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# M01 #11

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M01 #11 [#permalink]  25 Sep 2008, 13:24
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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%

[Reveal] Spoiler: OA
D

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SOLUTION IS HERE: m01-70731-20.html#p1202018

Last edited by Bunuel on 12 Dec 2013, 01:33, edited 2 times in total.
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Hi Siddarth,

You have a 4 cm cube, so the surface area is 4*4(area of one side)*6 sides..= 96, which you agree with.
Then figure out how many 1 cm cubes can fit into 4 cm cube. 4 cm cube's Volume is 4*4*4 = 64.
A 1 cm cube's Volume is 1*1*1 = 1 so 64/1 = 64 little cubes.

Now for the surface area of each little cube: 1*1(area of one side of one cube) * 6 sides= 6 surface area of one cube.
So, 64 cubes * 6 surface area/cube = 384 Total surface area.

So, 384 new/96 old is 4 times or 400% so 300% difference or 288 (difference in area)/96 (original) = 3 or 300% difference.
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Re: Cube's Surface Area [#permalink]  29 Oct 2008, 09:32
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(d) 300%

Before cutting:Side:4cm
Surface Area= 6a^2. = 6*16=96 cm^2
Volume= a^3=64cm^3

After cutting:
side: 1cm
Volume= 1cm^3.

Since the total volume remains the same before and after.
# of 1cm cubes = 64/1 = 64

Therefore, SA of 1cm cubes after cutting = 64* (6 a^2) = 64*6=384

% increase= (before-after)/before
= (288/96)*100 = 300%.
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Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]  25 Sep 2008, 13:44
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4 cm cube has 6 facets of 16 sq. cm each (96 sq. cm in all). After cutting the cube into 1 cm cubes we'll end up with 64 1 cm cubes. Each will have the surface area of 6 sq. cm. $$\frac{6*64}{6*16} = \frac{4}{1} = 400%$$. Therefore the increase in surface area must have been 300%. Did that without looking into the OE . Let's check now...
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Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]  09 Oct 2008, 03:03
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Original Surface Area= 6 x 4 x 4 = 96
new surface area per cube 6 x 1 x 1 = 6
Number of new cubes 4/1 = 4

so total new area = 6 * 4 = 24

96/24 = 4 so 400% (e) is the correct one

Is it ? It should be lol

Thanks
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Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]  09 Oct 2008, 03:20
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We have to find the percentage increase of the surface area and not just the ratio. It has to be 300% (D).

We had 1 cube with a side of 4 cm and after cutting we have 64 cubes with a side of 1 cm.

kam wrote:
Original Surface Area= 6 x 4 x 4 = 96
new surface area per cube 6 x 1 x 1 = 6
Number of new cubes 4/1 = 4

so total new area = 6 * 4 = 24

96/24 = 4 so 400% (e) is the correct one

Is it ? It should be lol

Thanks

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Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]  09 Oct 2008, 03:50
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O ya.. its % precent incrase problem

man these small stupid mistakes are bugging me
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Re: PS: Cubes GMAT Test m01 [#permalink]  30 Mar 2009, 23:13
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Agreed.
SA of bigger cube = 6l^2

SA of smaller cubes = 64*(6*(l/4)^2) = 24l^2

%increase = 24-6/6 *100 % = 300%
priyankur_saha@ml.com wrote:
IMO D - 300%

total 4*4*4 = 64 squares with side 1cm
total surface area = 64 * 6 cm square
surface area for 4cm cube is = 16 * 6 cm square

so surface area increase = (64-16)/16 * 100 = 300%
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A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

4%
166%
266%
300%
400%
The easiest way to solve this problem is to calculate the original surface area and then the final. The original area is 4*4*6. The new area is 1*1*6*4*4*4. So, the difference is 1:4. Therefore, the increase is 300%. You can also solve it logically, but that's more risky.

I couldnt quite understand the explanation here...

The original area is 4*4*6 i agree, but the new area should be 1*1*6*4, why has 4 been multiplied 3 times. Could someone please explain. The question says that the original cube has been cut into 1cm cubes so there are 4 cubes in all now, and every cube will have 1cm side so the SA of every cube will be 1*1*6 and since we have four such cubes the Area of all these will be 6*4.

I am not sure what i am missing here.
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Re: Cube's Surface Area [#permalink]  29 Oct 2008, 09:37
easiest way is to get the volume, of the big cube, which is 64 cm cube..

smalle cube each will 1 cube volume there fore there are 64 such small cubes

surface area =64 and big one has 16..difference is 48/16*100 or 300%
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Re: PS: Cubes GMAT Test m01 [#permalink]  30 Mar 2009, 22:23
IMO D - 300%

total 4*4*4 = 64 squares with side 1cm
total surface area = 64 * 6 cm square
surface area for 4cm cube is = 16 * 6 cm square

so surface area increase = (64-16)/16 * 100 = 300%
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Re: PS: Cubes GMAT Test m01 [#permalink]  17 Apr 2009, 03:35
gmat911 wrote:
priyankur_saha@ml.com wrote:
IMO D - 300%

total 4*4*4 = 64 squares with side 1cm
total surface area = 64 * 6 cm square
surface area for 4cm cube is = 16 * 6 cm square

so surface area increase = (64-16)/16 * 100 = 300%

how did you know that there were going to be 64 additional squares?

it is 300% - I like how one of the participants just used l and did not input a variable in.
one knows that there are 64 additional squares because discussed 3-dim shapes are cubes therefore all sides are equal.
Consequently one can fit (4)/(1) lengths into one dimension = 4. So 4 little cubes in on dimension and then cube it.

Hmmm that was a bit complicated - hope that made sense.

che
dg
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Re: M01 #11 [#permalink]  19 Mar 2010, 06:41
elmagnifico wrote:
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

(A) 4%
(B) 166%
(C) 266%
(D) 300%
(E) 400%

[Reveal] Spoiler: OA
D

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surface area of 4 m cube = 6*4*4
surface area of 1 m cube = 6
no of cubes = 4*4*4
increase in surface area = (4*4*4*6 - 6*4*4)*100/6*4*4 = 300%
hence D
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Re: M01 #11 [#permalink]  18 Mar 2011, 06:32
New surface area = 64 * 6 * (1)^2

Old Surface Area = 6 * (4)^2

So %age increase = {64 * 6 * (1)^2 - 6 * (4)^2}/6 * (4)^2 *100

= (64 - 16)/16 * 100 = 48/16 * 100 = 300 %

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Re: M01 #11 [#permalink]  18 Mar 2011, 11:59
I got E because I never read the instructions... I was just like "Oh, 16 is 400% of 4, E!", I better keep track of this mistake in the future...
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Re: M01 #11 [#permalink]  18 Mar 2011, 15:51
Total surface area of initial cube = 6(4^2) = 96
Total surface area of final cube = 64 * 6 *(1^2)

% change = ((final cube area-initial cube area) / initial cube area)*100 = 300%
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Re: M01 #11 [#permalink]  22 Mar 2012, 12:22

Surface area of 4 cm cube = (surface area of one side)*(number of sides) = (4*4) * (6)
Surface area of all cubes: = (number of cubes)*(surface area of cube) = (4*4*4) * (6)

By simply looking at these two equations we see that there is 4 times more surface area with the little cubes, thus 300% increase.
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Re: M01 #11 [#permalink]  26 Mar 2012, 00:28
300%

Key to solve problem is to determine how many new cubes will be there......

Best approch= Original cube volume/ New cube volume
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Re: M01 #11 [#permalink]  26 Mar 2012, 06:07
a tricky one...i had failed....i will go with D(300%) after the explanations
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Re: M01 #11 [#permalink]  26 Mar 2012, 06:41
Expert's post
elmagnifico wrote:
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

(A) 4%
(B) 166%
(C) 266%
(D) 300%
(E) 400%

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

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 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): $$Percent=\frac{Change}{Original}*100$$

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

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Re: M01 #11   [#permalink] 26 Mar 2012, 06:41

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