{"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":"5b4aca48-859b-5448-b4fd-2a32d9bf060c","task_key":"prealgebra--test--5b4aca48-859b-5448-b4fd-2a32d9bf060c","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, $PQ=PR$ and $\\angle QRP = 65^\\circ$.","config":"prealgebra","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"In the diagram, $PQ=PR$ and $\\\\angle QRP = 65^\\\\circ$.\\n\\n[asy]\\ndraw((0,0)--(cos(13pi/36),sin(13pi/36))--(2cos(13pi/36),0)--(0,0), linewidth(1));\\ndraw((0,0)--(sin(13pi/18)*cos(5pi/36),sin(13pi/18)*sin(5pi/36)), linewidth(1));\\ndraw(((15/16)*sin(13pi/18)*cos(5pi/36),(15/16)*sin(13pi/18)*sin(5pi/36))--((15/16)*sin(13pi/18)*cos(5pi/36)+(1/16)*sin(13pi/18)*sin(5pi/36),(15/16)*sin(13pi/18)*sin(5pi/36)-(1/16)*sin(13pi/18)*cos(5pi/36))--(sin(13pi/18)*cos(5pi/36)+(1/16)*sin(13pi/18)*sin(5pi/36),sin(13pi/18)*sin(5pi/36)-(1/16)*sin(13pi/18)*cos(5pi/36)), linewidth(1));\\nlabel(\\\"$Q$\\\", (0,0), SW);\\nlabel(\\\"$R$\\\", (2cos(13pi/36),0), SE);\\nlabel(\\\"$S$\\\", (sin(13pi/18)*cos(5pi/36),sin(13pi/18)*sin(5pi/36)), NE);\\nlabel(\\\"$P$\\\", (cos(13pi/36),sin(13pi/36)), N);\\nlabel(\\\"$65^\\\\circ$\\\", (2cos(13pi/36)-0.04,0), NW);\\nlabel(\\\"$x^\\\\circ$\\\", (0.05,0.11), E);\\n[/asy]\\n\\nWhat is the value of $x?$\",\"type\":\"Prealgebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}