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CAT 1991 — QA Question 30

Venn DiagramEasy

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

Correct answer: 25

  • A

    20

  • 25

  • C

    50

  • D

    70

Solution

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).

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CAT 1991 QA Q30: There are 3 clubs A, B & C in a town with 40, 50 & 60 members respectively. While 10 people are members of all — Solution | TheCATExam