{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"amc","formal_name":"AMC (AIMO validation set)","introduction":"83 AMC 12 problems assembled by Project Numina as a validation set for the AIMO competition. They sit a step below AIME in difficulty, which makes them a useful lower rung on the same scale.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"7785c1e0-ec5b-57cf-b369-f406ecb7ad80","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f19","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_19","short_description":"In $\\triangle{ABC}$ medians $\\overline{AD}$ and $\\overline{BE}$ intersect at $G$…","config":"default","split":"train","body":"{\"problem\":\"In $\\\\triangle{ABC}$ medians $\\\\overline{AD}$ and $\\\\overline{BE}$ intersect at $G$ and $\\\\triangle{AGE}$ is equilateral. Then $\\\\cos(C)$ can be written as $\\\\frac{m\\\\sqrt p}n$, where $m$ and $n$ are relatively prime positive integers and $p$ is a positive integer not divisible by the square of any prime. What is $m+n+p?$\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}