{"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":"bb1a8267-9693-5a79-8fbd-2a414550cb69","task_key":"geometry--test--bb1a8267-9693-5a79-8fbd-2a414550cb69","task_revision_id":"1","upstream_id":"","short_description":"Let $ABCD$ be a rectangle. Let $E$ and $F$ be points on $BC$ and $CD$,…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $ABCD$ be a rectangle.  Let $E$ and $F$ be points on $BC$ and $CD$, respectively, so that the areas of triangles $ABE$, $ADF$, and $CEF$ are 8, 5, and 9, respectively.  Find the area of rectangle $ABCD$.\\n\\n[asy]\\nunitsize(1.5 cm);\\n\\npair A, B, C, D, E, F;\\n\\nA = (0,2);\\nB = (0,0);\\nC = (3,0);\\nD = (3,2);\\nE = (3*B + 2*C)/5;\\nF = (2*D + C)/3;\\n\\ndraw(A--B--C--D--cycle);\\ndraw(A--E--F--cycle);\\n\\nlabel(\\\"$A$\\\", A, NW);\\nlabel(\\\"$B$\\\", B, SW);\\nlabel(\\\"$C$\\\", C, SE);\\nlabel(\\\"$D$\\\", D, NE);\\nlabel(\\\"$E$\\\", E, S);\\nlabel(\\\"$F$\\\", F, dir(0));\\nlabel(\\\"$8$\\\", (A + B + E)/3);\\nlabel(\\\"$5$\\\", (A + D + F)/3);\\nlabel(\\\"$9$\\\", (C + E + F)/3);\\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":[]}