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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.

Difficulty: Medium

Statement I alone is sufficient; Statement II alone is not sufficient.
Statement II alone is sufficient; Statement I alone is not sufficient.
Either Statement I alone or Statement II alone is sufficient.
Both Statements I and II together are not sufficient.
Both Statements I and II together are sufficient, but neither alone is sufficient.

Correct Answer: Statement I alone is sufficient; Statement II alone is not sufficient.

Explanation:

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.

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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