2011 AMC 10A Problem 25

Let R be a square region and n\ge4 an integer. A point X in the interior of R is called n\text{-}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 \qquad\textbf{(B)}\,1560 \qquad\textbf{(C)}\,2320 \qquad\textbf{(D)}\,2480 \qquad\textbf{(E)}\,2500

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