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Difference between revisions of "1989 AJHSME Problems/Problem 14"

(New page: ==Problem== When placing each of the digits <math>2,4,5,6,9</math> in exactly one of the boxes of this subtraction problem, what is the smallest difference that is possible? <mat...)
 
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When placing each of the digits <math>2,4,5,6,9</math> in exactly one of the boxes of this [[subtraction]] problem, what is the smallest [[difference]] that is possible?
 
When placing each of the digits <math>2,4,5,6,9</math> in exactly one of the boxes of this [[subtraction]] problem, what is the smallest [[difference]] that is possible?
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<math>\text{(A)}\ 58 \qquad \text{(B)}\ 123 \qquad \text{(C)}\ 149 \qquad \text{(D)}\ 171 \qquad \text{(E)}\ 176</math>
 
  
 
<cmath>\begin{tabular}[t]{cccc}
 
<cmath>\begin{tabular}[t]{cccc}
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- & & \boxed{} & \boxed{} \\ \hline
 
- & & \boxed{} & \boxed{} \\ \hline
 
\end{tabular}</cmath>
 
\end{tabular}</cmath>
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<math>\text{(A)}\ 58 \qquad \text{(B)}\ 123 \qquad \text{(C)}\ 149 \qquad \text{(D)}\ 171 \qquad \text{(E)}\ 176</math>
  
 
==Solution==
 
==Solution==
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{{AJHSME box|year=1989|num-b=13|num-a=15}}
 
{{AJHSME box|year=1989|num-b=13|num-a=15}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 10:49, 30 July 2023

Problem

When placing each of the digits $2,4,5,6,9$ in exactly one of the boxes of this subtraction problem, what is the smallest difference that is possible?

\[\begin{tabular}[t]{cccc} & \boxed{} & \boxed{} & \boxed{} \\ - & & \boxed{} & \boxed{} \\ \hline \end{tabular}\]

$\text{(A)}\ 58 \qquad \text{(B)}\ 123 \qquad \text{(C)}\ 149 \qquad \text{(D)}\ 171 \qquad \text{(E)}\ 176$

Solution

When trying to minimize $a-b$, we minimize $a$ and maximize $b$. Since in this problem, $a$ is three digit and $b$ is two digit, we set $a=245$ and $b=96$. Their difference is $149\rightarrow \boxed{\text{C}}$.

See Also

1989 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 13 		Followed by
Problem 15
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
All AJHSME/AMC 8 Problems and Solutions

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