2005 AMC 8 Problems/Problem 8

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 $\boxed{\textbf{(E)}\ 3mn}$ . HI

2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2005 AMC 8 Problems/Problem 8

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