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    Question

    What is the highest possible sum of (m + n) if the

    number '9m813n2' is divisible by 12?
    A 15 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 16 Correct Answer Incorrect Answer
    D 18 Correct Answer Incorrect Answer

    Solution

    ATQ,

    A number is divisible by 12 if it is divisible by both 3 and 4.

    A number is divisible by 4 when the last two digits of the number are divisible by 4.

    'n2' is divisible by 4 when 'n' = 0, 2, 4, 6, or 8.

    Since we have to find the maximum value, so 'n' = 8.

    A number is divisible by 3 when the sum of its digits is divisible by 3.

    So, (9 + m + 8 + 1 + 3 + 8 + 2) = (31 + m) must be divisible by 3.

    So, 'm' = 2, 5, or 8.

    Since we have to find the maximum value, so 'm' = 8.

    Therefore, required value = 8 + 8 = 16 .

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