Discussion
If the 7-digit number 41x483y is divisible by 72, what is the value of \(x+y\)?
Answer: D
Correct answer: 7
Since \(72 = 8 \times 9\), apply both tests.
Divisibility by 8. The last three digits are 83y, that is \(830 + y\). Because \(830 = 8\times 103 + 6\), we need \(6 + y \equiv 0 \pmod 8\), giving \(y = 2\) as the only digit.
Divisibility by 9. The digit sum is \(4+1+x+4+8+3+2 = 22 + x\), which must be a multiple of 9. Only \(x = 5\) qualifies, for a sum of 27.
The number is 4154832, and \(4154832 \div 72 = 57706\). Hence \(x + y = 5 + 2 = 7\).
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