Difference between revisions of "1996 AHSME Problems/Problem 1"

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The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?
 
The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?
 
   
 
   
<math> \begin{tabular}{r}&\ \texttt{6 4 1}\\ \texttt{8 5 2} &+\texttt{9 7 3}\\ \hline  \texttt{2 4 5 6}\end{tabular} </math>
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<math> \begin{tabular}{rr}&\ \texttt{6 4 1}\\ &\texttt{8 5 2}\\ &+\texttt{9 7 3}\\ \hline  &\texttt{2 4 5 6}\end{tabular} </math>
  
 
<math> \text{(A)}\ 4\qquad\text{(B)}\ 5\qquad\text{(C)}\ 6\qquad\text{(D)}\ 7\qquad\text{(E)}\ 8 </math>
 
<math> \text{(A)}\ 4\qquad\text{(B)}\ 5\qquad\text{(C)}\ 6\qquad\text{(D)}\ 7\qquad\text{(E)}\ 8 </math>

Latest revision as of 19:51, 10 March 2015

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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

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