Difference between revisions of "2014 AMC 10A Problems/Problem 25"

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\textbf{(D) }281\qquad
 
\textbf{(D) }281\qquad
 
\textbf{(E) }282\qquad</math>
 
\textbf{(E) }282\qquad</math>
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==Solution==
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==See Also==
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{{AMC10 box|year=2014|ab=A|num-b=24|after=Last Problem}}
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{{MAA Notice}}

Revision as of 23:21, 6 February 2014

Problem

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 \[5^n<2^m<2^{m+2}<5^{n+1}?\] $\textbf{(A) }278\qquad \textbf{(B) }279\qquad \textbf{(C) }280\qquad \textbf{(D) }281\qquad \textbf{(E) }282\qquad$

Solution

See Also

2014 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 24
Followed by
Last Problem
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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