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    Question

    How many numbers in the range from 50 to 500 are divisible

    by 3, 6, and 9?
    A 37 Correct Answer Incorrect Answer
    B 22 Correct Answer Incorrect Answer
    C 25 Correct Answer Incorrect Answer
    D 43 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ;

    If a number is a multiple of 3, 6, and 9, then the number is a multiple of the L.C.M of 3, 6, and 9.

    L.C.M of 3, 6, and 9 = 18

    Smallest multiple of 18 between 50 and 500 = 54

    Largest multiple of 18 between 50 and 500 = 486

    Common difference = 18

    Let the required number of terms be 'n'.

    So, 54 + (n - 1) × 18 = 486

    Or, n - 1 = (486 - 54) ÷ 18 = 24

    So, n = 24 + 1 = 25

    So, there are 25 numbers between 50 and 500 which are multiples of 3, 6, and 9.

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