Discussion

If the 8-digit number 179x091y is divisible by 88, then what is the value of \((x - y)\) ?

Answer: B

The value of \((x - y)\) is 2.

\(88 = 8 \times 11\), and 8 and 11 are co-prime, so the number must be divisible by both.

Divisible by 8: the last three digits 91y must be divisible by 8. Among 910 to 919 only 912 is (\(912 = 8 \times 114\)), so \(y = 2\).

Divisible by 11: the difference between the sums of alternate digits of 179x0912 must be a multiple of 11.

\[ \begin{aligned} (1 + 9 + 0 + 1) &= 11 \\ (7 + x + 9 + 2) &= 18 + x \\ (18 + x) - 11 &= 7 + x \end{aligned} \]

For \(7 + x\) to be a multiple of 11 with x a single digit, \(x = 4\). So \(x - y = 4 - 2 = 2\). The value 4 is x itself, not \(x - y\).

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