{"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":"9339b6ff-cac1-5f95-94fb-e4d87fde0db8","task_key":"geometry--test--9339b6ff-cac1-5f95-94fb-e4d87fde0db8","task_revision_id":"1","upstream_id":"","short_description":"Four semi-circles are shown with $AB:BC:CD = 1:2:3$. What is the ratio of the…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Four semi-circles are shown with $AB:BC:CD = 1:2:3$. What is the ratio of the shaded area to the unshaded area in the semi circle with diameter $AD$? Express your answer as a common fraction. [asy]\\nimport olympiad; import geometry; size(150); defaultpen(linewidth(0.8));\\nfilldraw(arc((6,0),6,0,180)--cycle);\\nfilldraw(arc((3,0),3,0,180)--cycle,fillpen=white); filldraw(arc((8,0),2,0,180)--cycle,fillpen=white); filldraw(arc((11,0),1,0,180)--cycle,fillpen=white);\\nlabel(\\\"$A$\\\",(12,0),S); label(\\\"$B$\\\",(10,0),S); label(\\\"$C$\\\",(6,0),S); label(\\\"$D$\\\",(0,0),S);\\n[/asy]\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}