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Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.”

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by BTGmoderatorDC » Wed Jan 22, 2020 4:31 pm
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



OA D

Source: Princeton Review
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Re: Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “matc

by Jay@ManhattanReview » Thu Jan 23, 2020 12:03 am
BTGmoderatorDC wrote: ↑
Wed Jan 22, 2020 4:31 pm
 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

OA D

Source: Princeton Review
Let’s factorize 63,000.

63,000 = 3^2 x 7 x 2^3 x 5^3 = 3*3*7*2*2*2*5*5*5

Since there are 9 garments and Dave has more than one of each, every prime factor, including appearing more than once, represents the number of choices for a particular garment. Since we have three 5s, three garments must have 5 choices each.

The correct answer: D

Hope this helps!

-Jay
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