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Eleven members of the Middle School Math Club each paid the same integer amount for a guest speaker to talk about problem solving at their math club meeting. In all, they paid their guest speaker $$\overline{1A2}$$. What is the missing digit $A$ of this $3$-digit number? (2014 AMC 8 Problem, Question \#8) 
Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
$1+2-A=0$, $A=3$. 