Last visit was: 25 Apr 2026, 19:34 It is currently 25 Apr 2026, 19:34
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Geometry|      
User avatar
b2bt
User avatar
Joined: 25 Sep 2012
Last visit: 14 Apr 2024
Posts: 192
Own Kudos:
651
 [36]
Given Kudos: 242
Location: India
Concentration: Strategy, Marketing
Schools: Weatherhead '18 (A$) Northeastern '18 (WL)
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Products:
My Reviews
Schools: Weatherhead '18 (A$) Northeastern '18 (WL)
GMAT 2: 680 Q48 V34
Posts: 192
Kudos: 651
 [36]
A cube of side 7 cm is coloured on pair of opposite faces by 04 Nov 2013, 22:31
1
Kudos
Add Kudos
35
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

63% (02:09) correct 37% (02:17) wrong based on 495 sessions

History

Date
Time
Result
Not Attempted Yet
A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

A) 150
B) 125
C) 60
D) 49
E) 40
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
devanshu92
User avatar
Joined: 24 Jul 2017
Last visit: 04 Feb 2018
Posts: 25
Own Kudos:
43
 [14]
Given Kudos: 38
Location: India
WE:Information Technology (Computer Software)
Posts: 25
Kudos: 43
 [14]
A cube of side 7 cm is coloured on pair of opposite faces by 09 Sep 2017, 07:47
7
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,830
Own Kudos:
811,287
 [11]
Given Kudos: 105,886
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,830
Kudos: 811,287
 [11]
A cube of side 7 cm is coloured on pair of opposite faces by 05 Nov 2013, 00:45
8
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
b2bt
A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

A) 150
B) 125
C) 60
D) 49
E) 40
Show more

Look at the figure below:
Attachment:
Untitled.png
Untitled.png [ 67.67 KiB | Viewed 18770 times ]
Only the edge cubes marked with dots will have exactly two colored faces. 5 cubes per edge * 12 edges = 60 cubes.

Answer: C.

Hope it's clear.

P.S. A cube has 12 edges. There are 4 edges on the top square, 4 on the bottom square and 4 more that connect the 2 squares.
General Discussion
avatar
hanvd1990
avatar
Joined: 09 Oct 2017
Last visit: 23 Oct 2022
Posts: 10
Own Kudos:
5
 [1]
Given Kudos: 72
Location: Viet Nam
GMAT 1: 530 Q35 V28
GPA: 3.1
GMAT 1: 530 Q35 V28
Posts: 10
Kudos: 5
 [1]
A cube of side 7 cm is coloured on pair of opposite faces by 30 Sep 2019, 19:51
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
devanshu92
Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks
Show more

Hi devanshu92 and bunuel, can you please elaborate more on the above formula? What does n stand for? Is that n= length of side?
User avatar
sachinsavailable
User avatar
Joined: 13 May 2018
Last visit: 03 Mar 2026
Posts: 38
Own Kudos:
53
Given Kudos: 470
Posts: 38
Kudos: 53
A cube of side 7 cm is coloured on pair of opposite faces by 22 Nov 2019, 16:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hanvd1990
devanshu92
Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks

Hi devanshu92 and bunuel, can you please elaborate more on the above formula? What does n stand for? Is that n= length of side?
Show more
hanvd1990 nstands for the number of cubes formed . In this case the side is 7 and the cube is cut into unit cubes hence n=7
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,005
 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,005
 [1]
A cube of side 7 cm is coloured on pair of opposite faces by 05 Sep 2021, 23:48
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total edges in cube = 12

The corner most cubes on an edge have three faces painted. So out of all cubes on edges, take the 2 cubes out.

Since its side is 7cm and it is cut into a unit cube that means there are 7 cubes on 1 edge and we will take 2 cubes out: 7 - 2 = 5.

Total cubes with 2 face painted = 12 * 5 = 60

Answer C
User avatar
Ananabanana
User avatar
Joined: 06 Apr 2020
Last visit: 21 Mar 2025
Posts: 18
Own Kudos:
18
Given Kudos: 119
GPA: 3.61
WE:Corporate Finance (Manufacturing)
Posts: 18
Kudos: 18
A cube of side 7 cm is coloured on pair of opposite faces by 16 Feb 2022, 12:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,
from the given data that the original cube has side = 7cm, how can we know that each unit cube is 1x1x1 cm? assuming 7cm = 7units? :?

Thanks
User avatar
SDW2
User avatar
Joined: 17 Jun 2020
Last visit: 05 Mar 2024
Posts: 100
Own Kudos:
11
Given Kudos: 314
Location: India
Schools: Simon '25
Schools: Simon '25
Posts: 100
Kudos: 11
A cube of side 7 cm is coloured on pair of opposite faces by 14 Oct 2022, 09:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
b2bt
A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

A) 150
B) 125
C) 60
D) 49
E) 40

Look at the figure below:
Attachment:
Untitled.png
Only the edge cubes marked with dots will have exactly two colored faces. 5 cubes per edge * 12 edges = 60 cubes.

Answer: C.

Hope it's clear.

P.S. A cube has 12 edges. There are 4 edges on the top square, 4 on the bottom square and 4 more that connect the 2 squares.
Show more

Hi Bunuel
What about the cubes in the middle? Why didnt we consider them?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,986
Own Kudos:
1,118
Posts: 38,986
Kudos: 1,118
A cube of side 7 cm is coloured on pair of opposite faces by 21 Oct 2023, 04:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109830 posts
Krunaal
Tuck School Moderator
852 posts