AMC 8 2008 Problem 22

For how many positive integer values of $n$ are both $\frac{n}{3}$ and $3n$ three-digit whole numbers? $\textbf{(A)}\ 12 \textbf{(B)}\ 21 \textbf{(C)}\ 27 \textbf{(D)}\ 33 \textbf{(E)}\ 34$