Discussion

If the 7-digit number 134x58y is divisible by 72, then the value of (2x + y) is

Answer: C

The value of 2x + y is 8.

72 = 8 × 9, and 8 and 9 have no common factor, so the number must be divisible by both.

By 8: the last three digits, 58y, must be divisible by 8. Among 580 to 589 only 584 is, so y = 4.

By 9: the digit sum must be a multiple of 9.

\[ \begin{aligned} 1+3+4+x+5+8+4 &= 25 + x \\ 25 + x = 27 &\Rightarrow x = 2 \end{aligned} \]

(x = 11 is impossible for a digit.) So 2x + y = 4 + 4 = 8, and the number is 1342584. The values 6, 7 and 9 come from a wrong digit for x or y.

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