{"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":"50541352-f59a-56d2-8d96-cf967f8ccebe","task_key":"precalculus--test--50541352-f59a-56d2-8d96-cf967f8ccebe","task_revision_id":"1","upstream_id":"","short_description":"If $0^\\circ < x < 180^\\circ$ and $\\cos x + \\sin x = \\frac{1}{2},$ then $\\tan x$…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"If $0^\\\\circ < x < 180^\\\\circ$ and $\\\\cos x + \\\\sin x = \\\\frac{1}{2},$ then $\\\\tan x$ can be expressed in the form $-\\\\frac{a + \\\\sqrt{b}}{c}$ when simplified, where $a,$ $b,$ and $c$ are positive integers.  Find $a + b + c.$\",\"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":[]}