Discussion
If a 8-digit number \(947x19y2\) is divisible by 72, then which of the following is not true?
Answer: D
The statement that is not true is x = 7 and y = 3. A number is divisible by 72 when it is divisible by both 8 and 9. For divisibility by 8, the last three digits 9y2 must be divisible by 8, which holds for y = 1, 5 and 9 (912, 952 and 992 are divisible by 8) and not for y = 3 (932 is not).
For divisibility by 9 the digit sum must be a multiple of 9:
\[ 9 + 4 + 7 + x + 1 + 9 + y + 2 = 32 + x + y \]
So x + y = 4 or 13. This gives x = 3, y = 1; x = 8, y = 5; and x = 4, y = 9, which are the first three options. The pair x = 7, y = 3 fails both tests, so the fourth option is the one that is not true.
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