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UKMT Grey Kangaroo, 2021

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A student correctly added the two two-digit numbers on the left of the board and got the answer 137. What answer will she obtain if she adds the two four-digit numbers on the right of the board? $\begin{array}{cc} \begin{array}{r}AB\\+CD\\\hline 137\end{array} & \begin{array}{r}ADCB\\+CBAD\\\hline ?\end{array}\end{array}$

(A) $13737$ (B) $13837$ (C) $14747$ (D) $23723$ (E) $137137$

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