{"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":"9690f309-00fc-52ab-bb76-337c71d63fc5","task_key":"intermediate~5falgebra--test--9690f309-00fc-52ab-bb76-337c71d63fc5","task_revision_id":"1","upstream_id":"","short_description":"Let $r_1,$ $r_2,$ $\\dots,$ $r_7$ be the distinct complex roots of the polynomial…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $r_1,$ $r_2,$ $\\\\dots,$ $r_7$ be the distinct complex roots of the polynomial $P(x) = x^7 - 7.$  Let\\n\\\\[K = \\\\prod_{1 \\\\le i < j \\\\le 7} (r_i + r_j).\\\\]In other words, $K$ is the product of all numbers of the of the form $r_i + r_j,$ where $i$ and $j$ are integers for which $1 \\\\le i < j \\\\le 7.$  Determine $K^2.$\",\"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":[]}