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

 It is currently 22 Sep 2018, 23:55

### 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

# M01-11

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49303

### Show Tags

16 Sep 2014, 00:15
1
11
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:08) correct 34% (01:30) wrong based on 192 sessions

### HideShow timer Statistics

If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

A. 4%
B. 166%
C. 266%
D. 300%
E. 400%

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49303

### Show Tags

16 Sep 2014, 00:15
1
2
Official Solution:

If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

A. 4%
B. 166%
C. 266%
D. 300%
E. 400%

A cube has 6 faces.

The surface area of a cube with the length of the side of 4 cm is $$6*4^2=6*16$$ $$cm^2$$.

Now, since the volume of the big cube is $$4^3=64$$ $$cm^3$$ and the volume of the smaller cubes is $$1^3=1$$ $$cm^3$$, then when the big cube is cut into the smaller cubes we'll get $$\frac{64}{1}=64$$ little cubes. Each of those little cubes will have the surface area equal to $$6*1^2=6$$ $$cm^2$$, so total surface are of those 64 little cubes will be $$6*64$$ $$cm^2$$.

$$6*64$$ is 4 times more than $$6*16$$ which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): $$\text{Percent} = \frac{\text{Change}}{\text{Original}}*100$$

So the percent increase will be: $$Percent=\frac{\text{Change}}{\text{Original}}*100=\frac{6*64-6*16}{6*16}*100=300%$$.

_________________
Manager
Joined: 05 Jul 2015
Posts: 104
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3

### Show Tags

19 Feb 2016, 12:42
2
Bunuel, is it just luck that it worked out by ratios?

The way I got it is that since the ratio is 4:1 then 4 is 300% greater than 1.
If we had changed the larger cube for a ratio of 5:1 it would have been 400% greater.
If we had changed the smaller cubes for a ratio of 4:2 the surface area would have been 100% greater.
Intern
Joined: 26 May 2014
Posts: 40
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

### Show Tags

25 Jul 2016, 12:25
how did you ascertain that there would be 64 smaller cubes?
Math Expert
Joined: 02 Sep 2009
Posts: 49303

### Show Tags

25 Jul 2016, 12:33
devbond wrote:
how did you ascertain that there would be 64 smaller cubes?

Since the volume of the big cube is $$4^3=64$$ $$cm^3$$ and the volume of the smaller cubes is $$1^3=1$$ $$cm^3$$, then when the big cube is cut into the smaller cubes we'll get $$\frac{64}{1}=64$$ little cubes.
_________________
Intern
Joined: 28 Nov 2015
Posts: 8
Schools: ISB '18, IIML IPMX"18

### Show Tags

12 Sep 2016, 06:04
Hi,

How did you got below :

Each of those little cubes will have the surface area equal to 6∗1^2= 6 cm2
Math Expert
Joined: 02 Sep 2009
Posts: 49303

### Show Tags

12 Sep 2016, 06:14
karandedhia wrote:
Hi,

How did you got below :

Each of those little cubes will have the surface area equal to 6∗1^2= 6 cm2

A cube has 6 faces, the area of each is 1^2 = 1 cm^2, so the total surface area is 6∗1^2= 6 cm^2.
_________________
Current Student
Joined: 28 Aug 2016
Posts: 90
Concentration: Strategy, General Management

### Show Tags

29 Sep 2016, 04:58
I did everything correctly and fell for (E) which is a trap answer... Gotta always remember to read the question correctly.

The new total surface area is 400% of the original, which means 400%-100% = 300% increase. Dang it.
Intern
Joined: 20 Sep 2016
Posts: 25

### Show Tags

17 Sep 2017, 07:32
What confirms that we must calculate the volume of original cube and divide with the volume of smaller cube to know the number of smaller cubes.
can not we cut the original cube in dimension (length, width and height ) to know the number of cubes resulting from original cube.

am I missing something or have I got the concept all wrong ?
Math Expert
Joined: 02 Sep 2009
Posts: 49303

### Show Tags

17 Sep 2017, 08:41
jyotipes21@gmail.com wrote:
What confirms that we must calculate the volume of original cube and divide with the volume of smaller cube to know the number of smaller cubes.
can not we cut the original cube in dimension (length, width and height ) to know the number of cubes resulting from original cube.

am I missing something or have I got the concept all wrong ?

It's not clear what are you trying to do. Can you please elaborate?
_________________
Re: M01-11 &nbs [#permalink] 17 Sep 2017, 08:41
Display posts from previous: Sort by

# M01-11

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.