Difference between revisions of "2007 AMC 10B Problems/Problem 25"

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is an integer?
 
is an integer?
  
(A) 4
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<math> \textbf{(A) }4\qquad\textbf{(B) }6\qquad\textbf{(C) }9\qquad\textbf{(D) }12\qquad\textbf{(E) }\text{infinitely many} </math>
 
 
(B) 6
 
 
 
(C) 9
 
 
 
(D) 12
 
 
 
(E) infinitely many
 

Revision as of 18:48, 24 July 2011

How many pairs of positive integers (a,b) are there such that a and b have no common factors greater than 1 and:

$\frac{a}{b} + \frac{14b}{9a}$

is an integer?

$\textbf{(A) }4\qquad\textbf{(B) }6\qquad\textbf{(C) }9\qquad\textbf{(D) }12\qquad\textbf{(E) }\text{infinitely many}$