Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Apr 2014, 18:16

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Rectangular floor patterns

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17317
Followers: 2874

Kudos [?]: 18380 [0], given: 2348

GMAT Tests User CAT Tests
Rectangular floor patterns [#permalink] New post 19 Nov 2009, 11:50
Expert's post
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

40% (01:01) correct 60% (03:42) wrong based on 5 sessions
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?

(A) 104
(B) 213
(C) 3^5
(D) 705
(E) 726
[Reveal] Spoiler: OA

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

6 KUDOS received
Manager
Manager
Joined: 11 Sep 2009
Posts: 129
Followers: 4

Kudos [?]: 142 [6] , given: 6

GMAT Tests User
Re: Rectangular floor patterns [#permalink] New post 19 Nov 2009, 20:10
6
This post received
KUDOS
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.
Intern
Intern
Joined: 14 Aug 2009
Posts: 8
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: Rectangular floor patterns [#permalink] New post 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
Senior Manager
Joined: 31 Aug 2009
Posts: 423
Location: Sydney, Australia
Followers: 6

Kudos [?]: 91 [0], given: 20

GMAT Tests User
Re: Rectangular floor patterns [#permalink] New post 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
User avatar
Joined: 02 Sep 2009
Posts: 17317
Followers: 2874

Kudos [?]: 18380 [0], given: 2348

GMAT Tests User CAT Tests
Re: Rectangular floor patterns [#permalink] New post 20 Nov 2009, 07:54
Expert's post
AKProdigy87 wrote:
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.


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.

+1.

Answer: E (726).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

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

Kudos [?]: 13 [0], given: 1

Re: Rectangular floor patterns [#permalink] New post 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.
Senior Manager
Senior Manager
Joined: 05 Oct 2008
Posts: 275
Followers: 3

Kudos [?]: 24 [0], given: 22

GMAT Tests User
m 16 - combinations [#permalink] New post 07 Dec 2009, 04:10
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?


* 104
* 213
* 577
* 705
* 726
Manager
Manager
User avatar
Joined: 29 Oct 2009
Posts: 211
Followers: 64

Kudos [?]: 520 [0], given: 18

GMAT Tests User
Re: m 16 - combinations [#permalink] New post 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 = 726

Answer : E
_________________

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

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

Re: m 16 - combinations   [#permalink] 07 Dec 2009, 04:58
    Similar topics Author Replies Last post
Similar
Topics:
New posts A rectangular tiled floor consists of 70 square tiles. The sudhagar 6 10 Nov 2005, 23:50
New posts A rectangular floor measure 2 by 3 meters, there are 5 rkatl 8 12 Aug 2006, 16:48
New posts A rectangular tiled floor consists of 70 square tiles. The ArvGMAT 3 12 Aug 2006, 20:37
New posts A rectangular floor is covered by a rug except for a strip p ggarr 5 16 Aug 2007, 20:42
New posts 4 Experts publish their posts in the topic Rectangular Floors X and Y have equal area. If Floor X is 12 Bunuel 7 23 Jul 2012, 03:22
Display posts from previous: Sort by

Rectangular floor patterns

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.