{"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":"d0d74b6c-a292-5826-bef5-e99b4ed408b1","task_key":"intermediate~5falgebra--test--d0d74b6c-a292-5826-bef5-e99b4ed408b1","task_revision_id":"1","upstream_id":"","short_description":"For positive real numbers $a,$ $b,$ $c,$ and $d,$ find the minimum value of","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"For positive real numbers $a,$ $b,$ $c,$ and $d,$ find the minimum value of\\n\\\\[\\\\left\\\\lfloor \\\\frac{b + c + d}{a} \\\\right\\\\rfloor + \\\\left\\\\lfloor \\\\frac{a + c + d}{b} \\\\right\\\\rfloor + \\\\left\\\\lfloor \\\\frac{a + b + d}{c} \\\\right\\\\rfloor + \\\\left\\\\lfloor \\\\frac{a + b + c}{d} \\\\right\\\\rfloor.\\\\]\",\"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":[]}