GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Feb 2020, 13:48

### 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

# The outside surface of a white cube with a volume 64 is painted purple

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61484
The outside surface of a white cube with a volume 64 is painted purple  [#permalink]

### Show Tags

04 Dec 2019, 00:16
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:36) correct 39% (02:32) wrong based on 45 sessions

### HideShow timer Statistics

The outside surface of a white cube with a volume 64 is painted purple. The cube is then cut evenly into smaller 2x2x2 cubes. such that the sides that originally faced outside will remain white. What is the ratio of the total purple surface area and the total white surface area of the smaller cubes ?

A. 3:1
B. 2:1
C. 1:1
D. 1:2
E. 1:3

Are You Up For the Challenge: 700 Level Questions

_________________
Intern
Joined: 26 Jun 2017
Posts: 23
Re: The outside surface of a white cube with a volume 64 is painted purple  [#permalink]

### Show Tags

04 Dec 2019, 08:27
1
Volume of Original cube : 64 units
Volume of smaller cube : 8 units

No. of Smaller cubes after cut = 64/8 = 8 cubes

all of the 8 cubes will be corner cubes and each of them will have 3 sides which were originally facing outside(White color). So the remaining 3 sides will be of purple color.

In other words, 3 faces of a cube has white color and rest of the 3 has purple color therefore, 1:1 is the answer
Manager
Joined: 03 Nov 2019
Posts: 54
Re: The outside surface of a white cube with a volume 64 is painted purple  [#permalink]

### Show Tags

04 Dec 2019, 00:50
Now total number of cubes of sides 2x2x2 that can be formed from the cube of volume 64= 64/(2*2*2) =8
Total number of sides of smaller cubes combined= 6*8=48
Sides painted white:
Total number of sides of smaller cube facing outside = 4*6 (i.e. 4 faces of smaller cubes per 1 face of larger cube* Total number of sides of larger cube) = 24
Sides painted Purple:
Total number of sides of smaller cube facing inside = 48- 24=24

total purple surface area/ total white surface area of the smaller cubes = 24*(2*2)/24*(2*2) = 1:1

Re: The outside surface of a white cube with a volume 64 is painted purple   [#permalink] 04 Dec 2019, 00:50
Display posts from previous: Sort by