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    Question

    Find the number of possible digits 'm' such that the number

    3816mn is divisible by 15.
    A 12 Correct Answer Incorrect Answer
    B 10 Correct Answer Incorrect Answer
    C 5 Correct Answer Incorrect Answer
    D 7 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Divisible by 15 ⇒ divisible by 5 and 3

    Divisible by 5: last digit n must be 0 or 5

    Divisible by 3: sum of digits must be divisible by 3

    Case 1: n = 0

    Sum = 3 + 8 + 1 + 6 + m + 0 = m + 18

    Divisible by 3 ⇒ m = 0, 3, 6, 9

    Case 2: n = 5

    Sum = 3 + 8 + 1 + 6 + m + 5 = m + 23

    Divisible by 3 ⇒ m = 1, 4, 7

    Total values of m: 4 + 3 = 7

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