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}{ | + | <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> | ||
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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. | ||
| − | 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>. | + | 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== | ||
| + | {{AHSME box|year=1996|before=First question|num-a=2}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:06, 14 July 2021
Problem
The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?
Solution
Doing the addition as is, we get 
. This number is 
larger than the desired sum of 
. Therefore, we must make one of the three numbers smaller.
We may either change 
, 
, or 
. Either change results in a valid sum. The largest digit that could be changed is thus the 
in the number 
, and the answer is 
.
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
