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CAT 2025 Slot 3 · Quant · Permutations, Combinations and Sets · easy

In a class of 60 students, 35 play cricket, 30 play football, and 12 play neither sport. How many students play both cricket and football?

Single correct option

In a class of 60 students, 35 play cricket, 30 play football, and 12 play neither sport. How many students play both cricket and football?
  1. A. 15
  2. B. 17
  3. C. 19
  4. D. 22
Show answer and solution

Answer: (B) 17

Number of students playing at least one sport = Total − Neither = 60 − 12 = 48. By the set formula, |C∪F| = |C| + |F| − |C∩F|, so 48 = 35 + 30 − |C∩F|, giving |C∩F| = 65 − 48 = 17. So 17 students play both cricket and football.
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Original question written in the CAT 2025 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake