{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"aime-2024","formal_name":"AIME 2024","introduction":"The 30 problems of the 2024 American Invitational Mathematics Examination (AIME I and II). Every answer is an integer from 0 to 999, with no options and no partial credit. It is a frequent reference point for reasoning models.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/Maxwell-Jia/AIME_2024","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"c93df5c3-615b-53b2-a818-7428b52651df","task_key":"default--train--c93df5c3-615b-53b2-a818-7428b52651df","task_revision_id":"2","upstream_id":"","short_description":"AIME 2024 train c93df5c3-615b-53b2-a818-7428b52651df","config":"default","split":"train","body":"{\"Problem\":\"Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations: \\n\\\\[\\\\log_2\\\\left({x \\\\over yz}\\\\right) = {1 \\\\over 2}\\\\]\\n\\\\[\\\\log_2\\\\left({y \\\\over xz}\\\\right) = {1 \\\\over 3}\\\\]\\n\\\\[\\\\log_2\\\\left({z \\\\over xy}\\\\right) = {1 \\\\over 4}\\\\]\\nThen the value of $\\\\left|\\\\log_2(x^4y^3z^2)\\\\right|$ is $\\\\tfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/Maxwell-Jia/AIME_2024","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}