{"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":"fd774e6e-0761-5220-95b2-443eb18fd47c","task_key":"geometry--test--fd774e6e-0761-5220-95b2-443eb18fd47c","task_revision_id":"1","upstream_id":"","short_description":"Points $E$ and $F$ are located on square $ABCD$ so that $\\triangle BEF$ is…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Points $E$ and $F$ are located on square $ABCD$ so that $\\\\triangle BEF$ is equilateral. What is the ratio of the area of $\\\\triangle DEF$ to that of $\\\\triangle ABE$?\\n\\n[asy]\\npair A,B,C,D,I,F;\\nA=(0,0);\\nB=(10,0);\\nC=(10,10);\\nD=(0,10);\\nF=(7.4,10);\\nI=(0,2.6);\\ndraw(B--I--F--cycle,linewidth(0.7));\\ndraw(A--B--C--D--cycle,linewidth(0.7));\\nlabel(\\\"$A$\\\",A,S);\\nlabel(\\\"$B$\\\",B,S);\\nlabel(\\\"$C$\\\",C,N);\\nlabel(\\\"$D$\\\",D,N);\\nlabel(\\\"$E$\\\",I,W);\\nlabel(\\\"$F$\\\",F,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":[]}