1989 AJHSME Problems/Problem 14

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 (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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All AJHSME/AMC 8 Problems and Solutions

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