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

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Doing the addition as is, we get <math>641 + 852 + 973 = 2466</math>.  This number is <math>10</math> larger than the desired sum of <math>2456</math>.  Therefore, we must make one of the three numbers <math>10</math> smaller.
 
Doing the addition as is, we get <math>641 + 852 + 973 = 2466</math>.  This number is <math>10</math> larger than the desired sum of <math>2456</math>.  Therefore, we must make one of the three numbers <math>10</math> smaller.
  
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We may either change <math>641 \rightarrow 631</math>, <math>852 \rightarrow 842</math>, or <math>973 \rightarrow 963</math>.  Either change results in a valid sum.  The largest digit that could be changed is thus the <math>7</math> in the number <math>973</math>, and the answer is <math>\boxed{D}</math>.
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We may either change <math>641 \rightarrow 631</math>, <math>852 \rightarrow 842</math>, or <math>973 \rightarrow 963</math>.  Either change results in a valid sum.  The largest digit that could be changed is thus the <math>7</math> in the number <math>973</math>, and the answer is <math>\boxed{\textbf{(D) }7}</math>.
  
 
==See also==
 
==See also==
 
{{AHSME box|year=1996|before=First question|num-a=2}}
 
{{AHSME box|year=1996|before=First question|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 15:06, 14 July 2021

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 $\boxed{\textbf{(D) }7}$.

See also

1996 AHSME (Problems • Answer Key • Resources)
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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