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State PCS PYQPrelims 2022

BPSC – Combined Competitive Examination · Question 84

In a class of 55 students, 34 like cricket and 26 like badminton; every student likes at least one. How many like both?

  1. 4
  2. 5
  3. 6
  4. 3
  5. None of the above / More than one of the above
Show answer & explanation

Answer: (B) 5

Explanation

n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 34 + 26 − 55 = 5.

  • (A) Incorrect

    Wrong: 34 + 26 − 55 = 5.

  • (B) Correct

    Correct: both = 34 + 26 − 55 = 5.

  • (C) Incorrect

    Wrong: 34 + 26 − 55 = 5.

  • (D) Incorrect

    Wrong: 34 + 26 − 55 = 5.

  • (E) Incorrect

    Wrong: only one of the options A–D is correct.