{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"571d49f2-de1c-5073-854f-4e8ce3ac4ad4","task_key":"precalculus--test--571d49f2-de1c-5073-854f-4e8ce3ac4ad4","task_revision_id":"1","upstream_id":"","short_description":"An angle $x$ is chosen at random from the interval $0^{\\circ} < x < 90^{\\circ}$.…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"An angle $x$ is chosen at random from the interval $0^{\\\\circ} < x < 90^{\\\\circ}$.  Let $p$ be the probability that the numbers $\\\\sin^2 x$, $\\\\cos^2 x$, and $\\\\sin x \\\\cos x$ are not the lengths of the sides of a triangle.  Given that $p=d/n$, where $d$ is the number of degrees in $\\\\arctan m$ and $m$ and $n$ are positive integers with $m+n<1000$, find $m+n$.\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}