GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Jan 2019, 20:51

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# A cube is painted with blue and red color such that each color is pain

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 May 2013
Posts: 20
A cube is painted with blue and red color such that each color is pain  [#permalink]

### Show Tags

Updated on: 02 Sep 2014, 03:05
4
00:00

Difficulty:

75% (hard)

Question Stats:

56% (02:10) correct 44% (02:00) wrong based on 126 sessions

### HideShow timer Statistics

A cube is painted with blue and red color such that each color is painted on three faces.The cube is now cut into 27 smaller and identical cubes. How many smaller cubes have only two faces painted in two different colors?

(1) Two opposite faces have red paint on them.
(2) Each face with blue paint is adjacent to every other face with blue paint.

_________________

Press Kudos!! if you like my post !!!

Originally posted by pran21 on 02 Sep 2014, 01:06.
Last edited by Bunuel on 02 Sep 2014, 03:05, edited 1 time in total.
Edited the question.
Manager
Joined: 29 Apr 2014
Posts: 67
Location: India
Concentration: Other, Finance
GMAT 1: 770 Q51 V42
WE: Analyst (Retail Banking)
Re: A cube is painted with blue and red color such that each color is pain  [#permalink]

### Show Tags

02 Sep 2014, 01:57
1
1
pran21 wrote:
A cube is painted with blue and red color such that each color is painted on three faces.The cube is now cut into 27 smaller and identical cubes.How many smaller cubes have only two faces painted in two different colors?

a. two opposite faces have red paint on them.
b. each face with blue paint is adjacent to every other face with blue paint.

a) If two opposite faces have red paint on them, no matter which face we paint red, the other three faces will be blue in color. Now, three adjacent faces have the color red and the other three adjacent faces will have the color blue.

Also, as the cube is being cut into 27 different pieces, this means that we are making 6 cuts (two each across the two opposite faces). Only the center part of each edge will have colours on two faces as each edge is getting cut into 3 pieces. Once we know how this cube is painted and how it's being cut, we can count the number of small cubes with only two faces painted in two different colors. ----> Sufficient

b) Gives the same info as (a). ----> Sufficient

Since, both a & b are sufficient, the answer is D.

Hope that makes it clear.
_________________

Psst...If that helped press the thumb on the left

Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: A cube is painted with blue and red color such that each color is pain  [#permalink]

### Show Tags

02 Sep 2014, 03:18
A cube is painted with blue and red color such that each color is painted on three faces.The cube is now cut into 27 smaller and identical cubes. How many smaller cubes have only two faces painted in two different colors?

Painting a cube in such a way can only be done in two ways:
(i) Three adjacent faces are of the same color (bottom and two adjacent side faces).
(ii) Two opposite faces and a face joining them are of the same color (bottom, top and one of the side faces).

So, basically we need to know which case we have (we'll have all the information possible so would be able to answer the question no matter what the actual answer would be).

(1) Two opposite faces have red paint on them. We have the second case. Sufficient.

(2) Each face with blue paint is adjacent to every other face with blue paint. We have the second case. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: A cube is painted with blue and red color such that each color is pain  [#permalink]

### Show Tags

02 Sep 2014, 03:19
Bunuel wrote:
A cube is painted with blue and red color such that each color is painted on three faces.The cube is now cut into 27 smaller and identical cubes. How many smaller cubes have only two faces painted in two different colors?

Painting a cube in such a way can only be done in two ways:
(i) Three adjacent faces are of the same color (bottom and two adjacent side faces).
(ii) Two opposite faces and a face joining them are of the same color (bottom, top and one of the side faces).

So, basically we need to know which case we have (we'll have all the information possible so would be able to answer the question no matter what the actual answer would be).

(1) Two opposite faces have red paint on them. We have the second case. Sufficient.

(2) Each face with blue paint is adjacent to every other face with blue paint. We have the second case. Sufficient.

Similar questions to practice:
the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html
a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html
if-a-4-cm-cube-is-cut-into-1-cm-cubes-then-what-is-the-107843.html
a-large-cube-consists-of-125-identical-small-cubes-how-110256.html
a-cube-of-side-5cm-is-painted-on-all-its-side-if-it-is-sliced-into-48513.html

3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html
_________________
Senior Manager
Joined: 04 Jun 2018
Posts: 388
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)
Re: A cube is painted with blue and red color such that each color is pain  [#permalink]

### Show Tags

31 Jul 2018, 10:56
Could someone represent the solution graphically? I thing this would go a long way towards making understanding easier.
_________________

A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated!

Senior Manager
Joined: 23 Jun 2012
Posts: 380
Location: Pakistan
GPA: 3.76
Re: A cube is painted with blue and red color such that each color is pain  [#permalink]

### Show Tags

01 Aug 2018, 23:21
Both the statement gives u same info so its either D or E
rule out A, B and C
without going into details, one can see that it gives clear picture of cube and by dividing it into 27 small pieces, one can see that its central part that gives two colors...answer is D
_________________

Push yourself again and again. Don't give an inch until the final buzzer sounds. -Larry Bird
Success isn't something that just happens - success is learned, success is practiced and then it is shared. -Sparky Anderson
-S

Re: A cube is painted with blue and red color such that each color is pain &nbs [#permalink] 01 Aug 2018, 23:21
Display posts from previous: Sort by