An eight-digit number, 81x3y72 is divisible by 72. Find

Solution

Given number is 81x3y72. 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 y72. So, the possible values of y are 0, 2, 4, 6, 8. For the number to be divisible by 9, the sum digits of the given number should be a multiple of 9. So, sum of the digits of the given number
= 8 + 1 + x + 3 + y + 7 + 2 = 21 + x + y So, next multiples of 9 after 21 are 27 and 36. So, possible values of (x + y) are 6 and 15. When, x + y = 15, take y = 8 and x = 7. So, this case is valid and sufficient to conclude that maximum value of x + y = 15. Hence, option A.