{"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":"e7cb2dcd-24fa-5243-aff6-c0b4081986a0","task_key":"intermediate~5falgebra--test--e7cb2dcd-24fa-5243-aff6-c0b4081986a0","task_revision_id":"1","upstream_id":"","short_description":"Let $a,$ $b,$ and $c$ be real numbers such that $ab + ac + bc = 0$ and $(a + b +…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $a,$ $b,$ and $c$ be real numbers such that $ab + ac + bc = 0$ and $(a + b + c + 1)^2 = abc.$  Find all possible values of\\n\\\\[(ab - c)(ac - b)(bc - a).\\\\]Enter the possible values, separated by commas.  For example, if you think the possible values are 3, 4, and 5, enter \\\"3, 4, 5\\\", without the quotation marks.\",\"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":[]}