{"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":"9573ff44-b80e-5372-81b1-568ae76a4f83","task_key":"intermediate~5falgebra--test--9573ff44-b80e-5372-81b1-568ae76a4f83","task_revision_id":"1","upstream_id":"","short_description":"Steve says to Jon, \"I am thinking of a polynomial whose roots are all positive…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Steve says to Jon, \\\"I am thinking of a polynomial whose roots are all positive integers. The polynomial has the form $P(x) = 2x^3-2ax^2+(a^2-81)x-c$ for some positive integers $a$ and $c$. Can you tell me the values of $a$ and $c$?\\\"\\n\\nAfter some calculations, Jon says, \\\"There is more than one such polynomial.\\\"\\n\\nSteve says, \\\"You're right. Here is the value of $a$.\\\" He writes down a positive integer and asks, \\\"Can you tell me the value of $c$?\\\"\\n\\nJon says, \\\"There are still two possible values of $c$.\\\"\\n\\nFind the sum of the two possible values of $c$.\",\"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":[]}