Difference between revisions of "Mock AIME 1 Pre 2005 Problems/Problem 9"
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385 & = (p - 1)(q - 1)(r - 1) \\ | 385 & = (p - 1)(q - 1)(r - 1) \\ | ||
\end{align*}</cmath> | \end{align*}</cmath> | ||
| − | From here, you can factor <math>385</math> as <math>5 \cdot 7 \cdot 11</math>, giving corresponding values of <math>6, 8,</math> and <math> | + | From here, you can factor <math>385</math> as <math>5 \cdot 7 \cdot 11</math>, giving corresponding values of <math>6, 8,</math> and <math>12</math>. The answer is <math>6 \cdot 8 \cdot 12=576</math>. |
== See also == | == See also == | ||
Revision as of 12:49, 5 April 2008
Problem
and 
are three non-zero integers such that 
and
![\[\frac{1}{p} + \frac{1}{q} + \frac{1}{r} + \frac{360}{pqr} = 1\]](http://latex.artofproblemsolving.com/6/8/8/68867ee7b08e34c84bd7054c465e0b101d58f786.png)
Compute 
.
Solution
From here, you can factor 
as 
, giving corresponding values of 
and 
. The answer is 
.
See also
| Mock AIME 1 Pre 2005 (Problems, Source) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
