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    Question

    An eight-digit number, 73x216y4 is divisible by 72. Find

    the maximum possible value of x + y.
    A 10 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 13 Correct Answer Incorrect Answer
    D 15 Correct Answer Incorrect Answer

    Solution

    Given number is 73x216y4 For a number to be divisible by 72, then it should be divisible by both 8 and 9. So, we will check the divisibility rule of 8 and 9. For the given number to be divisible by 8, the last three digits of the number should be divisible by 8. Last three digits of the given number are 6y4 So, the possible values of y are 2 and 6 For the number to be divisible by 9, the sum of the digits of the given number should be a multiple of 9. So, sum of the digits of the given number
    = 7 + 3 + x + 2 + 1 + 6 + y + 4
    = 23 + x + y So, next multiples of 9 after 23 are 27 and 36 So, possible values of (x + y) are 4 and 13 When, x + y = 13, take y = 6 and x = 7 So, this case is valid and sufficient to conclude that maximum value of x + y = 13 Hence, option C 

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