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Minimum Overlap of Four Sets

XAT 2013 · Quantitative Ability & Data Interpretation · Medium · Set Theory

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70% of the students who joined XCRI last year play football, 75% play cricket, 80% play basketball and 85% play carrom. The minimum percentage of students who play all four games is:

  1. A.

    5%

  2. B.

    10%

  3. C.

    15%

  4. D.

    20%

  5. E.

    None of the above

Answer

B

Explanation

Using the formula for minimum intersection of nn sets: Min(A∩B∩C∩D)=100−[(100−70)+(100−75)+(100−80)+(100−85)]=100−[30+25+20+15]=100−90=10%\text{Min}(A \cap B \cap C \cap D) = 100 - [(100-70) + (100-75) + (100-80) + (100-85)] = 100 - [30 + 25 + 20 + 15] = 100 - 90 = 10\%.

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