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Difference between revisions of "2013 AMC 10B Problems/Problem 5"

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Latest revision as of 15:45, 3 July 2013

Problem

Positive integers $a$ and $b$ are each less than $6$. What is the smallest possible value for $2 \cdot a - a \cdot b$?


$\textbf{(A)}\ -20\qquad\textbf{{(B)}}\ -15\qquad\textbf{{(C)}}\ -10\qquad\textbf{{(D)}}\ 0\qquad\textbf{{(E)}}\ 2$

Solution

Factoring the equation gives $a(2 - b)$. From this we can see that to obtain the least possible value, $2 - b$ should be negative, and should be as small as possible. To do so, $b$ should be maximized. Because $2 - b$ is negative, we should maximize the positive value of $a$ as well. The maximum values of both $a$ and $b$ are $5$, so the answer is $5(2 - 5) = \boxed{\textbf{(B)}\ -15}$.

See also

2013 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
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All AMC 10 Problems and Solutions

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