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    Question

    How many numbers in the range from 300 to 900 are

    divisible by 7, 14, and 28?
    A 37 Correct Answer Incorrect Answer
    B 22 Correct Answer Incorrect Answer
    C 55 Correct Answer Incorrect Answer
    D 43 Correct Answer Incorrect Answer

    Solution

    ATQ;

    If a number is a multiple of 7, 14, and 28, then the number is a multiple of the L.C.M of 7, 14, and 28.

    L.C.M of 7, 14, and 28 = 28

    Smallest multiple of 28 between 300 and 900 = 308

    Largest multiple of 28 between 300 and 900 = 896

    Common difference = 28

    Let the required number of terms be 'n'.

    So, 308 + (n - 1) × 28 = 896

    Or, n - 1 = (896 - 308) ÷ 28 = 21

    So, n = 21 + 1 = 22

    So, there are 22 numbers between 300 and 900 which are multiples of 7, 14, and 28.

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