{"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":"5c280494-ebe2-5586-b0a1-96d9de6636dd","task_key":"precalculus--test--5c280494-ebe2-5586-b0a1-96d9de6636dd","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{a}$ and $\\mathbf{b}$ be two nonzero vectors such that $\\mathbf{a} +…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $\\\\mathbf{a}$ and $\\\\mathbf{b}$ be two nonzero vectors such that $\\\\mathbf{a} + \\\\mathbf{b}$ and $\\\\mathbf{b}$ are orthogonal, and $\\\\mathbf{a} + 2 \\\\mathbf{b}$ and $\\\\mathbf{a}$ are orthogonal.  Find $\\\\frac{\\\\|\\\\mathbf{a}\\\\|}{\\\\|\\\\mathbf{b}\\\\|}.$\",\"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":[]}