{"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":"b129a58d-b521-5f66-84d1-f78bcb66225f","task_key":"geometry--test--b129a58d-b521-5f66-84d1-f78bcb66225f","task_revision_id":"1","upstream_id":"","short_description":"In rectangle $ABCD$, points $F$ and $G$ lie on $\\overline{AB}$ so that $AF = FG…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In rectangle $ABCD$, points $F$ and $G$ lie on $\\\\overline{AB}$ so that $AF = FG = GB$ and $E$ is the midpoint of $\\\\overline{DC}$. Also, $\\\\overline{AC}$ intersects $\\\\overline{EF}$ at $H$ and $\\\\overline{EG}$ at $J$. The area of rectangle $ABCD$ is 70. Find the area of triangle $EHJ$.\\n\\n[asy]\\npair A,B,C,D,I,F,G,H,J;\\nA=(0,0);\\nB=(9,0);\\nC=(9,5);\\nD=(0,5);\\nF=(3,0);\\nG=(6,0);\\nI=(4.5,5);\\nH=(3.5,1.67);\\nJ=(5,3.33);\\ndraw(A--B--C--D--cycle);\\ndraw(A--C);\\ndraw(F--I--G);\\nlabel(\\\"$A$\\\",A,W);\\nlabel(\\\"$B$\\\",B,E);\\nlabel(\\\"$C$\\\",C,E);\\nlabel(\\\"$D$\\\",D,W);\\nlabel(\\\"$E$\\\",I,N);\\nlabel(\\\"$F$\\\",F,S);\\nlabel(\\\"$G$\\\",G,S);\\nlabel(\\\"$H$\\\",H,NW);\\nlabel(\\\"$J$\\\",J,NE);\\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":[]}