{"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":"5b9d1fae-c6c7-59de-b78d-fbc7befd978e","task_key":"prealgebra--test--5b9d1fae-c6c7-59de-b78d-fbc7befd978e","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, the three concentric circles have radii of $4,$ $6,$ and $7.$…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In the diagram, the three concentric circles have radii of $4,$ $6,$ and $7.$ Three regions are labeled $X,$ $Y,$ or $Z$ below. Of these three regions, what is the difference between the area of the region with the greatest area and the area of the region with the smallest area? Express your answer in exact form.\\n\\n[asy]\\nimport graph;\\nfilldraw(circle((0,0),7), lightgray, black+linewidth(1));\\nfilldraw(circle((0,0),6), gray, black+linewidth(1));\\nfilldraw(circle((0,0),4), white, black+linewidth(1));\\ndot((0,0));\\nlabel(\\\"$X$\\\",(2,0));\\nlabel(\\\"$Y$\\\",(5,0));\\nlabel(\\\"$Z$\\\",(6.5,0));\\n[/asy]\",\"type\":\"Prealgebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}