{"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":"0a2650fe-57de-5c59-90ec-1e23f860d3c3","task_key":"intermediate~5falgebra--test--0a2650fe-57de-5c59-90ec-1e23f860d3c3","task_revision_id":"1","upstream_id":"","short_description":"Find all positive integers $k$ with the following property:","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Find all positive integers $k$ with the following property:\\n\\nFor all positive integers $a,$ $b,$ and $c$ that make the roots of\\n\\\\[ax^2 + bx + c = 0\\\\]rational, the roots of $4ax^2 + 12bx + kc = 0$ will also be rational.\\n\\nEnter all the possible values of $k,$ separated by commas.\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}