{"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":"fea62cd7-c3a9-5169-83cd-5a3bc45758d2","task_key":"intermediate~5falgebra--test--fea62cd7-c3a9-5169-83cd-5a3bc45758d2","task_revision_id":"1","upstream_id":"","short_description":"Let $x,$ $y,$ and $z$ be positive real numbers. Then the minimum value of","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $x,$ $y,$ and $z$ be positive real numbers.  Then the minimum value of\\n\\\\[\\\\frac{(x^4 + 1)(y^4 + 1)(z^4 + 1)}{xy^2 z}\\\\]is of the form $\\\\frac{a \\\\sqrt{b}}{c},$ for some positive integers $a,$ $b,$ and $c,$ where $a$ and $c$ are relatively prime, and $b$ is not divisible by the square of a prime.  Enter $a + b + c.$\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}