It is currently 21 Oct 2017, 00:21

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many different ways can 3 cubes be painted if each cube is painted

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

BSchool Forum Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 841 [0], given: 595

GMAT ToolKit User Premium Member CAT Tests
How many different ways can 3 cubes be painted if each cube is painted [#permalink]

Show Tags

New post 18 Apr 2017, 04:54
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (01:15) correct 61% (01:05) wrong based on 62 sessions

HideShow timer Statistics

How many different ways can 3 cubes be painted if each cube is painted with one colour and only three colours red,green and blue are available?(Order is not considered, for example green,green,blue is considered the same as green blue green)

A)27
B)10
C)9
D)3
E)2




Source => NOVA

What is the best way to tackle this one?Making individual cases ?
[Reveal] Spoiler: OA

_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 841 [0], given: 595

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [1], given: 12190

Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

Show Tags

New post 18 Apr 2017, 05:04
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
stonecold wrote:
How many different ways can 3 cubes be painted if each cube is painted with one colour and only three colours red,green and blue are available?(Order is not considered, for example green,green,blue is considered the same as green blue green)

A)27
B)10
C)9
D)3
E)2




Source => NOVA

What is the best way to tackle this one?Making individual cases ?


XXX - 3 cases (red, red, red; green, green, green; blue, blue, blue)

XXY - \(C^1_3*2 = 6\), where \(C^1_3\) is the number of ways to choose which color will be used for two identical colored cubes (XX) and *2 because there will be 2 colors left to choose from for Y.

XYZ - 1 case (red, green, blue)

3 + 6 + 1 = 10.

Answer: B.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129061 [1], given: 12190

Expert Post
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4985

Kudos [?]: 5496 [0], given: 112

Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

Show Tags

New post 18 Apr 2017, 05:14
stonecold wrote:
How many different ways can 3 cubes be painted if each cube is painted with one colour and only three colours red,green and blue are available?(Order is not considered, for example green,green,blue is considered the same as green blue green)

A)27
B)10
C)9
D)3
E)2




Source => NOVA

What is the best way to tackle this one?Making individual cases ?



Hi..

Yes picking up indl cases would be better easier and less error prone.
1) all of same colour-3
2) two of same colour..
Two colours can be choosen in 3C2=3!/2!=3 ways and any of these two can be on TWO cubes. So 3*2=6
3) all of one colour-1..

Total -- 3+6+1=10
B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5496 [0], given: 112

Manager
Manager
avatar
G
Joined: 07 Aug 2016
Posts: 98

Kudos [?]: 131 [0], given: 72

Location: India
Concentration: Marketing, Operations
GMAT 1: 690 Q48 V35
GPA: 4
WE: Engineering (Telecommunications)
Reviews Badge CAT Tests
Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

Show Tags

New post 25 Aug 2017, 05:21
Hi Bunuel

Can you please me why this approach cannot be used.

1st cube can be painted in 3 ways. Same with 2nd and 3rd.

So total 3*3*3 = 27 ways.

Kudos [?]: 131 [0], given: 72

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [0], given: 12190

Re: How many different ways can 3 cubes be painted if each cube is painted [#permalink]

Show Tags

New post 25 Aug 2017, 05:55
gauravraos wrote:
Hi Bunuel

Can you please me why this approach cannot be used.

1st cube can be painted in 3 ways. Same with 2nd and 3rd.

So total 3*3*3 = 27 ways.


We are told that "Order is not considered, for example green,green,blue is considered the same as green blue green)". Among other duplications, your approach will give for example {red, green, blue} as well as {blue, red, green} or {red, green, green} as well as {green, green, red}.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129061 [0], given: 12190

Re: How many different ways can 3 cubes be painted if each cube is painted   [#permalink] 25 Aug 2017, 05:55
Display posts from previous: Sort by

How many different ways can 3 cubes be painted if each cube is painted

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.