February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 Jul 2009
Posts: 94

A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
Updated on: 20 Dec 2012, 02:53
Question Stats:
55% (01:36) correct 45% (01:48) wrong based on 316 sessions
HideShow timer Statistics
A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted? (A) 3 (B) 6 (C) 8 (D) 12 (E) 27
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by apoorvasrivastva on 14 Jan 2010, 13:21.
Last edited by Bunuel on 20 Dec 2012, 02:53, edited 1 time in total.
Renamed the topic.




Math Expert
Joined: 02 Sep 2009
Posts: 53063

Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
20 Dec 2012, 02:59
apoorvasrivastva wrote: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted?
(A) 3 (B) 6 (C) 8 (D) 12 (E) 27 If the base of the cube is red, then in order the adjacent faces to be painted with the different colors, the top must also be red. 4 side faces can be painted in GreenBlueGreenBlue OR BlueGreenBlueGreen (2 options). But we can have the base painted in either of the three colors, thus the total number of ways to paint the cube is 3*2=6. 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? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 25 Jun 2009
Posts: 276

Re: Permutations Again :)
[#permalink]
Show Tags
14 Jan 2010, 13:37
apoorvasrivastva wrote: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted? (A) 3 (B) 6 (C) 8 (D) 12 (E) 27 OA is Am I missing some thing here? Any one side of the cube will be having 4 sides which can be termed as adjacent.. Isn't it ? Say for e.g side A it will be having 4 sides adjacent to it, one on left, one on right, one above and one below. Please correct me if I am assuming this wrong..! thanks



Intern
Joined: 31 Dec 2009
Posts: 13

Re: Permutations Again :)
[#permalink]
Show Tags
14 Jan 2010, 13:59
nitishmahajan, I agree with your assessment. There are 4 adjacent sides for every face of the cube.
Let's say side 1 is painted red, then the 4 adjacent sides can be either green or blue alternating. This can be done in 2 ways. GBGB BGBG Sixth side should be the same color as side 1.
For each color chosen for side 1(and side6) there are 2 ways of painting side 2,3,4 and 5. No. of colors that can be chosen for side 1(and side6) is 3. So 3*2 = 6..
Good question!!



Director
Joined: 29 Nov 2012
Posts: 749

Re: Permutations Again :)
[#permalink]
Show Tags
19 Dec 2012, 23:48
How do you solve this one?



Senior Manager
Joined: 13 Aug 2012
Posts: 420
Concentration: Marketing, Finance
GPA: 3.23

Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
28 Dec 2012, 00:48
So, do they asked this on test day? This drove me nuts. Imagine a flattened cube... The three colored region will establish the other colors of the remaining faces of the cube. For example: We assumed the sequence of color in the given image as RED on face#1 and BLUE on face#2 and GREEN on face#3. Since face#1 is RED then we know #4 and #5 cannot be RED. Since face #2 is BLUE, we know that #5 and #6 cannot be BLUE. Since face#3 is GREEN, we know #4 and #6 (the bottom) cannot be GREEN. So, all we need is to count the possible number of arrangements of 3 colors. 3! = 6
Attachments
CUBE.jpg [ 14 KiB  Viewed 16071 times ]
_________________
Impossible is nothing to God.



Director
Joined: 29 Nov 2012
Posts: 749

Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
28 Dec 2012, 18:30
mbaiseasy wrote: So, do they asked this on test day? This drove me nuts.
Imagine a flattened cube... The three colored region will establish the other colors of the remaining faces of the cube.
For example: We assumed the sequence of color in the given image as RED on face#1 and BLUE on face#2 and GREEN on face#3. Since face#1 is RED then we know #4 and #5 cannot be RED. Since face #2 is BLUE, we know that #5 and #6 cannot be BLUE. Since face#3 is GREEN, we know #4 and #6 (the bottom) cannot be GREEN.
So, all we need is to count the possible number of arrangements of 3 colors.
3! = 6 Yes these are the questions that GMAT will ask I think its from the quant review or from gmat prep, they want you to apply the knowledge



Intern
Joined: 18 Jun 2013
Posts: 4
Location: United States
Concentration: Technology, Strategy

Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
12 Sep 2013, 02:26
How about this approach? There are 3 colors and 6 sides. Same color can't be next to each other so put them on opposite sides. There are 3 opposite sides. So 3 colors 3 sides no. of ways 3*2*1 = 6
Any flaw in this thinking?
Posted from my mobile device



SVP
Joined: 06 Sep 2013
Posts: 1694
Concentration: Finance

Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
13 Feb 2014, 08:00
Actually this one works out like this. Cube has 6 faces and we are told adjacent are different therefore base different from side different from front. Three sides to choose the colors to paint them with. Well since we have three colors then 3! =6 (B) is the right answer
Hope it clarifies Cheers J



Director
Joined: 23 Jan 2013
Posts: 554

Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
02 Mar 2015, 22:35
for every R,G,B combination we have one possibility,
Total possibilities are = 3!=6
B



Manager
Joined: 12 Mar 2018
Posts: 126

Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
Show Tags
11 Oct 2018, 13:56
Bunuel wrote: apoorvasrivastva wrote: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted?
(A) 3 (B) 6 (C) 8 (D) 12 (E) 27 If the base of the cube is red, then in order the adjacent faces to be painted with the different colors, the top must also be red. 4 side faces can be painted in GreenBlueGreenBlue OR BlueGreenBlueGreen (2 options). But we can have the base painted in either of the three colors, thus the total number of ways to paint the cube is 3*2=6. Answer: B. IMO "GreenBlueGreenBlue OR BlueGreenBlueGreen" these two options mean indeed only 1 as you cannot distinguish these two dies when put next to each other.




Re: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three
[#permalink]
11 Oct 2018, 13:56






