{"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":"6fbe95e4-a4ad-5b29-b000-56fbdff79d49","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f24","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_24","short_description":"Suppose that $a$, $b$, $c$ and $d$ are positive integers satisfying all of the…","config":"default","split":"train","body":"{\"problem\":\"Suppose that $a$, $b$, $c$ and $d$ are positive integers satisfying all of the following relations.\\n\\\\[abcd=2^6\\\\cdot 3^9\\\\cdot 5^7\\\\]\\n\\\\[\\\\text{lcm}(a,b)=2^3\\\\cdot 3^2\\\\cdot 5^3\\\\]\\n\\\\[\\\\text{lcm}(a,c)=2^3\\\\cdot 3^3\\\\cdot 5^3\\\\]\\n\\\\[\\\\text{lcm}(a,d)=2^3\\\\cdot 3^3\\\\cdot 5^3\\\\]\\n\\\\[\\\\text{lcm}(b,c)=2^1\\\\cdot 3^3\\\\cdot 5^2\\\\]\\n\\\\[\\\\text{lcm}(b,d)=2^2\\\\cdot 3^3\\\\cdot 5^2\\\\]\\n\\\\[\\\\text{lcm}(c,d)=2^2\\\\cdot 3^3\\\\cdot 5^2\\\\]\\nWhat is $\\\\text{gcd}(a,b,c,d)$?\"}","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":[]}