Discussion

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

Answer: B

The value of (3x + y) is 5.

88 = 8 × 11, and 8 and 11 have no common factor, so the number must be divisible by both.

By 8: the last three digits, 67y, must be divisible by 8. Among 670 to 679 only 672 works, so y = 2.

By 11: the difference between the sums of alternate digits of 3 0 x 0 8 6 7 2 must be a multiple of 11:

\[ \begin{aligned} &(3 + x + 8 + 7) - (0 + 0 + 6 + 2) \\ &= 18 + x - 8 = 10 + x \end{aligned} \]

With x a single digit, 10 + x = 11 gives x = 1. Then 3x + y = 3 + 2 = 5. The number is 30108672 = 88 × 342144.

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