2005 AMC 8 Problems/Problem 8

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Problem

Suppose m and n are positive odd integers. Which of the following must also be an odd integer?

$\textbf{(A)}\ m+3n\qquad\textbf{(B)}\ 3m-n\qquad\textbf{(C)}\ 3m^2 + 3n^2\qquad\textbf{(D)}\ (nm + 3)^2\qquad\textbf{(E)}\ 3mn$

Solution

Assume WLOG that $m$ and $n$ are both $1$. Plugging into each of the choices, we get $4, 2, 6, 16,$ and $3$. The only odd integer is $\boxed{\textbf{(E)}\ 3mn}$.

See Also

2005 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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All AJHSME/AMC 8 Problems and Solutions

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