{"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":"b37db5af-d34a-5fd7-93e5-c6e4eff495e6","task_key":"counting~5fand~5fprobability--test--b37db5af-d34a-5fd7-93e5-c6e4eff495e6","task_revision_id":"1","upstream_id":"","short_description":"A point with coordinates $(x,\\ y)$ is randomly selected such that $0\\leq x…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"A point with coordinates $(x,\\\\ y)$ is randomly selected such that $0\\\\leq x \\\\leq10$ and $0\\\\leq y \\\\leq10$. What is the probability that the coordinates of the point will satisfy $2x+5y \\\\geq 20$? Express your answer as a common fraction.\\n\\n[asy]\\n\\nsize(5cm,5cm);\\n\\ndraw((-2,0)--(12,0),Arrows);\\n\\ndraw((0,-2)--(0,12),Arrows);\\n\\npair a,b,x;\\n\\nx=(0,0);\\n\\na=(10,0);\\n\\nb=(0,10);\\n\\nadd(pathticks(x--a,2,0.1,0,25));\\n\\nadd(pathticks(x--a,2,0.2,0,25));\\n\\nadd(pathticks(x--a,2,0.3,0,25));\\n\\nadd(pathticks(x--a,2,0.4,0,25));\\n\\nadd(pathticks(x--a,2,0.5,0,25));\\n\\nadd(pathticks(x--a,2,0.6,0,25));\\n\\nadd(pathticks(x--a,2,0.7,0,25));\\n\\nadd(pathticks(x--a,2,0.8,0,25));\\n\\nadd(pathticks(x--a,2,0.9,0,25));\\n\\nadd(pathticks(x--a,2,1,0,25));\\n\\nadd(pathticks(x--b,2,0.1,0,25));\\n\\nadd(pathticks(x--b,2,0.2,0,25));\\n\\nadd(pathticks(x--b,2,0.3,0,25));\\n\\nadd(pathticks(x--b,2,0.4,0,25));\\n\\nadd(pathticks(x--b,2,0.5,0,25));\\n\\nadd(pathticks(x--b,2,0.6,0,25));\\n\\nadd(pathticks(x--b,2,0.7,0,25));\\n\\nadd(pathticks(x--b,2,0.8,0,25));\\n\\nadd(pathticks(x--b,2,0.9,0,25));\\n\\nadd(pathticks(x--b,2,1,0,25));\\n\\n[/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":[]}