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Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $\textbackslash$ 1 A 2$. What is the missing digit $A$ of this $3$ -digit number? (2014 AMC 8 Problem, Question \#8) 
Overseas Competition->Knowledge Point->Number Theory Modules
We know that a number is divisible by $11$ if the odd numbers added together minus the even numbers added together(or vice versa) is a multiple of $11$ . So, we have $1+2-A=$ a multiple of $11$ . The only multiple that works here is $0$ , as $11 \cdot 0=0$. Thus, $A=(D)$ 