{"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":"d8f5488f-1b68-56f3-81c0-f68947cf8392","task_key":"intermediate~5falgebra--test--d8f5488f-1b68-56f3-81c0-f68947cf8392","task_revision_id":"1","upstream_id":"","short_description":"Given a real number $x$, let $\\lfloor x\\rfloor$ denote the greatest integer less…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Given a real number $x$, let $\\\\lfloor x\\\\rfloor$ denote the greatest integer less than or equal to $x$. For a certain integer $k$, there are exactly 70 positive integers $n_1$, $n_2, \\\\ldots,$ $n_{70}$ such that\\n\\\\[k = \\\\lfloor \\\\sqrt[3]{n_1} \\\\rfloor = \\\\lfloor \\\\sqrt[3]{n_2} \\\\rfloor =\\\\cdots= \\\\lfloor \\\\sqrt[3]{n_{70}} \\\\rfloor\\\\]and $k$ divides $n_i$ for all $i$ such that $1 \\\\leq i \\\\leq 70$.\\n\\nFind the maximum value of $\\\\displaystyle\\\\frac{n_i}{k}$ for $1 \\\\leq i \\\\leq 70$.\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}