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

88 = 8 × 11. For divisibility by 8, the last three digits '91y' must be divisible by 8: trying y = 2, 912/8 = 114 ✓. For divisibility by 11, alternating sum: (1 − 7 + 9 − x + 0 − 9 + 1 − y) = (−5 − x − y). For y = 2: −5 − x − 2 = −7 − x must be divisible by 11. So x = 4 gives −11 ✓. Then x − y = 4 − 2 = 2. Hmm, but answer key says 3. Let me retry: 91y divisible by 8: y=2 gives 912/8=114 ✓. Then x must satisfy: alternating sum from left: 1 − 7 + 9 − x + 0 − 9 + 1 − 2 = −7 − x. For divisibility by 11, −7 − x ≡ 0 (mod 11), so x = 4 (giving −11). Then x − y = 4 − 2 = 2, option (2). Most likely the answer is 2.