December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 17 Oct 2012
Posts: 65
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)

You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
09 Sep 2013, 05:45
Question Stats:
31% (01:55) correct 69% (01:56) wrong based on 228 sessions
HideShow timer Statistics
You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.) (A) 24 (B) 30 (C) 48 (D) 60 (E) 120
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51291

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
10 Sep 2013, 05:16




Manager
Joined: 17 Oct 2012
Posts: 65
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
10 Sep 2013, 06:56
Bunuel wrote: chetan86 wrote: You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24 (B) 30 (C) 48 (D) 60 (E) 120 Paint one of the faces red and make it the top face. 5 options for the bottom face. Now, four side faces can be painted in (41)! = 3! = 6 ways (circular arrangements of 4 colors). Total = 5*6 = 30. Answer: B. Similar question to practice: acubemarked12345and6onitssixfacesthree89198.htmlThanks Bunues, great explanation!!



Intern
Joined: 22 Nov 2013
Posts: 3
Concentration: Nonprofit, Entrepreneurship

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
27 Dec 2013, 19:12
Bunuel wrote: chetan86 wrote: You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24 (B) 30 (C) 48 (D) 60 (E) 120 Paint one of the faces red and make it the top face. 5 options for the bottom face. Now, four side faces can be painted in (41)! = 3! = 6 ways (circular arrangements of 4 colors). Total = 5*6 = 30. Answer: B. Similar question to practice: Can you give more detail on how you determined what method to use to solve this problem? I have never heard of the "circular arrangement" technique you used.



Math Expert
Joined: 02 Sep 2009
Posts: 51291

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
28 Dec 2013, 02:56



Intern
Joined: 22 Nov 2013
Posts: 3
Concentration: Nonprofit, Entrepreneurship

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
28 Dec 2013, 20:30
This helps a great deal! Thank you Bunuel!



SVP
Joined: 06 Sep 2013
Posts: 1720
Concentration: Finance

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
27 May 2014, 05:19
Bunuel wrote: chetan86 wrote: You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24 (B) 30 (C) 48 (D) 60 (E) 120 Paint one of the faces red and make it the top face. 5 options for the bottom face. Now, four side faces can be painted in (41)! = 3! = 6 ways (circular arrangements of 4 colors). Total = 5*6 = 30. Answer: B. Similar question to practice: acubemarked12345and6onitssixfacesthree89198.htmlI really didn't get how you used circular arrangements here. We have six different colors and 6 different sides. How many ways can we paint the cube with each side a different color? Shouldn't it be 6! ? Please clarify Great problem btw Cheers J



Intern
Joined: 08 Aug 2011
Posts: 21

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
28 May 2014, 02:41
jlgdr wrote: Bunuel wrote: chetan86 wrote: You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24 (B) 30 (C) 48 (D) 60 (E) 120 Paint one of the faces red and make it the top face. 5 options for the bottom face. Now, four side faces can be painted in (41)! = 3! = 6 ways (circular arrangements of 4 colors). Total = 5*6 = 30. Answer: B. Similar question to practice: http://gmatclub.com/forum/acubemarked ... 89198.htmlI really didn't get how you used circular arrangements here. We have six different colors and 6 different sides. How many ways can we paint the cube with each side a different color? Shouldn't it be 6! ? Please clarify Great problem btw Cheers J Painting a cube with six different colors is more complicated than arranging six distinct things in a row. If you have six distinct colors, say ROYGBP, you could place them in the slots below in 6! ways. Why? Any of the 6 colors could go in the first slot, any of the five remaining could go in the second, and so on. So the total is 6*5*4*3*2*1=6! _ _ _ _ _ _ Now the cube is a combination of slots and a circular arrangement. Here is my sophisticated diagram for that: _ _ _ _ _ _ The four slots between the top and bottom 'faces' actually wrap around the whole cube. So, let's say for the four 'slots' you choose ROYG. ROYG =GROY = YGRO = OYGR = ROYG All of these arrangements are the same because essentially each one is just a rotation of the cube by 90 degrees, not a different paint job. So we treat the four 'slots' in the middle the same way we would a circular table. Hence the above solutions: you can choose any color for the top face, you can choose one of the five remaining colors for the bottom face (5 ways), and since the four middle faces are 'in a circle' they can be arranged (41)!=3! ways. So the total is 5*3! The tricky part is that we don't count the ways in which we can choose the color of the first face, since every color is going to be chosen anyway. Essentially, you are finding the ways you can paint the other sides relative to one of painted sides. Otherwise you are including in your total the number of different ways you can look at the cube (which don't constitute a new paint job). Posted from my mobile device



Manager
Joined: 17 Jun 2014
Posts: 70
Location: India
GMAT 1: 720 Q50 V38 GMAT 2: 740 Q50 V40
GPA: 3.8
WE: Management Consulting (Insurance)

You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
15 Oct 2014, 21:32
Bunuel wrote: chetan86 wrote: You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24 (B) 30 (C) 48 (D) 60 (E) 120 Paint one of the faces red and make it the top face. 5 options for the bottom face. Now, four side faces can be painted in (41)! = 3! = 6 ways (circular arrangements of 4 colors). Total = 5*6 = 30. Answer: B. @Bunuel , why haven't the ways to paint the first (top)face have been counted, i.e 6C1 ways to choose from amongst the 6 diffferent paints?? And what does the wording provided in the question in the parentheses entails?
_________________
The Mind is everything . What you think you become.  Lord Buddha
Consider giving KUDOS if you appreciate my post !!



Manager
Joined: 04 Jan 2014
Posts: 84

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
15 Jan 2015, 21:57
Bunuel wrote: chetan86 wrote: You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24 (B) 30 (C) 48 (D) 60 (E) 120 Paint one of the faces red and make it the top face. 5 options for the bottom face. Now, four side faces can be painted in (41)! = 3! = 6 ways (circular arrangements of 4 colors). Total = 5*6 = 30. Answer: B. Similar question to practice: acubemarked12345and6onitssixfacesthree89198.htmlHi Bunuel, Need your help on this. I could understand the circular and bottom face things. that's 5*(41)!. But I am not able to understand that top part. If initially no sides are painted, then we could chose 1 among 6 paints right? so shouldn't we multiply 5*(41)! with 6, as we have six choices initially?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8690
Location: Pune, India

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
15 Jan 2015, 22:29
Vinitkhicha1111 wrote: Bunuel wrote: chetan86 wrote: You have a sixsided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24 (B) 30 (C) 48 (D) 60 (E) 120 Paint one of the faces red and make it the top face. 5 options for the bottom face. Now, four side faces can be painted in (41)! = 3! = 6 ways (circular arrangements of 4 colors). Total = 5*6 = 30. Answer: B. @Bunuel , why haven't the ways to paint the first (top)face have been counted, i.e 6C1 ways to choose from amongst the 6 diffferent paints?? And what does the wording provided in the question in the parentheses entails? Why don't we consider the 6 ways in which we can color the top face? Which face is the top face? All faces are identical. You pick any color and put it on any one side. This can be done in one way only. This is like placing the first person at a round table. All places are identical so place the first one can be put anywhere. Similarly, the first paint can be put on any face of the cube. Now you have a top face (which we have just painted) and a bottom face and 4 identical sides.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 03 Apr 2013
Posts: 275
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
23 Jun 2017, 07:00
@Bunuel What about this one? Is this a GMAT question? or this too is out of scope? I found a lot of difficulty solving this one..and got it wrong the first time. Sent from my Pixel XL using GMAT Club Forum mobile app
_________________
Spread some love..Like = +1 Kudos



Math Expert
Joined: 02 Sep 2009
Posts: 51291

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
23 Jun 2017, 07:22



Senior Manager
Joined: 03 Apr 2013
Posts: 275
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
23 Jun 2017, 10:19
Bunuel wrote: ShashankDave wrote: BunuelWhat about this one? Is this a GMAT question? or this too is out of scope? I found a lot of difficulty solving this one..and got it wrong the first time. Sent from my Pixel XL using GMAT Club Forum mobile app ___________________ No, this question is fine. Okay. Please suggest somewhere to read about these types of problems..and can you also explain any other method to approach this question? Combinatorics is kind of my strength, I don't want to miss questions such as these on the GMAT. Please help me.
_________________
Spread some love..Like = +1 Kudos



Math Expert
Joined: 02 Sep 2009
Posts: 51291

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
23 Jun 2017, 10:35
ShashankDave wrote: Bunuel wrote: ShashankDave wrote: BunuelWhat about this one? Is this a GMAT question? or this too is out of scope? I found a lot of difficulty solving this one..and got it wrong the first time. Sent from my Pixel XL using GMAT Club Forum mobile app ___________________ No, this question is fine. Okay. Please suggest somewhere to read about these types of problems..and can you also explain any other method to approach this question? Combinatorics is kind of my strength, I don't want to miss questions such as these on the GMAT. Please help me. This question does not represent any particular/special type of combinatorics questions  we use circular permutation there and that's it. Links to circular permutation questions are given above. Don't know what else to suggest. Hopefully more practice should help.
_________________
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8690
Location: Pune, India

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
12 Jul 2017, 03:51
VeritasPrepKarishma wrote: Why don't we consider the 6 ways in which we can color the top face?
Which face is the top face? All faces are identical. You pick any color and put it on any one side. This can be done in one way only. This is like placing the first person at a round table. All places are identical so place the first one can be put anywhere. Similarly, the first paint can be put on any face of the cube. Now you have a top face (which we have just painted) and a bottom face and 4 identical sides. Responding to a pm: Quote: Unfortunately, the way I did this one, I am getting only 15 ways of painting the cube. Wanted your views on this:
As you rightly mentioned, all six faces are identical. So we begin by painting a pair of opposite faces: this pair forms the TOP and BOTTOM of the cube. We can choose the colors by 6C2 (for the TOP and BOTTOM faces). Rest of the 4 sides are identical by all means and the order in which these are painted does not matter reorienting a cube to look like another cube, then the two cubes are not distinct
So total number of ways remain 6C2 only. PS: The TOP and BOTTOM faces are also exchangeable since the cube can be reoriented (turned upside down). Hence I did not add 2! to my answer.
Note that 6C2 is the number of ways in which you select 2 faces out of 6 DISTINCT faces. The case here is that you have 6 IDENTICAL faces. You pick any one for a colour of your choice in 1 way and call it TOP. Now you automatically have a fixed BOTTOM face. So there is no choosing. You choose a colour for it in 5 ways. Next, you have 4 IDENTICAL sides. You pick any 1 in 1 way for a colour of your choice. The rest of the 3 faces are DISTINCT now so you can distribute the 3 colours to them in 3! ways. So total ways = 5*3! = 30
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 20 May 2017
Posts: 20

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
22 Aug 2018, 09:52
While painting the top face..why don't we count the number of ways of choosing a colour.
Posted from my mobile device



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8690
Location: Pune, India

Re: You have a sixsided cube and six cans of paint, each a diff
[#permalink]
Show Tags
23 Aug 2018, 09:18
MithilaGauri wrote: While painting the top face..why don't we count the number of ways of choosing a colour.
Posted from my mobile device I have addressed it here: https://gmatclub.com/forum/youhaveas ... l#p1469980
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: You have a sixsided cube and six cans of paint, each a diff &nbs
[#permalink]
23 Aug 2018, 09:18






