{"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":"14d9f0f1-be0d-5472-990b-359c84cddb00","task_key":"number~5ftheory--test--14d9f0f1-be0d-5472-990b-359c84cddb00","task_revision_id":"1","upstream_id":"","short_description":"Recall that if $b$ is a residue $\\pmod{m}$, then the modular inverse of $b$ is…","config":"number_theory","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Recall that if $b$ is a residue $\\\\pmod{m}$, then the modular inverse of $b$ is the residue $c$ for which $bc \\\\equiv 1\\\\pmod{m}$. The table below shows the inverses of the first 9 positive residues modulo 47.  \\\\begin{tabular}{c|ccccccccc}\\n$b$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\\\\\\ \\\\hline\\ninverse of $\\\\,b$ & 1 & 24 & 16 & 12 & 19 & 8 & 27 & 6 & 21\\n\\\\end{tabular}Find the modular inverse of $35\\\\pmod{47}$.\\n\\nExpress your answer as an integer from $0$ to $46$, inclusive.\",\"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":[]}