{"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":"edfe1acb-e472-5939-b702-3d4056000410","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f22","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_22","short_description":"Let $c$ be a real number, and let $z_1$ and $z_2$ be the two complex numbers…","config":"default","split":"train","body":"{\"problem\":\"Let $c$ be a real number, and let $z_1$ and $z_2$ be the two complex numbers satisfying the equation\\n$z^2 - cz + 10 = 0$. Points $z_1$, $z_2$, $\\\\frac{1}{z_1}$, and $\\\\frac{1}{z_2}$ are the vertices of (convex) quadrilateral $\\\\mathcal{Q}$ in the complex plane. When the area of $\\\\mathcal{Q}$ obtains its maximum possible value, let $c=\\\\sqrt{m}$. what is the value of m\"}","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":[]}