2014 AMC 8 Problem 8

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 \$\underline{1}\underline{A}\underline{2}. What is the missing digit A of this 3-digit number?

\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.