{"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":"df772347-7a98-52bb-9cdd-415893ce56c5","task_key":"number~5ftheory--test--df772347-7a98-52bb-9cdd-415893ce56c5","task_revision_id":"1","upstream_id":"","short_description":"Two sequences $A=\\{a_0, a_1, a_2,\\ldots\\}$ and $B=\\{b_0,b_1,b_2,\\ldots\\}$ are…","config":"number_theory","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Two sequences $A=\\\\{a_0, a_1, a_2,\\\\ldots\\\\}$ and $B=\\\\{b_0,b_1,b_2,\\\\ldots\\\\}$ are defined as follows: \\\\[a_0=0, ~a_1=1, ~a_n= a_{n-1} +b_{n-2} \\\\hspace{2mm}\\\\text{for}\\\\hspace{2mm} n\\\\ge2\\\\] \\\\[b_0=1, ~b_1=2, ~b_n=a_{n-2} +b_{n-1}\\\\hspace{2mm}\\\\text{for}\\\\hspace{2mm} n\\\\ge2\\\\] What is the remainder when $a_{50}+b_{50}$ is divided by $5$?\",\"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":[]}