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Points 100 ray partitional but not 60 ray partitional

Source: 2011 AMC A Problem 25

June 25, 2011
geometryalgebrafunctiondomainAMC

Problem Statement

Let RR be a square region and n≥4n\ge4 an integer. A point XX in the interior of RR is called n-rayn\text{-}ray partitional if there are nn rays emanating from XX that divide RR into nn triangles of equal area. How many points are 100-ray partitional but not 60-ray partitional?
<spanclass=′latex−bold′>(A)</span> 1500<spanclass=′latex−bold′>(B)</span> 1560<spanclass=′latex−bold′>(C)</span> 2320<spanclass=′latex−bold′>(D)</span> 2480<spanclass=′latex−bold′>(E)</span> 2500<span class='latex-bold'>(A)</span>\,1500 \qquad<span class='latex-bold'>(B)</span>\,1560 \qquad<span class='latex-bold'>(C)</span>\,2320 \qquad<span class='latex-bold'>(D)</span>\,2480 \qquad<span class='latex-bold'>(E)</span>\,2500
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