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Problem Solving - Need help to solve this

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Problem Solving - Need help to solve this [#permalink] New post 08 Jun 2011, 05:58
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (02:58) correct 0% (00:00) wrong based on 4 sessions
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
[Reveal] Spoiler: OA

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Re: Problem Solving - Need help to solve this [#permalink] New post 08 Jun 2011, 06:10
there could be other methods to solve this, but most simplest --
There are 9 different kinds of clothes.

so if you find the prime factors of 63000
i.e. 3 * 3 * 7 * 2 * 2 *2 *5 * 5 *5 * 1

But the guy has everything greater than 1... so ignoring that there are exactly
9 factors.

and 5 is 3 times.

so Answer is D.
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Re: Problem Solving - Need help to solve this [#permalink] New post 08 Jun 2011, 06:34
agdimple333,

Sorry, i didn't understand your solution.
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Re: Problem Solving - Need help to solve this [#permalink] New post 08 Jun 2011, 06:57
kichha51 wrote:
agdimple333,

Sorry, i didn't understand your solution.


there could be other methods to solve this, but most simplest --

Q is asking you how many clothes are exactly 5 in #s.

There are 9 different kinds of clothes.
And each of the kind is more than 1.

so if you find the prime factors of 63000
i.e. 3 * 3 * 7 * 2 * 2 *2 *5 * 5 *5 * 1

But the guy has everything greater than 1... so ignoring that, there are
9 factors.
From this 2 kind of garments are 3 each, 1 kind of garment is 7, 3 kind of garments 2 each and 3 kind of garments 5 each.

or you can think that a possibility there are 7 shirt, 2 pants, 2 boxers, 2 jackets, 3 left sock, 3 right sock, 5 left shoe, 5 right shoe and 5 tie. And if you do it backward you have to select one each from the above to form an outfit

so 7C1 * 2C1 * 2C1 * 2C1 * 3C1 * 3C1 * 5C1 * 5C1 * 5C1
and the result is 63,000. which is given as different forms out of outfit that can be formed.

Hope this helps.

so Answer is D.
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Re: Problem Solving - Need help to solve this [#permalink] New post 10 Jun 2011, 21:22
yes it helps..good explanation
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Re: Problem Solving - Need help to solve this   [#permalink] 10 Jun 2011, 21:22
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