{"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":"762ca880-9b4f-5f53-bc65-52291bf57ff6","task_key":"geometry--test--762ca880-9b4f-5f53-bc65-52291bf57ff6","task_revision_id":"1","upstream_id":"","short_description":"In the figure below, side $AE$ of rectangle $ABDE$ is parallel to the $x$-axis,…","config":"geometry","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"In the figure below, side $AE$ of rectangle $ABDE$ is parallel to the $x$-axis, and side $BD$ contains the point $C$. The vertices of triangle $ACE$ are $A(1, 1)$, $C(3, 3)$ and $E(4, 1)$. What is the ratio of the area of triangle $ACE$ to the area of rectangle $ABDE$? Express your answer as a common fraction.\\n\\n[asy]unitsize(1inch);\\ndraw((0,0)--(4.5,0),Arrow);\\ndraw((0,0)--(0,3.5),Arrow);\\ndraw((-0.1,1)--(0.1,1));\\ndraw((-0.1,2)--(0.1,2));\\ndraw((-0.1,3)--(0.1,3));\\ndraw((1,0.1)--(1,-0.1));\\ndraw((2,0.1)--(2,-0.1));\\ndraw((3,0.1)--(3,-0.1));\\ndraw((4,0.1)--(4,-0.1));\\ndraw((1,1)--(1,3)--(4,3)--(4,1)--cycle);\\ndraw((1,1)--(3,3)--(4,1));\\nfill((1,1)--(3,3)--(1,3)--cycle,gray(0.7));\\nfill((3,3)--(4,3)--(4,1)--cycle,gray(0.7));\\nlabel(\\\"$A$\\\",(1,1),SW);\\nlabel(\\\"$B$\\\",(1,3),NW);\\nlabel(\\\"$C$\\\",(3,3),N);\\nlabel(\\\"$D$\\\",(4,3),NE);\\nlabel(\\\"$E$\\\",(4,1),SE);\\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":[]}