{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A)}\\ 1500 \\qquad<br>\\textbf{(B)}\\ 1560 \\qquad<br>\\textbf{(C)}\\ 2320 \\qquad<br>\\textbf{(D)}\\ 2480 \\qquad<br>\\textbf{(E)}\\ 2500$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">R</span>  be a unit square region and  <span class=\"katex--inline\">n \\geq 4</span>  an integer. A point  <span class=\"katex--inline\">X</span>  in the interior of  <span class=\"katex--inline\">R</span>  is called &#8216;&#8216;n-ray partitional&#8217;&#8217; 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  <span class=\"katex--inline\">100</span> -ray partitional but not  <span class=\"katex--inline\">60</span> -ray partitional?</p>&#10;<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>&#10;<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": 5, "problem_name": "2011 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p23", "prev": "/problem/11_amc12A_p21"}}