2006 AMC 8 Problems/Problem 24

Problem

In the multiplication problem below $A$ , $B$ , $C$ , $D$ and are different digits. What is $A+B$ ?

\[\begin{tabular}{cccc}& A & B & A\\ \times & & C & D\\ \hline C & D & C & D\\ \end{tabular}\] (Error compiling LaTeX. Unknown error_msg)

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 9$

$CDCD = CD \cdot 101$ , so $ABA = 101$ . Therefore, $A = 1$ and $B = 0$ , so $A+B=1+0=\boxed{\textbf{(A)}\ 1}$ .

2006 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 23	Followed by Problem 25
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