{"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":"6fe09e4e-62d8-5df4-b60a-560b290c1af7","task_key":"geometry--test--6fe09e4e-62d8-5df4-b60a-560b290c1af7","task_revision_id":"1","upstream_id":"","short_description":"Triangle $PAB$ and square $ABCD$ are in perpendicular planes. Given that $PA=3$,…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Triangle $PAB$ and square $ABCD$ are in perpendicular planes. Given that $PA=3$, $PB=4$, and $AB=5$, what is $PD$? [asy]\\nsize(100); defaultpen(linewidth(0.8)); dotfactor=4;\\ndraw((0,-0.5)--(0,3)--(5,3)--(5,-0.5)--cycle);\\nfilldraw((0,0)--(-2,-2)--(3,-2)--(5,0)--cycle,white,defaultpen);\\ndraw((1.5,0)--(3.5,0)--(3.5,2)--(1.5,2)--cycle);\\ndraw((1.5,0)--(1.6,-0.5)--(3.5,0));\\ndot(\\\"$B$\\\",(1.5,0),SW); dot(\\\"$A$\\\",(3.5,0),SE); dot(\\\"$C$\\\",(1.5,2),W); dot(\\\"$D$\\\",(3.5,2),E); dot(\\\"$P$\\\",(1.6,-0.5),S);\\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":[]}