2008 AMC 10A Problem 9

Suppose that \frac{2x}{3}-\frac{x}{6} is an integer. Which of the following statements must be true about x?

\begin{array}{l} \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.} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.