{"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":"47abb250-cfc8-53e7-8a82-ed8361bc72d6","task_key":"test--47abb250-cfc8-53e7-8a82-ed8361bc72d6","task_revision_id":"1","upstream_id":"","short_description":"We can view these conditions as a geometry diagram as seen below. So, we know…","config":"","split":"test","body":"{\"problem\":\"We can view these conditions as a geometry diagram as seen below. So, we know that $\\\\frac{e}{f}=\\\\frac{3}{4}$ (since $e=a-b=\\\\frac{3}{4} c-\\\\frac{3}{4} d=\\\\frac{3}{4} f$ and we know that $\\\\sqrt{e^{2}+f^{2}}=15$ (since this is $\\\\left.\\\\sqrt{a^{2}+c^{2}}-\\\\sqrt{b^{2}+d^{2}}\\\\right)$. Also, note that $a c+b d-a d-b c=(a-b)(c-d)=e f$. So, solving for $e$ and $f$, we find that $e^{2}+f^{2}=225$, so $16 e^{2}+16 f^{2}=3600$, so $(4 e)^{2}+(4 f)^{2}=3600$, so $(3 f)^{2}+(4 f)^{2}=3600$, so $f^{2}\\\\left(3^{2}+4^{2}\\\\right)=3600$, so $25 f^{2}=3600$, so $f^{2}=144$ and $f=12$. Thus, $e=\\\\frac{3}{4} 12=9$. Therefore, \\\\boldsymbol{e f}=\\\\mathbf{9} * \\\\mathbf{1 2}=\\\\mathbf{1 0 8}$.\"}","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":[]}