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2008 AMC 12A Question 5

AMC12 · 2008 AMC 12A

Question 5

Suppose that $$
\dfrac{2x}{3} - \dfrac{x}{6}
$$ is an integer. Which of the following statements must be true about $x?$
  1. It is negative.
  2. It is even, but not necessarily a multiple of
    $3.$
  3. It is a multiple of $3,$ but not necessarily even.
  4. It is a multiple of $6,$ but not necessarily a multiple of
    $12.$
  5. It is a multiple of $12.$