{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A)}\\,1500 \\qquad\\textbf{(B)}\\,1560 \\qquad\\textbf{(C)}\\,2320 \\qquad\\textbf{(D)}\\,2480 \\qquad\\textbf{(E)}\\,2500$", "description_html": "<p>Let  <span class=\"katex--inline\">R</span>  be a square region and  <span class=\"katex--inline\">n\\ge4</span>  an integer.  A point  <span class=\"katex--inline\">X</span>  in the interior of  <span class=\"katex--inline\">R</span>  is called  <span class=\"katex--inline\">n\\text{-}ray</span>  partitional if there are  <span class=\"katex--inline\">n</span>  rays emanating from  <span class=\"katex--inline\">X</span>  that divide  <span class=\"katex--inline\">R</span>  into  <span class=\"katex--inline\">n</span>  triangles of equal area.  How many points are 100-ray partitional but not 60-ray partitional?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\,1500 \\qquad\\textbf{(B)}\\,1560 \\qquad\\textbf{(C)}\\,2320 \\qquad\\textbf{(D)}\\,2480 \\qquad\\textbf{(E)}\\,2500</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2011 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/11_amc10A_p24"}}