{"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":"a0fd2eb9-9063-5aae-8cb2-3f4c1b5f4672","task_key":"intermediate~5falgebra--test--a0fd2eb9-9063-5aae-8cb2-3f4c1b5f4672","task_revision_id":"1","upstream_id":"","short_description":"The equation","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The equation\\n\\\\[x^{10}+(13x-1)^{10}=0\\\\,\\\\]has 10 complex roots $r_1,$ $\\\\overline{r}_1,$ $r_2,$ $\\\\overline{r}_2,$ $r_3,$ $\\\\overline{r}_3,$ $r_4,$ $\\\\overline{r}_4,$ $r_5,$ $\\\\overline{r}_5,$ where the bar denotes complex conjugation. Find the value of\\n\\\\[\\\\frac 1{r_1\\\\overline{r}_1}+\\\\frac 1{r_2\\\\overline{r}_2}+\\\\frac 1{r_3\\\\overline{r}_3}+\\\\frac 1{r_4\\\\overline{r}_4}+\\\\frac 1{r_5\\\\overline{r}_5}.\\\\]\",\"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":[]}