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    Question

    There are is chest containing only diamond and emeralds

    in the ratio 2:5. When 2 of them are picked at random form the chest, the probability that both are diamonds is 1/14. What is the difference between the number of diamonds and emeralds?
    A 12 Correct Answer Incorrect Answer
    B 8 Correct Answer Incorrect Answer
    C 15 Correct Answer Incorrect Answer
    D 7 Correct Answer Incorrect Answer
    E 9 Correct Answer Incorrect Answer

    Solution

    Let the number of diamonds and emeralds in the chest be 2k and 5k respectively.

    P(2 diamonds) = 1/14

    ( 2k C2 )/( 7k C2 ) = 1/14

    2k(2k - 1)/7k(7k - 1) = 1/14

    7k - 1 = 4(2k - 1)

    7k - 1 = 8k - 4

    k = 3

    Required difference = 5k - 2k = 9

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