{"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":"93cef7c1-b104-5c60-ba38-f7b8aacd99c5","task_key":"number~5ftheory--test--93cef7c1-b104-5c60-ba38-f7b8aacd99c5","task_revision_id":"1","upstream_id":"","short_description":"If $a,b,c$ are positive integers less than $13$ such that \\begin{align*}","config":"number_theory","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"If $a,b,c$ are positive integers less than $13$ such that \\\\begin{align*}\\n2ab+bc+ca&\\\\equiv 0\\\\pmod{13}\\\\\\\\\\nab+2bc+ca&\\\\equiv 6abc\\\\pmod{13}\\\\\\\\\\nab+bc+2ca&\\\\equiv 8abc\\\\pmod {13}\\n\\\\end{align*}then determine the remainder when $a+b+c$ is divided by $13$.\",\"type\":\"Number Theory\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}