If the 9-digit number 5y97405x2, is divisible by 72, find the value of (x – 2y) for the greatest value of x.
For the number 5y97405x2 to be divisible by 72: Divisibility by 8: Last three digits (5x2) must be divisible by 8. For x = 4, (542) is divisible by 8. Divisibility by 9: Sum of digits (36 + y) must be divisible by 9. For (y = 0), (36) is divisible by 9. Thus, with (x = 4) and (y = 0), (x - 2y = 4 - 2(0) = 4.
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