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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three [#permalink]

Show Tags

14 Jan 2010, 14:21

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

50% (02:04) correct
50% (01:17) wrong based on 202 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 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

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.

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..

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

Show Tags

20 Dec 2012, 03:59

3

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

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 Green-Blue-Green-Blue OR Blue-Green-Blue-Green (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.

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

Show Tags

28 Dec 2012, 01:48

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.

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

Show Tags

28 Dec 2012, 19:30

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 _________________

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

Show Tags

12 Sep 2013, 03:26

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

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

Show Tags

13 Feb 2014, 09:00

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

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

Show Tags

02 Mar 2015, 18:45

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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

Show Tags

15 May 2016, 10:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

MBA Admission Calculator Officially Launched After 2 years of effort and over 1,000 hours of work, I have finally launched my MBA Admission Calculator . The calculator uses the...

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

The London Business School Admits Weekend officially kicked off on Saturday morning with registrations and breakfast. We received a carry bag, name tags, schedules and an MBA2018 tee at...