An eight-digit number, 18x297y6 is divisible by 72.

Solution

Given number is 18x297y6. 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 7y6. So, the possible values of y are 3 and 7. 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
= 1 + 8 + x + 2 + 9 + 7 + y + 6 = 33 + x + y So, next multiples of 9 after 33 are 36 and 45. So, possible values of (x + y) are 3 and 12. When, x + y = 12, take y = 7 and x = 5. So, this case is valid and sufficient to conclude that maximum value of x + y = 12. Hence, option B.