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Dave has no fashion sense, and will wear any combination of

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by BTGmoderatorDC » Mon Aug 26, 2019 10:17 pm

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Answers

A

B

C

D

E

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Difficulty—

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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by swerve » Tue Aug 27, 2019 11:26 am
BTGmoderatorDC 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

OA D

Source: Princeton Review
\(63000= 2^3 \cdot 3^2 \cdot 5^3 \cdot 7 = 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot {\color{red}{5\cdot 5\cdot 5}}\cdot 7\)

If Dave has more than one of each of the 9 listed garments, then there are 3 garments in which Dave has exactly 5 choices.

Therefore, __D__
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by Scott@TargetTestPrep » Mon Sep 02, 2019 5:56 pm
BTGmoderatorDC 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

OA D

Source: Princeton Review

First, let's factor 63,000:

63,000 = 63 x 1,000 = 3^2 x 7 x 2^3 x 5^3

Since there are 9 garments and Dave has more than one of each garment, every prime factor (including repeated ones) represents the number of choices for a certain garment. Since we have a factor of 5^3, 3 garments must have 5 choices each.

Answer: D

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