Discussion
If 8A5146B is divisible by 88, then what is the value of B-A?
Answer: C
Correct answer: 1
Since \(88 = 8 \times 11\), both tests must pass.
Divisibility by 8. The last three digits are 46B, that is \(460 + B\). Because \(460 = 8\times 57 + 4\), we need \(4 + B \equiv 0 \pmod 8\), so \(B = 4\).
Divisibility by 11. With \(B = 4\), take the alternating sum of 8A5146B from the right:
\[(4 + 4 + 5 + 8) - (6 + 1 + A) = 21 - (7 + A) = 14 - A\]
This must be 0 or a multiple of 11. Only \(14 - A = 11\) leaves \(A\) a digit, so \(A = 3\).
The number is 8351464, and \(8351464 \div 88 = 94903\). Hence \(B - A = 4 - 3 = 1\).
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