{"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":"453f92d8-8b45-52ae-9037-96fbb0e87b9f","task_key":"intermediate~5falgebra--test--453f92d8-8b45-52ae-9037-96fbb0e87b9f","task_revision_id":"1","upstream_id":"","short_description":"Let $a,$ $b,$ $c$ be positive real numbers. Find the minimum value of","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $a,$ $b,$ $c$ be positive real numbers.  Find the minimum value of\\n\\\\[\\\\left( 2a + \\\\frac{1}{3b} \\\\right)^2 + \\\\left( 2b + \\\\frac{1}{3c} \\\\right)^2 + \\\\left( 2c + \\\\frac{1}{3a} \\\\right)^2.\\\\]\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}