Minimum Overlap of Four Sets

CAT 2003 Slot 1 · DILR · Medium · Set Theory

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Seventy percent of the employees in a multinational corporation have VCD players, 75% have microwave ovens, 80% have ACs and 85% have washing machines. At least what percentage of employees has all four gadgets?

  1. A.

    15

  2. B.

    5

  3. C.

    10

  4. D.

    Cannot be determined

Answer

C

Explanation

Minimum overlap for NN sets in percentage: 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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