓✗
D
25✓✗
Explanation
English only = Total English - Both = 30 - 15 = 15
Question 5
Out of 1000 persons, 25 per cent were industrial workers and the rest were agricultural workers. 300 persons enjoyed World Cup matches on TV. 30 per cent of the people who had not watched World Cup matches were industrial workers. What is the number of agricultural workers who had enjoyed World Cup matches on TV?
A
230✓✗
B
250✓✗
C
240✓✗
D
260✓✗
Explanation
Industrial workers = 250, Agricultural workers = 750.
Non-watchers = 1000 - 300 = 700. Industrial among non-watchers = 30% of 700 = 210.
So industrial watchers = 250 - 210 = 40.
Agricultural watchers = Total watchers - Industrial watchers = 300 - 40 = 260
Question 6
A town has a total population of 50,000. Out of it, 28,000 read the newspaper X and 23,000 read Y while 4,000 read both the papers. The number of persons not reading X and Y both is
A
2,000✓✗
B
3,000✓✗
C
2,500✓✗
D
none of these✓✗
Explanation
Reading at least one paper = 28,000 + 23,000 - 4,000 = 47,000
Not reading either paper = 50,000 - 47,000 = 3,000
Question 7
Out of a total of 150 students, 45 passed in Accounts, 30 in Economics and 50 in Maths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 in both Accounts and Economics, and 25 students passed in all three subjects. Find the number who passed in at least one of the subjects.
A
63✓✗
B
53✓✗
C
73✓✗
D
None of these✓✗
Explanation
Using the inclusion-exclusion principle:
Passed at least one = 45 + 30 + 50 - 30 - 32 - 35 + 25 = 53
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