{"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":"31065225-b9a3-5a77-8757-ff106340ddcf","task_key":"counting~5fand~5fprobability--test--31065225-b9a3-5a77-8757-ff106340ddcf","task_revision_id":"1","upstream_id":"","short_description":"Rectangle $ABCD$ has center $O$ and $AB/AD=k$. A point is randomly chosen from…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Rectangle $ABCD$ has center $O$ and $AB/AD=k$. A point is randomly chosen from the interior of rectangle $ABCD$. What is the probability that it is closer to $O$ than to any of the four vertices?  [asy]\\nsize(200);\\ndraw((-250,100)--(250,100)--(250,-100)--(-250,-100)--cycle);\\ndot((0,0));\\nlabel(\\\"$O$\\\",(0,0),N);\\nlabel(\\\"$A$\\\",(-250,100),NW); label(\\\"$B$\\\",(250,100),NE); label(\\\"$C$\\\",(250,-100),SE); label(\\\"$D$\\\",(-250,-100),SW);[/asy]\",\"type\":\"Counting & Probability\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}