{"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":"8de693bc-7669-5efa-940d-9d4becb64337","task_key":"precalculus--test--8de693bc-7669-5efa-940d-9d4becb64337","task_revision_id":"1","upstream_id":"","short_description":"The matrix","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The matrix\\n\\\\[\\\\mathbf{A} = \\\\begin{pmatrix} 4 & 7 \\\\\\\\ c & d \\\\end{pmatrix}\\\\]has the property that if you are told the value of $\\\\|\\\\mathbf{v}\\\\|,$ then you can derive the value of $\\\\|\\\\mathbf{A} \\\\mathbf{v}\\\\|.$  Compute $|c - d|,$ assuming that $c$ and $d$ are real numbers.\",\"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":[]}