{"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":"93a34c6c-05de-594b-b3b1-876731564506","task_key":"intermediate~5falgebra--test--93a34c6c-05de-594b-b3b1-876731564506","task_revision_id":"1","upstream_id":"","short_description":"A polynomial \\[","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"A polynomial \\\\[\\nP(x)=c_{2004}x^{2004}+ c_{2003}x^{2003}+ \\\\cdots+ c_{1}x+ c_{0}\\n\\\\]has real coefficients with $c_{2004} \\\\neq 0$ and 2004 distinct complex zeros $z_{k}=a_{k}+ b_{k}i$, $1 \\\\leq k \\\\leq 2004$ with $a_k$ and $b_k$ real, $a_1 = b_1 = 0$, and \\\\[\\n\\\\sum_{k=1}^{2004} a_{k}= \\\\sum_{k=1}^{2004} b_{k}.\\n\\\\]Which of the following quantities can be a nonzero number?\\n\\nA. $c_0$\\n\\nB. $c_{2003}$\\n\\nC. $b_{2}b_{3} \\\\dotsm b_{2004}$\\n\\nD. $\\\\sum_{k=1}^{2004}a_{k}$\\n\\nE. $\\\\sum_{k=1}^{2004}c_{k}$\",\"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":[]}