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    Question

    How many numbers in the range from 150 to 1000 are

    divisible by 5, 10, and 20?
    A 37 Correct Answer Incorrect Answer
    B 28 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 5, 10, and 20, then the number is a multiple of the L.C.M of 5, 10, and 20.

    L.C.M of 5, 10, and 20 = 20

    Smallest multiple of 20 between 150 and 1000 = 160

    Largest multiple of 20 between 150 and 1000 = 1000

    Common difference = 20

    Let the required number of terms be 'n'.

    So, 160 + (n - 1) × 20 = 1000

    Or, n - 1 = (1000 - 160) ÷ 20 = 42

    So, n = 42 + 1 = 43

    So, there are 43 numbers between 150 and 1000 which are multiples of 5, 10, and 20.

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