{"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":"e8eee2b1-65ec-50dc-874b-cb240b9abdfa","task_key":"precalculus--test--e8eee2b1-65ec-50dc-874b-cb240b9abdfa","task_revision_id":"1","upstream_id":"","short_description":"The set of vectors $\\left\\{ \\begin{pmatrix} 3 \\\\ 7 \\end{pmatrix},…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"The set of vectors $\\\\left\\\\{ \\\\begin{pmatrix} 3 \\\\\\\\ 7 \\\\end{pmatrix}, \\\\begin{pmatrix} k \\\\\\\\ -2 \\\\end{pmatrix} \\\\right\\\\}$ is linearly independent.  Find all possible values of $k.$  Enter your answer as an interval.\",\"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":[]}