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# A rectangular floor measures 2 by 3 meters. There are 5

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Current Student
Joined: 11 May 2008
Posts: 551
A rectangular floor measures 2 by 3 meters. There are 5 [#permalink]

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02 Aug 2008, 03:03
A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different color patterns can the floor be parqueted?

104
213
577
705
726

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Current Student
Joined: 11 May 2008
Posts: 551

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02 Aug 2008, 05:12
hmmm... how did u arrive at that result...?
Director
Joined: 27 May 2008
Posts: 531

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02 Aug 2008, 06:14
arjtryarjtry wrote:
A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different color patterns can the floor be parqueted?

104
213
577
705
726

lets change the question language to undertand it better... suppose we have 6W, 6B and 6R tiles avaibale..... and we have 2by3 = 6 places to put these tiles....
the question is, in how many ways these tiles can be put, if we cant have only one color pattern..... (means at leat one tiles has to be of different color than rest )

each place can have 3 color to choose from... without any restrctions
total number of ways = 3^6 = 729

but we cant have all W, all B or all R = 3
desired ways = 729-3 = 726 .. option E
Current Student
Joined: 11 May 2008
Posts: 551

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02 Aug 2008, 10:06
yep!! that right both of you
Manager
Joined: 15 Jul 2008
Posts: 205

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02 Aug 2008, 11:41
durgesh79 wrote:
arjtryarjtry wrote:
A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different color patterns can the floor be parqueted?

104
213
577
705
726

lets change the question language to undertand it better... suppose we have 6W, 6B and 6R tiles avaibale..... and we have 2by3 = 6 places to put these tiles....
the question is, in how many ways these tiles can be put, if we cant have only one color pattern..... (means at leat one tiles has to be of different color than rest )

each place can have 3 color to choose from... without any restrctions
total number of ways = 3^6 = 729

but we cant have all W, all B or all R = 3
desired ways = 729-3 = 726 .. option E

I had a logically different but mathematically same approach. Looking for critique..

You have 5 tiles of each color..
So for the first slot, you have a min of 3 option - one of the 3 colors. Same for 2nd 3rd 4th and 5th. For the 6th slot, you have
a min of 2 options. So total options = 3^5 x 2 = 726.
I have a feeling that this reasoning is flawed, but am unable to point it. Please let me know if you think that it is erroneous.
BTW.. did you actually beat that in under 2 mins ?!!!
Director
Joined: 27 May 2008
Posts: 531

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02 Aug 2008, 11:55
bhushangiri wrote:
I had a logically different but mathematically same approach. Looking for critique..

You have 5 tiles of each color..
So for the first slot, you have a min of 3 option - one of the 3 colors. Same for 2nd 3rd 4th and 5th. For the 6th slot, you have
a min of 2 options. So total options = 3^5 x 2 = 726.
I have a feeling that this reasoning is flawed, but am unable to point it. Please let me know if you think that it is erroneous.
BTW.. did you actually beat that in under 2 mins ?!!!

i did try this approach earlier and found that 3^5 * 2 = 486 ... and its not one of the options ....

frankly, i couldnt do it in under 2 minutes.... took me more than 3 to visualise the logic ... but thats fine for one or two questions i guess... generally i finish maths section with 15 minutes to go .....
Manager
Joined: 15 Jul 2008
Posts: 205

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02 Aug 2008, 17:47
durgesh79 wrote:
bhushangiri wrote:
I had a logically different but mathematically same approach. Looking for critique..

You have 5 tiles of each color..
So for the first slot, you have a min of 3 option - one of the 3 colors. Same for 2nd 3rd 4th and 5th. For the 6th slot, you have
a min of 2 options. So total options = 3^5 x 2 = 726.
I have a feeling that this reasoning is flawed, but am unable to point it. Please let me know if you think that it is erroneous.
BTW.. did you actually beat that in under 2 mins ?!!!

i did try this approach earlier and found that 3^5 * 2 = 486 ... and its not one of the options .... :wink:

frankly, i couldnt do it in under 2 minutes.... took me more than 3 to visualise the logic ... but thats fine for one or two questions i guess... generally i finish maths section with 15 minutes to go .....

3^5 * 2 = 486 . :beat

generally i finish maths section with 15 minutes to go :king

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: challenging one...   [#permalink] 02 Aug 2008, 17:47
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# A rectangular floor measures 2 by 3 meters. There are 5

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