Discussion
If a six digits number 72x292 is divisible by 36, then the value of (3x+2) is :
Answer: B
The value of \(3x + 2\) is 17.
A number is divisible by 36 when it is divisible by both 4 and 9. The last two digits, 92, are divisible by 4, so that condition holds for any \(x\). For 9, the digit sum must be a multiple of 9:
\[ \begin{aligned} 7 + 2 + x + 2 + 9 + 2 &= 22 + x \\ 22 + x = 27 &\Rightarrow x = 5 \\ 3x + 2 &= 3(5) + 2 = 17 \end{aligned} \]
The next multiple, 36, would need \(x = 14\), which is not a digit. 16, 20 and 15 correspond to \(x\) values that do not make 72x292 divisible by 9.
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