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    Question

    A 7-digit number ‘538p7q2’ is divisible by 24.

    Determine the minimum possible value of (p × q).
    A 2 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer
    D 4 Correct Answer Incorrect Answer

    Solution

    ATQ,

    ‘538p7q2’ is divisible by 24.

    So, it must be divisible by both ‘3’ and ‘8’.

    Divisibility by ‘8’: Last three digits must be divisible by ‘8’.

    Divisibility by ‘3’: Sum of the digits of the number must be divisible by ‘3’.

    So, 7q2 has to be divisible by 8.

    Possible values for q = 1, 5, 9

    Again, for the number to be divisible by 3,

    (5 + 3 + 8 + p + 7 + q + 2) = (25 + p + q) has to be divisible by 3.

    If q = 1, then (26 + p) will be divisible by 3 if p = 1, 4, 7

    If q = 5, then (30 + p) will be divisible by 3 if p = 0, 3, 6, 9

    If q = 9, then (34 + p) will be divisible by 3 if p = 2, 5, 8

    Minimum value of (p × q) from all the combinations = 1 × 1 = 1

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