{"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":"94d3245b-5063-5382-815e-05d1a6551acf","task_key":"geometry--test--94d3245b-5063-5382-815e-05d1a6551acf","task_revision_id":"1","upstream_id":"","short_description":"In right triangle $ABC$, $\\angle B = 90^\\circ$, and $D$ and $E$ lie on $AC$ such…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In right triangle $ABC$, $\\\\angle B = 90^\\\\circ$, and $D$ and $E$ lie on $AC$ such that $\\\\overline{BD}$ is a median and $\\\\overline{BE}$ is an altitude.  If $BD=2\\\\cdot DE$, compute $\\\\frac{AB}{EC}$. [asy]\\n\\npair A,B,C,D,E;\\n\\nA=(0,0); C=(2,0); B=(1.5,sqrt(3)/2); D=(1,0); E=(1.5,0);\\n\\ndraw(A--B--C--cycle); draw(B--D); draw(B--E);\\n\\nlabel(\\\"$A$\\\",A,SW); label(\\\"$B$\\\",B,N); label(\\\"$C$\\\",C,SE); label(\\\"$D$\\\",D,S); label(\\\"$E$\\\",E,S);\\n\\ndraw(rightanglemark(B,E,D,2));\\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":[]}