{"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":"f08ebe16-94c9-5de2-ba45-9860cdabcbd8","task_key":"number~5ftheory--test--f08ebe16-94c9-5de2-ba45-9860cdabcbd8","task_revision_id":"1","upstream_id":"","short_description":"For each positive integer $n$, the set of integers $\\{0,1,\\ldots,n-1\\}$ is known…","config":"number_theory","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"For each positive integer $n$, the set of integers $\\\\{0,1,\\\\ldots,n-1\\\\}$ is known as the $\\\\textit{residue system modulo}$ $n$. Within the residue system modulo $2^4$, let $A$ be the sum of all invertible integers modulo $2^4$ and let $B$ be the sum all of non-invertible integers modulo $2^4$. What is $A-B$?\",\"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":[]}