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CAT 2016 Slot 1 · Quant · Permutations, Combinations and Sets · medium

In a class of 60 students, 35 like tea, 30 like coffee and 10 like neither. How many students like exactly one of the two beverages?

Single correct option

In a class of 60 students, 35 like tea, 30 like coffee and 10 like neither. How many students like exactly one of the two beverages?
  1. A. 35
  2. B. 30
  3. C. 25
  4. D. 20
Show answer and solution

Answer: (A) 35

Students who like at least one = 60 − 10 = 50.

n(T ∩ C) = n(T) + n(C) − n(T ∪ C) = 35 + 30 − 50 = 15.

Exactly one = (at least one) − (both) = 50 − 15 = 35.

(Tea only = 20, coffee only = 15.)

Trap: Answering 15 (those who like both) or 50 (at least one).
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Original question written in the CAT 2016 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake