{"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":"22527db3-2a83-58df-ab98-82bfcb84d0b1","task_key":"prealgebra--test--22527db3-2a83-58df-ab98-82bfcb84d0b1","task_revision_id":"1","upstream_id":"","short_description":"A $30^\\circ$-$60^\\circ$-$90^\\circ$ triangle is drawn on the exterior of an…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A $30^\\\\circ$-$60^\\\\circ$-$90^\\\\circ$ triangle is drawn on the exterior of an equilateral triangle so the hypotenuse of the right triangle is one side of the equilateral triangle. If the shorter leg of the right triangle is 6 units, what is the distance between the two vertices that the triangles do not have in common? Express your answer in simplest radical form. [asy]\\ndraw((2,0)--(0,0)--(1,1.732)--(2,1.732)--(2,0)--(1,1.732));\\ndraw((2,1.632)--(1.9,1.632)--(1.9,1.732));\\nlabel(\\\"$60^\\\\circ$\\\",(1,1.732),2SE+E);\\nlabel(\\\"$30^\\\\circ$\\\",(2,0),5NNW+4N);\\nlabel(\\\"6\\\",(1.5,1.732),N);\\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":[]}