{"status": "success", "data": {"description_md": "The number $5^{867}$ is between $2^{2013}$ and $2^{2014}$.  How many pairs of integers $(m,n)$ are there such that $1\\leq m\\leq 2012$ and $$5^n<2^m<2^{m+2}<5^{n+1}?$$\n\n$\\textbf{(A) }278\\qquad\\textbf{(B) }279\\qquad\\textbf{(C) }280\\qquad\\textbf{(D) }281\\qquad\\textbf{(E) }282\\qquad$", "description_html": "<p>The number  <span class=\"katex--inline\">5^{867}</span>  is between  <span class=\"katex--inline\">2^{2013}</span>  and  <span class=\"katex--inline\">2^{2014}</span> .  How many pairs of integers  <span class=\"katex--inline\">(m,n)</span>  are there such that  <span class=\"katex--inline\">1\\leq m\\leq 2012</span>  and  <span class=\"katex--display\">5^n&lt;2^m&lt;2^{m+2}&lt;5^{n+1}?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }278\\qquad\\textbf{(B) }279\\qquad\\textbf{(C) }280\\qquad\\textbf{(D) }281\\qquad\\textbf{(E) }282\\qquad</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2014 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/14_amc10A_p24"}}