{"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":"dca7a3c7-9260-54bd-8657-668aadb6b8ed","task_key":"intermediate~5falgebra--test--dca7a3c7-9260-54bd-8657-668aadb6b8ed","task_revision_id":"1","upstream_id":"","short_description":"For $x \\ge 1,$ let $f$ be the function defined as follows:","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"For $x \\\\ge 1,$ let $f$ be the function defined as follows:\\n\\\\[f(x) = \\\\left\\\\{\\n\\\\begin{array}{cl}\\n\\\\lfloor x \\\\rfloor \\\\left| x - \\\\lfloor x \\\\rfloor - \\\\dfrac{1}{2 \\\\lfloor x \\\\rfloor} \\\\right| & \\\\text{if $x < \\\\lfloor x \\\\rfloor + \\\\dfrac{1}{\\\\lfloor x \\\\rfloor}$}, \\\\\\\\\\nf \\\\left( x - \\\\dfrac{1}{\\\\lfloor x \\\\rfloor} \\\\right) & \\\\text{otherwise}.\\n\\\\end{array}\\n\\\\right.\\\\]Let $g(x) = 2^{x - 2007}.$ Compute the number of points in which the graphs of $f$ and $g$ intersect.\",\"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":[]}