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| − | ==Problem==
| + | #redirect [[2008 AMC 12A Problems/Problem 5]] |
| − | Suppose that
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| − | <cmath>\frac{2x}{3}-\frac{x}{6}</cmath>
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| − | is an integer. Which of the following statements must be true about <math>x</math>?
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| − | <math>\mathrm{(A)}\ \text{It is negative.}\qquad\mathrm{(B)}\ \text{It is even, but not necessarily a multiple of 3.}\\\qquad\mathrm{(C)}\ \text{It is a multiple of 3, but not necessarily even.}\\\qquad\mathrm{(D)}\ \text{It is a multiple of 6, but not necessarily a multiple of 12.}\\\qquad\mathrm{(E)}\ \text{It is a multiple of 12.}</math>
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| − | ==Solution==
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| − | <cmath>\frac{2x}{3}-\frac{x}{6}\quad\Longrightarrow\quad\frac{4x}{6}-\frac{x}{6}\quad\Longrightarrow\quad\frac{3x}{6}\quad\Longrightarrow\quad\frac{x}{2}</cmath>
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| − | For <math>\frac{x}{2}</math> to be an integer, <math>x</math> must be even, but not necessarily divisible by <math>3</math>. Thus, the answer is <math>\mathrm{(B)}</math>.
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| − | ==See also==
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| − | {{AMC10 box|year=2008|ab=A|num-b=8|num-a=10}}
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