{"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":"bd3c1dd8-c5c4-5f76-a066-a1321590c824","task_key":"intermediate~5falgebra--test--bd3c1dd8-c5c4-5f76-a066-a1321590c824","task_revision_id":"1","upstream_id":"","short_description":"For $0 < k < 6,$ the graphs of $\\frac{(x - k)^2}{9} + y^2 = 1$ and…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"For $0 < k < 6,$ the graphs of $\\\\frac{(x - k)^2}{9} + y^2 = 1$ and $\\\\frac{x^2}{9} + y^2 = 1$ intersect at $A$ and $C,$ and have $x$-intercepts at $B$ and $D$ respectively.  Compute the value of $k$ for which $ABCD$ is a square.\\n\\n[asy]\\nunitsize(1 cm);\\n\\npath ellone = xscale(3)*Circle((0,0),1);\\npath elltwo = shift((24/5,0))*xscale(3)*Circle((0,0),1);\\npair A, B, C, D;\\n\\nA = intersectionpoints(ellone,elltwo)[0];\\nC = intersectionpoints(ellone,elltwo)[1];\\nB = (-3 + 24/5,0);\\nD = (3,0);\\n\\ndraw(ellone);\\ndraw(elltwo);\\n\\ndraw((-3.5,0)--(9,0));\\ndraw((0,-1.5)--(0,1.5));\\ndraw(A--B--C--D--cycle);\\n\\nlabel(\\\"$A$\\\", A, N, fontsize(10));\\nlabel(\\\"$B$\\\", B, NW, fontsize(10));\\nlabel(\\\"$C$\\\", C, S, fontsize(10));\\nlabel(\\\"$D$\\\", D, NE, fontsize(10));\\n[/asy]\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}