January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52108

A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
19 Nov 2009, 11:50
Question Stats:
33% (02:35) correct 67% (02:39) wrong based on 97 sessions
HideShow timer Statistics




Manager
Joined: 11 Sep 2009
Posts: 129

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
19 Nov 2009, 20:10
I get E: 726.
I assumed that the rectangular floor is looked at unidirectionally. 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.




Intern
Joined: 14 Aug 2009
Posts: 6

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
19 Nov 2009, 22:23
i agree E should be the correct answer.
3^6 possible patterns  3 all same color patterns = 729 3 = 726 different color patterns



Senior Manager
Joined: 31 Aug 2009
Posts: 378
Location: Sydney, Australia

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
20 Nov 2009, 00:05
Nice work AKProdigy. I had 3^6 but couldn't figure out where to lose the 3. +1



Math Expert
Joined: 02 Sep 2009
Posts: 52108

A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
20 Nov 2009, 07:54
AKProdigy87 wrote: I get E: 726.
I assumed that the rectangular floor is looked at unidirectionally. 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: 3^63=726. Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 04 Nov 2009
Posts: 64
Schools: London Business School (int)
WE 1: Research
WE 2: Corporate Strat

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
02 Dec 2009, 22:27
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.



Manager
Joined: 29 Oct 2009
Posts: 196

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
07 Dec 2009, 04:58
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 = 726Answer : E
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 12 Nov 2012
Posts: 168
Location: India
Concentration: Finance, Technology
GPA: 2.7
WE: Analyst (Computer Software)

Permutation and Combination : Tiles arrangement
[#permalink]
Show Tags
11 Jul 2014, 23:34
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?
_________________
C'est la vie



Senior Manager
Joined: 13 Jun 2013
Posts: 275

Re: Permutation and Combination : Tiles arrangement
[#permalink]
Show Tags
12 Jul 2014, 01:05
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. hence answer answer should be 3^63= 726
Attachments
Capture.JPG [ 10.27 KiB  Viewed 2392 times ]



Intern
Joined: 21 Jun 2013
Posts: 25

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
25 Nov 2017, 17:38
Hi,
please can you help why simple combination formula is wrong to apply in this situation. As there are 15 tiles and 6 spaces, I thought of applying 15C6 as I have to choose 6 tiles from 15 and it can be any colors and arrangement doesn't matter. kindly help me advise why my approach is wrong.



Math Expert
Joined: 02 Sep 2009
Posts: 52108

Re: A rectangular floor measures 2 by 3 meters. There are 5 whit
[#permalink]
Show Tags
26 Nov 2017, 01:02




Re: A rectangular floor measures 2 by 3 meters. There are 5 whit &nbs
[#permalink]
26 Nov 2017, 01:02






