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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is  [Roorkee 1997]

    A) 3100

    B) 3300

    C) 2900

    D) 1400

    Correct Answer: B

    Solution :

    n = 40% of 10,000 = 4,000 n = 20% of 10,000 = 2,000 n = 10% of 10,000 = 1,000 n (A Ç B) = 5% of 10,000 = 500 n (B Ç C) = 3% of 10,000 = 300 n(C Ç A) = 4% of 10,000 = 400 n(A Ç B Ç C) = 2% of 10,000 = 200 We want to find n(A Ç Bc Ç Cc) = n[A Ç (B È C)c] = n - n[A Ç (B È C)] = n - n[(A Ç B) È (A Ç C)] = n - [n(A Ç B) + n(A Ç C) - n(A Ç B Ç C)] = 4000 - [500 + 400 - 200] = 4000 - 700 = 3300.


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