{"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":"e8528ad1-af97-55dc-8334-d8b96adc2a1e","task_key":"precalculus--test--e8528ad1-af97-55dc-8334-d8b96adc2a1e","task_revision_id":"1","upstream_id":"","short_description":"Two runners, $A$ and $B,$ start at a point $O$ on a linear track, and start…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Two runners, $A$ and $B,$ start at a point $O$ on a linear track, and start running in the same direction.  Runner $B$ runs three times as fast as runner $A.$  An observer stands at point $P$ so that $\\\\overline{OP}$ is perpendicular to the track.  Find the maximum of $\\\\angle APB,$ in degrees.\\n\\n[asy]\\nunitsize(2 cm);\\n\\npair A, B, O, P;\\n\\nA = (0.4,0);\\nB = (1.2,0);\\nO = (0,0);\\nP = (0,1);\\n\\ndraw((-0.5,0)--(2,0));\\ndraw(O--P);\\ndraw(P--A);\\ndraw(P--B);\\n\\nlabel(\\\"$A$\\\", A, S);\\nlabel(\\\"$B$\\\", B, S);\\nlabel(\\\"$O$\\\", O, S);\\nlabel(\\\"$P$\\\", P, N);\\n[/asy]\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}