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combinations

by maheshban » Sat May 08, 2010 3:11 am
Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they "match." Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 63,000 different outfits, then for how many garments does Dave have exactly five choices?

A.0
B.1
C.2
D.3
E.4
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by sanju09 » Sat May 08, 2010 3:41 am
maheshban wrote:Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they "match." Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 63,000 different outfits, then for how many garments does Dave have exactly five choices?

A.0
B.1
C.2
D.3
E.4
Dave has 9 different set of garments, hence 63000 needs to be split in 9 separate proper factors to accommodate all 9.

63000 = 63 × 1000 = 3 × 3 × 7 × 2 × 2 × 2 × 5 × 5 × 5

Above is the only possibility to accommodate all 9, and it can be seen that Dave has got [spoiler]3 garments with exactly five choices there.

D[/spoiler]
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by sumanr84 » Sat May 08, 2010 9:56 am
Nice soln by Sanju as always..

I had absolutely no idea to approach this problem until I encountered below link. So, If somebody needs to get more insight into the approach on-roll here, pls refer the below link,

https://blog.knewton.com/2010/05/06/gmat ... d-factors/
I am on a break !!
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