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

 It is currently 22 Sep 2019, 15:57

### 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

# If a 4 cm cube is cut into 1 cm cubes, then what is the

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 Aug 2010
Posts: 154
If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

15 Jan 2011, 15:07
3
31
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:56) correct 36% (02:13) wrong based on 472 sessions

### HideShow timer Statistics

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

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

Please can someone explain this problem better.
Math Expert
Joined: 02 Sep 2009
Posts: 58098
Re: surface area of cube  [#permalink]

### Show Tags

15 Jan 2011, 15:34
4
5
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 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): $$Percent=\frac{Change}{Original}*100$$

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

_________________
##### General Discussion
Board of Directors
Joined: 01 Sep 2010
Posts: 3402
Re: surface area of cube  [#permalink]

### Show Tags

15 Jan 2011, 17:19
generally you have at least two ways to solve a question......this mean that we should have different points of view to tackle a problem, right ??'

rethoric question I guess ........
_________________
Intern
Joined: 15 Jan 2011
Posts: 38
Re: surface area of cube  [#permalink]

### Show Tags

15 Jan 2011, 22:04
Hi,

when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64

Thanks

Bunuel wrote:
Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 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): $$Percent=\frac{Change}{Original}*100$$

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

_________________
The only place where success comes before work is in the dictionary.

If my post made you think, KUDO it. Its easy :D
Math Expert
Joined: 02 Sep 2009
Posts: 58098
Re: surface area of cube  [#permalink]

### Show Tags

16 Jan 2011, 02:55
rohu27 wrote:
Hi,

when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64

Thanks

Bunuel wrote:
Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 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): $$Percent=\frac{Change}{Original}*100$$

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

The big cube which dimensions 4*4*4 can "produce" 4*4*4 small cubes with dimensions of 1*1*1 (base layer can give 4*4 small cubes and as there are 4 layers than total of 4*4*4 small cubes).
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1768
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

04 Mar 2014, 04:09
1
Big cube surface area = 4*4*6 = 96

Small cubes surface area (Total) = 6 *64

% = 6*64*96/100 = 400

% Increase = 400-100 = 300% = Answer = D
_________________
Kindly press "+1 Kudos" to appreciate
Math Expert
Joined: 02 Sep 2009
Posts: 58098
Re: surface area of cube  [#permalink]

### Show Tags

04 Mar 2014, 04:15
Bunuel wrote:
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 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): $$Percent=\frac{Change}{Original}*100$$

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

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
a-large-cube-consists-of-125-identical-small-cubes-how-110256.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
_________________
Intern
Joined: 01 Mar 2014
Posts: 4
GMAT Date: 05-23-2014
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

13 Aug 2014, 04:08
1
I have problem with its verbal... 4cm cube! Does it mean that each side is 4cm or the area is 4cm...? is it popular to use this language in Geometry?
Math Expert
Joined: 02 Sep 2009
Posts: 58098
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

13 Aug 2014, 06:40
amirsalehi wrote:
I have problem with its verbal... 4cm cube! Does it mean that each side is 4cm or the area is 4cm...? is it popular to use this language in Geometry?

The area cannot be in units, it's in square units, so 4cm can only mean length of something.
_________________
Manager
Joined: 21 Jun 2011
Posts: 56
Location: United States
Concentration: Accounting, Finance
WE: Accounting (Accounting)
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

23 Nov 2014, 12:58
1
Bunuel wrote:
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 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): $$Percent=\frac{Change}{Original}*100$$

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

Hey Bunuel,

My question might sound stupid but why are you going back and calculating the volume of the bigger cube. Why can't we just take the the side to be 1 and hence the surface area=6a^2=6. What is wrong with my thinking
Math Expert
Joined: 02 Sep 2009
Posts: 58098
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

24 Nov 2014, 06:37
davidfrank wrote:
Bunuel wrote:
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 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): $$Percent=\frac{Change}{Original}*100$$

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

Hey Bunuel,

My question might sound stupid but why are you going back and calculating the volume of the bigger cube. Why can't we just take the the side to be 1 and hence the surface area=6a^2=6. What is wrong with my thinking

When a cube with a side of 4 units is cut into cubes with a side of 1 unit you get 64 little cubes. Each of them will have the surface area of 6 square units, thus the surface area of all 64 little cubes will be 6*64 square units.
_________________
Manager
Joined: 08 Sep 2016
Posts: 106
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

04 Apr 2018, 04:20
Hi Bunuel

Is it a coincidence (or luck) that this problem can be solved by ignoring the fact that we are asked to solve for the percent difference in surface area? We have something that is 4 times something else. What's the percent change?

((4-1)/1) *100 = 300
Math Expert
Joined: 02 Sep 2009
Posts: 58098
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

04 Apr 2018, 10:21
hdavies wrote:
Hi Bunuel

Is it a coincidence (or luck) that this problem can be solved by ignoring the fact that we are asked to solve for the percent difference in surface area? We have something that is 4 times something else. What's the percent change?

((4-1)/1) *100 = 300

What would you get with your approach if the big cube were cut into 2cm cubes, instead of 1cm cubes?
_________________
Intern
Joined: 31 Jul 2016
Posts: 10
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

04 Apr 2018, 10:47
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

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

Please can someone explain this problem better.

6×4×4 = 96 cubic cm

Totally #64 1cm cubes which equals 64×6 = 384 cubic cm

Percent increase = 382-96/96 * 100
= 288*100/96
= 300

Sent from my SM-G925I using GMAT Club Forum mobile app
Manager
Joined: 08 Sep 2016
Posts: 106
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

04 Apr 2018, 15:42
Bunuel wrote:
hdavies wrote:
Hi Bunuel

Is it a coincidence (or luck) that this problem can be solved by ignoring the fact that we are asked to solve for the percent difference in surface area? We have something that is 4 times something else. What's the percent change?

((4-1)/1) *100 = 300

What would you get with your approach if the big cube were cut into 2cm cubes, instead of 1cm cubes?

I see. The approach I mentioned above would show 100% change, but the real answer would be undefined I think.
Director
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

### Show Tags

24 Apr 2019, 10:17
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

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

Please can someone explain this problem better.

Volume of a 4 cm cube = 4^3 = 64
Volume of a 1 cm cube = 1^3 = 1

Total number of 1 cm cubes which can be taken out of 4 cm cube after cutting = 64/1 = 64

Surface area of 4 cm cube = 6*4^2= 6*16

Surface are of 1 cm cube = 6*1^2 = 6
Surface area of 64 1 cm cube = 6*64

Total increase in surface area = 6*64 - 6*16 = 6*48
%ge increase in surface area = 6*48/6*16 x 100 = 300%

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the   [#permalink] 24 Apr 2019, 10:17
Display posts from previous: Sort by