If the 9-digit number 924x597y4 is divisible by 88, then the maximum possible value of (5x − 3y) is:

Explanation

Divisible by 8: the last three digits 7y4 must be divisible by 8, so y = 0, 4 or 8. Divisible by 11: (9 + 4 + 5 + 7 + 4) − (2 + x + 9 + y) = 18 − x − y must be 0 or ±11, so x + y = 7 or 18. Valid pairs are (x, y) = (7, 0) and (3, 4). The values of 5x − 3y are 35 and 3, so the maximum is 35.