AMC 12 2011a Problem 22

Let $R$ be a unit square region and $n \geq 4$ an integer. A point $X$ in the interior of $R$ is called ''n-ray partitional'' if there are $n$ rays emanating from $X$ that divide $R$ into $n$ triangles of equal area. How many points are $100$-ray partitional but not $60$-ray partitional?

\textbf{(A)}\ 1500 \textbf{(B)}\ 1560 \textbf{(C)}\ 2320 \textbf{(D)}\ 2480 \textbf{(E)}\ 2500