{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-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":"920485a6-009a-54c9-bbf5-d76affa9917a","task_key":"test--920485a6-009a-54c9-bbf5-d76affa9917a","task_revision_id":"1","upstream_id":"","short_description":"Suppose that $x, y$, and $z$ are complex numbers of equal magnitude that satisfy…","config":"","split":"test","body":"{\"problem\":\"Suppose that $x, y$, and $z$ are complex numbers of equal magnitude that satisfy $$x+y+z=-\\\\frac{\\\\sqrt{3}}{2}-i \\\\sqrt{5}$$ and $$x y z=\\\\sqrt{3}+i \\\\sqrt{5}.$$ If $x=x_{1}+i x_{2}, y=y_{1}+i y_{2}$, and $z=z_{1}+i z_{2}$ for real $x_{1}, x_{2}, y_{1}, y_{2}, z_{1}$, and $z_{2}$, then $$\\\\left(x_{1} x_{2}+y_{1} y_{2}+z_{1} z_{2}\\\\right)^{2}$$ can be written as $\\\\frac{a}{b}$ for relatively prime positive integers $a$ and $b$. Compute $100 a+b$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}