Sets (Games) — Out of 64 students, 38 play both chess and cricket. How many play only chess? Statements: I. Of 64 students, 22 play no game; 4 play only cricket. II. Of 64 students, 20 are girls and 10 girls play no game.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Classic two-set (chess, cricket) problem asking for the 'only chess' count. Given Data / Assumptions: Total students = 64. Both chess & cricket = 38. I: None = 22; Only cricket = 4. II: Girl counts (irrelevant to chess/cricket split unless further data is given). Concept / Approach:Use inclusion–exclusion on the playing subset. Step-by-Step Solution: From I: Number who play at least one game = 64 − 22 = 42.Let x = only chess. Then x + (only cricket 4) + (both 38) = 42 ⇒ x = 0.Thus, 'only chess' = 0 (unique).From II alone: Gender information does not connect to game partitions; cannot solve. Verification / Alternative check:Check non-negativity and totals: 0 + 4 + 38 + 22 = 64 ✔. Why Other Options Are Wrong: B/C/D/E: II alone is irrelevant; I alone already suffices. Common Pitfalls:Forgetting that 'k between' style offsets do not apply here; misapplying inclusion–exclusion. Final Answer:A — Statement I alone suffices (Only chess = 0).

Sets (Games) — Out of 64 students, 38 play both chess and cricket. How many play only chess? Statements: I. Of 64 students, 22 play no game; 4 play only cricket. II. Of 64 students, 20 are girls and 10 girls play no game.

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