{"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":"5f8ee9e7-46d6-5a38-94eb-eb6eae13d354","task_key":"precalculus--test--5f8ee9e7-46d6-5a38-94eb-eb6eae13d354","task_revision_id":"1","upstream_id":"","short_description":"There exist constants $p$ and $q$ so that for any vectors $\\mathbf{a},$…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"There exist constants $p$ and $q$ so that for any vectors $\\\\mathbf{a},$ $\\\\mathbf{b},$ and $\\\\mathbf{c},$ the vectors $\\\\mathbf{a} - 2 \\\\mathbf{b} + 3 \\\\mathbf{c},$ $2 \\\\mathbf{a} + 3 \\\\mathbf{b} - 4 \\\\mathbf{c},$ and $p \\\\mathbf{b} + q \\\\mathbf{c}$ are always collinear.  Enter the ordered pair $(p,q).$\",\"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":[]}