{"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":"0f13c388-8f98-54be-b2d0-4c38d0ea01f5","task_key":"geometry--test--0f13c388-8f98-54be-b2d0-4c38d0ea01f5","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, square $ABCD$ has sides of length 4, and $\\triangle ABE$ is…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In the diagram, square $ABCD$ has sides of length 4, and $\\\\triangle ABE$ is equilateral. Line segments $BE$ and $AC$ intersect at $P$. Point $Q$ is on $BC$ so that $PQ$ is perpendicular  to $BC$ and $PQ=x$. [asy]\\npair A, B, C, D, E, P, Q;\\nA=(0,0);\\nB=(4,0);\\nC=(4,-4);\\nD=(0,-4);\\nE=(2,-3.464);\\nP=(2.535,-2.535);\\nQ=(4,-2.535);\\ndraw(A--B--C--D--A--E--B);\\ndraw(A--C);\\ndraw(P--Q, dashed);\\nlabel(\\\"$A$\\\", A, NW);\\nlabel(\\\"$B$\\\", B, NE);\\nlabel(\\\"$C$\\\", C, SE);\\nlabel(\\\"$D$\\\", D, SW);\\nlabel(\\\"$E$\\\", E, S);\\nlabel(\\\"$P$\\\", P, W);\\nlabel(\\\"$Q$\\\", Q, dir(0));\\nlabel(\\\"$x$\\\", (P+Q)/2, N);\\nlabel(\\\"4\\\", (A+B)/2, N);\\n[/asy]\\n\\nFind the value of $x$ in simplest radical form.\",\"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":[]}