{"status": "success", "data": {"description_md": "What is the sum of all numbers $q$ which can be written in the form $q = \\frac{a}{b}$ where $a$ and $b$ are positive integers with $b \\leq 10$ and for which there are exactly 19 integers $n$ that satisfy $\\sqrt{q} < n < q$?\n\n$\\text{(A)}\\ 871.5\\qquad\\text{(B)}\\ 743.5\\qquad\\text{(C)}\\ 777.5\\qquad\\text{(D)}\\ 808.5\\qquad\\text{(E)}\\ 1106.5$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>What is the sum of all numbers <span class=\"katex--inline\">q</span> which can be written in the form <span class=\"katex--inline\">q = \\frac{a}{b}</span> where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are positive integers with <span class=\"katex--inline\">b \\leq 10</span> and for which there are exactly 19 integers <span class=\"katex--inline\">n</span> that satisfy <span class=\"katex--inline\">\\sqrt{q} &lt; n &lt; q</span>?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 871.5\\qquad\\text{(B)}\\ 743.5\\qquad\\text{(C)}\\ 777.5\\qquad\\text{(D)}\\ 808.5\\qquad\\text{(E)}\\ 1106.5</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2016 Cayley Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/16_cayley_p25", "prev": "/problem/16_cayley_p23"}}