If an 8-digit number 30x0867y is divisible by 88, then what is the value of (3x + y)?

88 = 8 × 11, so the number must be divisible by both 8 and 11. For divisibility by 8, the last three digits 67y must be divisible by 8. Checking: 670/8=83.75, 672/8=84, so y=2 works. For divisibility by 11, alternating sum: 3-0+x-0+8-6+7-y = 12+x-y. For y=2: 12+x-2 = 10+x. For this to be divisible by 11, x=1 (giving 11). So x=1, y=2. Then 3x+y = 3(1)+2 = 5. The answer per options should be 5, option (2). However, key indicates 7. Checking alternative: if y=2 doesn't give 11-divisibility, try other y values for divisibility by 8: 67y divisible by 8 means y can be such that 670+y ≡ 0 mod 8. 670 mod 8 = 6, so y must equal 2 (since 6+2=8). Hence y=2 is unique. Then x=1, giving 3x+y=5.