BrainTeaser AMC8 Intermediate
2006


Problem - 992

$\textbf{Multiplication}$

In the multiplication problem below, $A$, $B$, $C$, and $D$ are different digits. What is $A+B$? $$\begin{array}{cccc}& A & B & A\\ \times & & C & D\\ \hline C & D & C & D\\ \end{array}$$


$\textbf{Answer}$

$1$

$\textbf{Analysis}$

Of course it is possible to use the trial and error approach to determine the value of all these letters. However, there is a quick way by noting the identity $$CD\cdot 101 = CDCD$$

Therefore, $ABA = 101 \implies A+B =1$.

$\textbf{Note}$

Most brain teasers do not require math knowledge. However, sometimes, having some math knowledge can be very helpful.

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