{"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":"464ae228-ed12-5b93-8bf9-756776ce8526","task_key":"number~5ftheory--test--464ae228-ed12-5b93-8bf9-756776ce8526","task_revision_id":"1","upstream_id":"","short_description":"Given $m\\geq 2$, denote by $b^{-1}$ the inverse of $b\\pmod{m}$. That is,…","config":"number_theory","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Given $m\\\\geq 2$, denote by $b^{-1}$ the inverse of $b\\\\pmod{m}$. That is, $b^{-1}$ is the residue for which $bb^{-1}\\\\equiv 1\\\\pmod{m}$. Sadie wonders if $(a+b)^{-1}$ is always congruent to $a^{-1}+b^{-1}$ (modulo $m$). She tries the example $a=2$, $b=3$, and $m=7$. Let $L$ be the residue of $(2+3)^{-1}\\\\pmod{7}$, and let $R$ be the residue of $2^{-1}+3^{-1}\\\\pmod{7}$, where $L$ and $R$ are integers from $0$ to $6$ (inclusive). Find $L-R$.\",\"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":[]}