{"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":"30245e8a-d9ce-5427-8eff-65d481e6a3a4","task_key":"geometry--test--30245e8a-d9ce-5427-8eff-65d481e6a3a4","task_revision_id":"1","upstream_id":"","short_description":"A chord of a circle is perpendicular to a radius at the midpoint of the radius.…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form $\\\\displaystyle\\n{{a\\\\pi+b\\\\sqrt{c}}\\\\over{d\\\\pi-e\\\\sqrt{f}}}$, where $a$, $b$, $c$, $d$, $e$, and $f$ are positive integers, $a$ and $e$ are relatively prime, and neither $c$ nor $f$ is divisible by the square of any prime.  Find the remainder when the product $a\\\\cdot\\nb\\\\cdot c\\\\cdot d\\\\cdot e\\\\cdot f$ is divided by 1000.\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}