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Mock AIME 1 Pre 2005 Problems/Problem 9

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Problem

p, q, and r are three non-zero integers such that p + q + r = 26 and \frac{1}{p} + \frac{1}{q} + \frac{1}{r} + \frac{360}{pqr} = 1 Compute pqr.

Solution

\begin{align*} \frac {1}{p} + \frac {1}{q} + \frac {1}{r} + \frac {360}{pqr} & = 1 \\pq + pr + qr + 360 & =  pqr \\36...

From here, you can factor 385 as 5 \cdot 7 \cdot 11, giving corresponding values of 6, 8, and 12. The answer is 6 \cdot 8 \cdot 12=576.

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
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