{"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":"1f7a00a0-aef5-56fc-a29c-10f6edbdc105","task_key":"prealgebra--test--1f7a00a0-aef5-56fc-a29c-10f6edbdc105","task_revision_id":"1","upstream_id":"","short_description":"Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the longer leg of the smaller triangle?\\n\\n[asy]size(150); pair O; for(int i = 2; i < 5; ++i){\\ndraw(O--((2/sqrt(3))^i)*dir(30*i));\\n}\\nfor(int g = 2; g < 4; ++g){\\ndraw( ((2/sqrt(3))^g)*dir(30*g)-- ((2/sqrt(3))^(g+1))*dir(30*g+30));\\n}\\nlabel(\\\"16 cm\\\", O--(16/9)*dir(120), W);\\n//label(\\\"$30^{\\\\circ}$\\\",.4*dir(0),dir(90));\\n//label(\\\"$30^{\\\\circ}$\\\",.4*dir(25),dir(115));\\nlabel(\\\"$30^{\\\\circ}$\\\",.4*dir(50),dir(140));\\nlabel(\\\"$30^{\\\\circ}$\\\",.4*dir(85),dir(175));\\nreal t = (2/(sqrt(3)));\\n//draw(rightanglemark((1,.1),(1,0),(.9,0),s=3));\\ndraw(rightanglemark(rotate(30)*(0,t**4),rotate(0)*(0,t**3),O,s=3));\\ndraw(rightanglemark(rotate(0)*(0,t**3),rotate(-30)*(0,t**2),O,s=3));\\n//draw(rightanglemark(rotate(-30)*(0,t**2),rotate(-60)*(0,t**1),O,s=3));\\n[/asy]\",\"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":[]}