Discussion
If a 8 - digit number 9 4 7 1 x 9 y 2 is divisible by 72, then which of the following statements is not true ?
Answer: C
The statement that is not true is x = 9 and y = 5.
72 = 8 × 9, so the number must be divisible by both 8 and 9. For 8, the last three digits 9y2 must be a multiple of 8: 912, 952 and 992 work, so y is 1, 5 or 9. For 9, the digit sum must be a multiple of 9:
\[ 9 + 4 + 7 + 1 + x + 9 + y + 2 = 32 + x + y \]
so x + y must be 4 or 13. The pairs (8, 5), (4, 9) and (3, 1) give 13, 13 and 4, but (9, 5) gives 14, which makes the digit sum 46, not a multiple of 9.
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