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    Question

    If a ten-digit number 57a61395z2 is divisible by 72, then

    find the number of possible values of ‘a’.
    A 1 Correct Answer Incorrect Answer
    B 4 Correct Answer Incorrect Answer
    C 2 Correct Answer Incorrect Answer
    D 3 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Since, the number 57a61395z2 is divisible by 72, therefore it has to be divisible by 8 and 9, individually

    If the number is divisible by 8, therefore last three digits should be divisible by 8

    Hence, z = 0, 4 and 8

    Now, check divisibility by 9

    When z = 0, sum of the digits = 47 + a

    Hence, a = 2

    When z = 4, sum of the digits = 51 + a

    Hence, a = 3

    When z = 8, sum of the digits = 55 + a

    Hence, a = 1

    Therefore, number of possible values of a = 3

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