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.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
Answer
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.
Final Answer:A — Statement I alone suffices (Only chess = 0).