{"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":"3cc1fd9c-a7f5-5e70-98a3-ebb541b3796e","task_key":"intermediate~5falgebra--test--3cc1fd9c-a7f5-5e70-98a3-ebb541b3796e","task_revision_id":"1","upstream_id":"","short_description":"Let $(a_1, a_2, \\dots, a_n)$ be a sequence of positive real numbers, such that","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $(a_1, a_2, \\\\dots, a_n)$ be a sequence of positive real numbers, such that\\n\\\\[\\\\sum_{i = 1}^n a_i = 96, \\\\quad \\\\sum_{i = 1}^n a_i^2 = 144, \\\\quad \\\\sum_{i = 1}^n a_i^3 = 216.\\\\]Find the sum of all possible values of $n.$\",\"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":[]}