{"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":"7dffa1de-3a9d-54fc-9c68-1c36ae3f6824","task_key":"precalculus--test--7dffa1de-3a9d-54fc-9c68-1c36ae3f6824","task_revision_id":"1","upstream_id":"","short_description":"In triangle $ABC$, $AB=\\sqrt{30}$, $AC=\\sqrt{6}$, and $BC=\\sqrt{15}$. There is a…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"In triangle $ABC$, $AB=\\\\sqrt{30}$, $AC=\\\\sqrt{6}$, and $BC=\\\\sqrt{15}$. There is a point $D$ for which $\\\\overline{AD}$ bisects $\\\\overline{BC}$, and $\\\\angle ADB$ is a right angle. Find the value of the ratio\\n\\\\[\\\\dfrac{[ADB]}{[ABC]}.\\\\]In other words, compute the ratio of the area of triangle $ADB$ to the area of triangle $ABC.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}