{"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":"4fa0a07f-c779-5980-a029-34d4e3baf467","task_key":"precalculus--test--4fa0a07f-c779-5980-a029-34d4e3baf467","task_revision_id":"1","upstream_id":"","short_description":"There exists a real number $k$ such that the equation","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"There exists a real number $k$ such that the equation\\n\\\\[\\\\begin{pmatrix} 4 \\\\\\\\ -1 \\\\end{pmatrix} + t \\\\begin{pmatrix} 5 \\\\\\\\ 2 \\\\end{pmatrix} = \\\\begin{pmatrix} 8 \\\\\\\\ k \\\\end{pmatrix} + s \\\\begin{pmatrix} -15 \\\\\\\\ -6 \\\\end{pmatrix}\\\\]has infinitely many solutions in $t$ and $s$.  Find $k$.\",\"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":[]}