{"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":"76316584-b775-51bc-bb8a-bd2b6b706bf1","task_key":"intermediate~5falgebra--test--76316584-b775-51bc-bb8a-bd2b6b706bf1","task_revision_id":"1","upstream_id":"","short_description":"Let $a_1, a_2, \\ldots, a_{2005}$ be real numbers such that…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $a_1, a_2, \\\\ldots, a_{2005}$ be real numbers such that $$\\\\begin{array}{ccccccccccc}\\na_1\\\\cdot 1 &+ &a_2 \\\\cdot 2 &+& a_3 \\\\cdot 3 &+ &\\\\cdots& + &a_{2005} \\\\cdot 2005 &=& 0 \\\\\\\\\\na_1\\\\cdot 1^2 &+& a_2\\\\cdot 2^2 &+& a_3 \\\\cdot 3^2 &+ &\\\\cdots& + & a_{2005} \\\\cdot 2005^2 &=& 0 \\\\\\\\\\na_1 \\\\cdot 1^3 &+& a_2 \\\\cdot 2^3 &+& a_3 \\\\cdot 3^3 &+ &\\\\cdots& + & a_{2005} \\\\cdot 2005^3 &=& 0 \\\\\\\\ \\\\vdots&&\\\\vdots&&\\\\vdots&&&&\\\\vdots&&\\\\vdots \\\\\\\\\\na_1\\\\cdot 1^{2004} &+& a_2\\\\cdot 2^{2004} &+& a_3\\\\cdot 3^{2004} &+ &\\\\cdots& + &a_{2005} \\\\cdot 2005^{2004} &=& 0\\n\\\\end{array}$$and $$\\\\begin{array}{ccccccccccc}\\na_1 \\\\cdot 1^{2005}& +& a_2\\\\cdot 2^{2005} &+& a_3\\\\cdot 3^{2005} &+ &\\\\cdots& + &a_{2005} \\\\cdot 2005^{2005} &=& 1.\\n\\\\end{array}$$What is the value of $a_1$?\",\"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":[]}