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CEMC Gauss (Grade 7), 2017

Algebra Difficulty 1.3 Junior Find the answer Canada

When $n=101$ , which of the following expressions has an even value?

Pick one

Solution

When $n=101$ :

$\begin{aligned} 3n&=3\times101=303\\ n+2&=101+2=103\\ n-12&=101-12=89\\ 2n-2&=2\times101-2=202-2=200\\ 3n+2&=3\times101+2=303+2=305.\end{aligned}$ Of the expressions given, $2n-2$ is the only expression which has an even value when $n=101$ .

(In fact, the value of $2n-2$ is an even integer for every integer $n$ . Can you see why?)

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