{"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":"5fca27d9-4393-574d-9fd0-4034e0c5944b","task_key":"geometry--test--5fca27d9-4393-574d-9fd0-4034e0c5944b","task_revision_id":"1","upstream_id":"","short_description":"Points $A(0,0), B(9,6)$ and $C(6,12)$ are vertices of triangle $ABC$. Point $D$…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Points $A(0,0), B(9,6)$ and $C(6,12)$ are vertices of triangle $ABC$. Point $D$ is on segment $AB$ such that $2(AD) = DB$, point $E$ is on segment $BC$ such that $2(BE) = EC$ and point $F$ is on segment $CA$ such that $2(CF) = FA$. What is the ratio of the area of triangle $DEF$ to the area of triangle $ABC$? Express your answer as a common fraction.\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}