{"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":"743c2de2-0f95-54b0-82e1-65cc60631d70","task_key":"intermediate~5falgebra--test--743c2de2-0f95-54b0-82e1-65cc60631d70","task_revision_id":"1","upstream_id":"","short_description":"Let $w_1, w_2, \\dots, w_n$ be complex numbers. A line $L$ in the complex plane…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $w_1, w_2, \\\\dots, w_n$ be complex numbers. A line $L$ in the complex plane is called a mean line for the points $w_1, w_2, \\\\dots, w_n$ if $L$ contains points (complex numbers) $z_1, z_2, \\\\dots, z_n$ such that\\n\\\\[\\\\sum_{k = 1}^n (z_k - w_k) = 0.\\\\]For the numbers $w_1 = 32 + 170i$, $w_2 = -7 + 64i$, $w_3 = -9 +200i$, $w_4 = 1 + 27i$, and $w_5 = -14 + 43i$, there is a unique mean line with $y$-intercept $3$. Find the slope of this mean line.\",\"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":[]}