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Interesting GMATFix Problem-39

by arora007 » Mon Oct 04, 2010 4:16 am
A movie producer wants to hire 4 men and 4 women from the actors who auditioned. If 7 women auditioned and 525 combinations are possible, how many men auditioned?
A)5
B)6
C)7
D)8
E)9
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by selango » Mon Oct 04, 2010 4:45 am
7C4*nC4=525

nC4=15

Number of Men=6

Pick B
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by Rahul@gurome » Mon Oct 04, 2010 7:53 am
Let the number of men auditioned = M
Therefore, 7C4 * MC4 = 525
(7!)/(4!)(3!) * (M!)/(4!)(M - 4)! = 525
[35] * (M!)/(4!)(M - 4)! = 525
(M!)/(4!)(M - 4) = 15, which implies M = 6

[spoiler]The correct answer is (B).[/spoiler]
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by Yanat » Mon Oct 04, 2010 8:18 am
7C4 * nC4 = 525
Solving for n got 6. There is no need to solve it completely and by plugging in the numbers we have to solve finally nC4=14 and so n = 6
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by arora007 » Tue Oct 05, 2010 6:33 am
yeah OA is B
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