{"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":"806c2f99-e7c0-5028-9710-3f791c6c8850","task_key":"geometry--test--806c2f99-e7c0-5028-9710-3f791c6c8850","task_revision_id":"1","upstream_id":"","short_description":"Coplanar squares $ABGH$ and $BCDF$ are adjacent, with $CD = 10$ units and $AH =…","config":"geometry","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Coplanar squares $ABGH$ and $BCDF$ are adjacent, with $CD = 10$ units and $AH = 5$ units. Point $E$ is on segments $AD$ and $GB$. What is the area of triangle $ABE$, in square units? Express your answer as a common fraction.\\n\\n[asy]\\ndraw((0,0)--(5,0)--(5,5)--(0,5)--(0,0)--cycle,linewidth(2));\\ndraw((5,0)--(15,0)--(15,10)--(5,10)--(5,0)--cycle,linewidth(2));\\n\\ndraw((0,0)--(15,10),linewidth(2));\\n\\nfilldraw((0,0)--(5,0)--(5,10/3)--(0,0)--cycle,gray,linewidth(2));\\n\\nlabel(\\\"A\\\",(0,0),SW);\\nlabel(\\\"B\\\",(5,0),S);\\nlabel(\\\"C\\\",(15,0),SE);\\nlabel(\\\"D\\\",(15,10),NE);\\nlabel(\\\"E\\\",(5,10/3),SE);\\nlabel(\\\"F\\\",(5,10),NW);\\nlabel(\\\"G\\\",(5,5),NW);\\nlabel(\\\"H\\\",(0,5),NW);\\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":[]}