{"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 algebra / test selection.","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":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"726a77d4-4599-5066-aba1-cd38278fdcbb","task_key":"algebra--test--726a77d4-4599-5066-aba1-cd38278fdcbb","task_revision_id":"2","upstream_id":"","short_description":"Two circles, one centered at $(-3,2)$ and the other centered at $(0,-1)$, are…","config":"algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Two circles, one centered at $(-3,2)$ and the other centered at $(0,-1)$, are internally tangent as shown. [asy]\\nimport graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-9.34,xmax=9.27,ymin=-9.36,ymax=7.89;\\n\\nLabel laxis; laxis.p=fontsize(10);\\n\\nxaxis(xmin,xmax,Ticks(laxis,Step=2.0,Size=2,OmitTick(0)),Arrows(6),above=true); yaxis(ymin,ymax,Ticks(laxis,Step=2.0,Size=2,OmitTick(0)),Arrows(6),above=true); draw(circle((0,-1),7.07)); draw(circle((-3,2),2.83));\\n\\ndot((0,-1),ds); label(\\\"$(0, -1)$\\\",(0.23,-1.87),SE*lsf); dot((-3,2),ds); label(\\\"$(-3, 2)$\\\",(-2.82,2.29),N*lsf); dot((1,6),ds); label(\\\"$(1, 6)$\\\",(1.2,6.3),NE*lsf); dot((-5,4),ds);\\n\\nclip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);\\n\\n[/asy] If the equation of the smaller circle can be written as $x^2 + y^2 + Dx + Ey + F = 0$, find $D + E + F$.\",\"type\":\"Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}