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$\overline{392AB}$ is a multiple of $45$, and $\overline{B34}$ is a three-digit even number. What is the sum of $A$ and $B$? 
Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
$45=5\times9$  $\overline{392AB}$ should be ended with $0$ or $5.$ But $0$ cannot be the first digit. Thus, $B$ can only be $5$ and $A$ should be $8.$ 