{"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":"95197f16-4ace-5fcb-b262-a61532b2ed41","task_key":"precalculus--test--95197f16-4ace-5fcb-b262-a61532b2ed41","task_revision_id":"1","upstream_id":"","short_description":"One line is described by","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"One line is described by\\n\\\\[\\\\begin{pmatrix} -1 \\\\\\\\ -3 \\\\\\\\ -5 \\\\end{pmatrix} + t \\\\begin{pmatrix} 3 \\\\\\\\ k \\\\\\\\ 7 \\\\end{pmatrix}.\\\\]Another line is described by\\n\\\\[\\\\begin{pmatrix} 2 \\\\\\\\ 4 \\\\\\\\ 6 \\\\end{pmatrix} + u \\\\begin{pmatrix} 1 \\\\\\\\ 4 \\\\\\\\ 7 \\\\end{pmatrix}.\\\\]Find $k$ so that the lines are coplanar (i.e. there is a plane that contains both lines).\",\"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":[]}