Problem #1846

 1846 For how many positive integers $n$ is $\frac{n}{30-n}$ also a positive integer? $\textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8$ This problem is copyrighted by the American Mathematics Competitions.
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