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    Question

    What is the highest possible sum of (u + v) if the

    number '6u317v4' 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.

    'v4' is divisible by 4 when 'v' = 0, 2, 4, 6, or 8.

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

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

    So, (6 + u + 3 + 1 + 7 + 8 + 4) = (29 + u) must be divisible by 3.

    So, 'u' = 1, 4, or 7.

    Since we have to find the maximum value, so 'u' = 7.

    Therefore, required value = 7 + 8 = 15 .

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