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    Question

    How many numbers between 200 and 1000 are divisible by both

    20 and 30?
    A 30 Correct Answer Incorrect Answer
    B 28 Correct Answer Incorrect Answer
    C 13 Correct Answer Incorrect Answer
    D 20 Correct Answer Incorrect Answer

    Solution

    ATQ,

    A number divisible by both 20 and 30 must be divisible by L.C.M. of 20 and 30 = 60

    We look for numbers divisible by 60 in the given range:

    First term (a) = 60 × 4 = 240

    Common difference (d) = 60

    Last term (L) = 60 × 16 = 960

    Let the number of terms be n.

    Use the A.P. formula:

    a + (n - 1)d = L

    Substitute values:

    240 + (n - 1) × 60 = 960

    ⇒ 240 + 60n - 60 = 960

    ⇒ 60n = 780

    ⇒ n = 780 ÷ 60 = 13

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