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CMAT 2020 · Quantitative Techniques & Data Interpretation · Easy · Set Theory

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In a certain town, 40% of people have brown hair, 30% of people have brown eyes and 12% have both brown hair and brown eyes. How many people in town have neither brown hair nor brown eyes ?

  1. A.

    44%

  2. B.

    43%

  3. C.

    41%

  4. D.

    42%

Answer

D

Explanation

Let AA be the set of people with brown hair and BB be the set of people with brown eyes.

P(A)=40%P(A) = 40\%, P(B)=30%P(B) = 30\%, P(A∩B)=12%P(A \cap B) = 12\%.

P(A∪B)=P(A)+P(B)−P(A∩B)=40%+30%−12%=58%P(A \cup B) = P(A) + P(B) - P(A \cap B) = 40\% + 30\% - 12\% = 58\%.

Percentage of people having neither = 100%−58%=42%100\% - 58\% = 42\%.

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