{"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":"b0025c24-0d9b-5cc5-b5ac-46c4a8f70357","task_key":"counting~5fand~5fprobability--test--b0025c24-0d9b-5cc5-b5ac-46c4a8f70357","task_revision_id":"1","upstream_id":"","short_description":"The figure below represents a figure with a total of 120 triangles and $n$…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The figure below represents a figure with a total of 120 triangles and $n$ points labeled as vertices on the horizontal base. What is the value of $n$?\\n\\n[asy]size(250,400);\\npair P = (3,4);\\nreal r = .05;\\ndraw((0,0)--P); draw((1,0)--P); draw((3,0)--P); draw((4.5,0)--P); draw((7,0)--P); draw((7,0)--(8,0)); fill(circle((8+3r,0),r)); fill(circle((8+7r,0),r)); draw((8+15r,0)--(9+15r,0)); draw((9+15r,0)--P); draw((11+15r,0)--P); fill(circle((8+11r,0),r)); draw((0,0)--(7,0)); draw((9+15r,0)--(11+15r,0));\\nlabel(\\\"$P$\\\",P,N); label(\\\"$A_1$\\\",(0,0),S); label(\\\"$A_2$\\\",(1,0),S); label(\\\"$A_3$\\\",(3,0),S); label(\\\"$A_4$\\\",(4.5,0),S); label(\\\"$A_5$\\\",(7,0),S); label(\\\"$A_{n-1}$\\\",(9+15r,0),S); label(\\\"$A_n$\\\",(11+15r,0),S);[/asy]\",\"type\":\"Counting & Probability\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}