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CAT 1997 — QA Question 22

Venn DiagramEasy
Passage / Data

Direction: Answer the questions based on the following information.

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC and 15% watched CNN.

What is the maximum percentage of people who can watch all the three channels?

Answer & solution

  • A

    12.5%

  • 8.5%

  • C

    15%

  • D

    Data insufficient

Solution

Here, a + b + c + d + e + f + g = 200 ...(i)
80% of the people watch DD implies
c + d + f + g = 160 ...(ii)
22% of the people watch BBC implies
a + d + e + g = 44 ...(iii)
15% of the people watch CNN implies
b + e + f + g = 30 ...(iv)
(ii) + (iii) + (iv) gives
a + b + c + 2(d + e + f) + 3g = 234
Subtracting (i) from this equation,
d + e + f + 2g = 34 ...(v)

To maximize g, in equation (v), we put d = e = f = 0
∴ Maximum value of g = 342 = 17

∴ Required percentage = 17200 × 100 = 8.5%

Hence, option (b).

CAT 1997 QA Q22: What is the maximum percentage of people who can watch all the three channels? — Solution | TheCATExam