CAT 1991 — QA Question 30
Answer the following questions based on the information given below:
There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
There are 3 clubs A, B & C in a town with 40, 50 & 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?
Answer & solution
- A
20
25
- C
50
- D
70
Given, x + y + z = 70
x + a + b = 40 – 10 = 30 ... (i)
y + b + c = 50 – 10 = 40 ... (ii)
z + a + c = 60 – 10 = 50 ... (iii)
From (i), (ii) and (iii), we get
(x + y + z) + 2(a + b + c) = 120
⇒ a + b + c = 25.
Hence, option (b).