{"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":"69d3f1ac-1b19-52be-900c-bcec6d2fcc87","task_key":"precalculus--test--69d3f1ac-1b19-52be-900c-bcec6d2fcc87","task_revision_id":"1","upstream_id":"","short_description":"In triangle $ABC,$ $D$ and $E$ are on side $\\overline{BC}$ such that $BD = DE =…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In triangle $ABC,$ $D$ and $E$ are on side $\\\\overline{BC}$ such that $BD = DE = EC.$  If $x = \\\\angle BAD,$ $y = \\\\angle DAE,$ and $z = \\\\angle EAC,$ then find\\n\\\\[\\\\frac{\\\\sin (x + y) \\\\sin (y + z)}{\\\\sin x \\\\sin z}.\\\\]\",\"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":[]}