{"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":"b5bdddfe-fd42-529f-8667-449ae398eb60","task_key":"geometry--test--b5bdddfe-fd42-529f-8667-449ae398eb60","task_revision_id":"1","upstream_id":"","short_description":"The area of the semicircle in Figure A is half the area of the circle in Figure…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The area of the semicircle in Figure A is half the area of the circle in Figure B. The area of a square inscribed in the semicircle, as shown, is what fraction of the area of a square inscribed in the circle? Express your answer as a common fraction.\\n\\n[asy]\\ndefaultpen(linewidth(0.8));\\n\\nsize(5cm,5cm);\\n\\ndraw((0,0)..(1,1)..(2,0)--(0,0));\\n\\ndraw((0.5,0)--(0.5,0.87)--(1.5,0.87)--(1.5,0));\\n\\ndraw(Circle((4,0),1));\\n\\npair A,B,C,D;\\n\\nA=(3.3,0.7);\\nB=(3.3,-0.7);\\nD=(4.7,0.7);\\nC=(4.7,-0.7);\\n\\ndraw(A--B--C--D--A);\\n\\nlabel(\\\"Figure A\\\",(1,1.3));\\nlabel(\\\"Figure B\\\",(4,1.3));\\n\\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":[]}