1996 AHSME Problems/Problem 1

Problem

The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?

$\begin{tabular}{rr}&\ \texttt{6 4 1}\\ &\texttt{8 5 2}\\ &+\texttt{9 7 3}\\ \hline  &\texttt{2 4 5 6}\end{tabular}$

$\text{(A)}\ 4\qquad\text{(B)}\ 5\qquad\text{(C)}\ 6\qquad\text{(D)}\ 7\qquad\text{(E)}\ 8$

Solution

Doing the addition as is, we get $641 + 852 + 973 = 2466$. This number is $10$ larger than the desired sum of $2456$. Therefore, we must make one of the three numbers $10$ smaller.

We may either change $641 \rightarrow 631$, $852 \rightarrow 842$, or $973 \rightarrow 963$. Either change results in a valid sum. The largest digit that could be changed is thus the $7$ in the number $973$, and the answer is $\boxed{D}$.

See also

1996 AHSME (ProblemsAnswer KeyResources)
Preceded by
First question
Followed by
Problem 2
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All AHSME Problems and Solutions

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