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    Question

    How many numbers in the range from 200 to 800 are

    divisible by 4, 8, and 16?
    A 37 Correct Answer Incorrect Answer
    B 28 Correct Answer Incorrect Answer
    C 55 Correct Answer Incorrect Answer
    D 75 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ;
    If a number is a multiple of 4, 8, and 16, then the number is a multiple of the L.C.M of 4, 8, and 16.

    L.C.M of 4, 8, and 16 = 16

    Smallest multiple of 16 between 200 and 800 = 208

    Largest multiple of 16 between 200 and 800 = 784

    Common difference = 16

    Let the required number of terms be 'n'.

    So, 208 + (n - 1) ├Ч 16 = 784

    Or, n - 1 = (784 - 208) ├╖ 16 = 36

    So, n = 36 + 1 = 37

    So, there are 37 numbers between 200 and 800 which are multiples of 4, 8, and 16.

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