{"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 <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;", "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"}}