{"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":"adeab690-1e45-5836-b353-bdcf7a2b6c6a","task_key":"intermediate~5falgebra--test--adeab690-1e45-5836-b353-bdcf7a2b6c6a","task_revision_id":"1","upstream_id":"","short_description":"The polynomial $4x^4 - ax^3 + bx^2 - cx + 5,$ where $a,$ $b,$ and $c$ are real…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The polynomial $4x^4 - ax^3 + bx^2 - cx + 5,$ where $a,$ $b,$ and $c$ are real coefficients, has four positive real roots $r_1,$ $r_2,$ $r_3,$ $r_4,$ such that\\n\\\\[\\\\frac{r_1}{2} + \\\\frac{r_2}{4} + \\\\frac{r_3}{5} + \\\\frac{r_4}{8} = 1.\\\\]Find $a.$\",\"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":[]}