Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

33% (02:31) correct
67% (02:16) wrong based on 49 sessions

HideShow timer Statistics

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 colors patterns can be floor be parqueted?

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit [#permalink]

Show Tags

19 Nov 2009, 21:10

6

This post received KUDOS

2

This post was BOOKMARKED

I get E: 726.

I assumed that the rectangular floor is looked at uni-directionally. So in essence:

[1 2 3] [4 5 6]

is represented as

[1 2 3 4 5 6]

So 3 ways to select the color of the first tile, 3 ways to select the color of the second tile, etc. Now assuming that there were 6 tiles of each color, you would have:

3 * 3 * 3 * 3 * 3 * 3 = 3^6 = 729 possibilities.

However, these possibilities allow the inclusion of an all black, an all white, and an all red parquet. You need to take away these three distinct possibilities (since we only have 5 tiles of each color).

729 - 3 = 726.

Therefore, there are 726 different color patterns available.

I assumed that the rectangular floor is looked at uni-directionally. So in essence:

[1 2 3] [4 5 6]

is represented as

[1 2 3 4 5 6]

So 3 ways to select the color of the first tile, 3 ways to select the color of the second tile, etc. Now assuming that there were 6 tiles of each color, you would have:

3 * 3 * 3 * 3 * 3 * 3 = 3^6 = 729 possibilities.

However, these possibilities allow the inclusion of an all black, an all white, and an all red parquet. You need to take away these three distinct possibilities (since we only have 5 tiles of each color).

729 - 3 = 726.

Therefore, there are 726 different color patterns available.

This question can be solved with two approaches: the long one and the short and elegant one, as AKProdigy87 proposed. With the later it's definitely possible to solve this problem in 2 mins.

A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?

A. 104 B. 213 C. 577 D. 705 E. 726

Imagine the case in which we have not 5 blocks of each color but 6, then each slot from 2*3=6 would have 3 color choices to be filled with: white, black, or red. That means that total different ways to fill 6 slots would be 3*3*3*3*3*3=3^6;

Now, what is the difference between this hypothetical case and the one in the question? As we allowed 6 blocks of each color instead of 5, then we would get 3 patterns which are impossible when we have 5 blocks of each color: all white, all red and all black. Thus we should subtract these 3 cases: 3^6-3=726.

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit [#permalink]

Show Tags

02 Dec 2009, 23:27

That's a very elegant solution. Was wondering - wouldn't there be a need to subtract out cases where 1 red tile is being replaced by another red tile? The colour pattern will be the same in the cases where we replace 1 coloured tile in a pattern with another tile of the same colour.

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit [#permalink]

Show Tags

07 Dec 2009, 05:58

Total number of squares we need to fill = 6

Number of colors we have = 3

Therefore, total number of patterns = 3*3*3*3*3*3 = 729

However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).

Thus our answer should be : 729 - 3 = 726

Answer : E _________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Permutation and Combination : Tiles arrangement [#permalink]

Show Tags

12 Jul 2014, 00:34

Can some one solve this question and post his/her detailed solution ? I found this question in gmat club question tests. I didn't understand the explanation thorouhly though Question : A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?
_________________

Re: Permutation and Combination : Tiles arrangement [#permalink]

Show Tags

12 Jul 2014, 02:05

1

This post received KUDOS

mshrek wrote:

Can some one solve this question and post his/her detailed solution ? I found this question in gmat club question tests. I didn't understand the explanation thorouhly though Question : A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?

as shown in the figure, we have a space of 6 tiles available with us. each measuring 1 by 1 meter. lets name these spaces as 1,2,3,4,5 and 6. In first (1) of these six spaces any of the 3 colors can occur . similarly for space 2,3,4,5 and 6 we have 3 options. now since each of three available colors has only 5 tiles, therefore we cannot fill the space with 6 tiles of same color. hence we must subtract three cases in which we have assumed that 6 spaces are filled with one of the three colors.

Can some one solve this question and post his/her detailed solution ? I found this question in gmat club question tests. I didn't understand the explanation thorouhly though Question : A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?

Merging similar topics. Please refer to the discussion above.
_________________

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...