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# M01 #11

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Math Expert
Joined: 02 Sep 2009
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25 Mar 2013, 05:07
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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

BELOW IS REVISED VERSION OF THIS QUESTION:

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 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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25 Mar 2013, 15:13

Explanation :
Original SA = 6*4*4 = 96
After cutting; SA = n*6*1*1 = 6n ; where n is the number of pieces of cubes of 1cm side.

to find the value of n; original volume = volume after cutting the cube.. which means 4^3 = n*1^3 which gives n is equal to 64.
so,
After cutting; SA =6*64=384.

Percentage increase = ((384-96)/96)*100=(288/96)*100=300% (Option D)
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Is increase from 1 to 4 considered 400% or 300%? [#permalink]

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30 Apr 2013, 22:50
This is going to this question: a-4-cm-cube-is-cut-into-1-cm-cube-what-is-the-percentage-37027.html?fl=similar

Don't want to repost it, since it seems to have been discussed many many times.

I understand the calculations, don't understand the reasoning for calling a 4-fold increase as an increase of 300% rather than 400. As I read that question, I take it to mean "how many fold did this increase" rather than "by how much did it increase". Am I just not reading the question correctly? Misinterpreting the keywords?

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Re: Is increase from 1 to 4 considered 400% or 300%? [#permalink]

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01 May 2013, 00:46
When the value increased to 4 from 1, increase is 3 ==> increase is 300%

100% of 1 is 1
200% of 1 is 2.
Similarly, 400% of 1 is 4.

The theory is:
• when you calculate % increase, divide increase by original value.
• when you calculate % for new value wrt original value, divide new value by original value.

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Math Expert
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Re: Is increase from 1 to 4 considered 400% or 300%? [#permalink]

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01 May 2013, 02:14
Dixon wrote:
This is going to this question: a-4-cm-cube-is-cut-into-1-cm-cube-what-is-the-percentage-37027.html?fl=similar

Don't want to repost it, since it seems to have been discussed many many times.

I understand the calculations, don't understand the reasoning for calling a 4-fold increase as an increase of 300% rather than 400. As I read that question, I take it to mean "how many fold did this increase" rather than "by how much did it increase". Am I just not reading the question correctly? Misinterpreting the keywords?

Merging similar topics.

Revised version of this question is here: m01-70731-20.html#p1202018

Hope it helps.
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Re: Is increase from 1 to 4 considered 400% or 300%? [#permalink]

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03 May 2013, 00:37
Dixon wrote:
This is going to this question: a-4-cm-cube-is-cut-into-1-cm-cube-what-is-the-percentage-37027.html?fl=similar

Don't want to repost it, since it seems to have been discussed many many times.

I understand the calculations, don't understand the reasoning for calling a 4-fold increase as an increase of 300% rather than 400. As I read that question, I take it to mean "how many fold did this increase" rather than "by how much did it increase". Am I just not reading the question correctly? Misinterpreting the keywords?

Hi,

two fold of something ===> twice of something
three fold of something====> thrice of something
four fold of somthing ===> four times of something

lets take any value X....==> FOUR FOLD OF X will be four times of X= 4X
Now if calculate percent increase then
((4X-X)/X)*100= 300 %

Hope it helps...

SKM
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03 May 2013, 09:53
Total Surface Area of bigger cube = 6a^2 = 6*(4)^2 = 96
Total Surface Area of 1 smaller cube = 6*a^2 = 6*(1)^2 = 6

Let 'x' be total number of small cubes formed after cutting
Volume of bigger cube = (x) Volume of smaller cube => 4^3 = (x)1^3 => x = 64
Hence,total surface area of 64 smaller cubes = 64 * 6 = 384

Now % increase in Total Surface Area = [(Final Area - Initial Area)/Initial Area]*100=> [(384-96/96 )]*100 = 300%
Hence Ans (D)

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Re: M01 #11   [#permalink] 03 May 2013, 09:53

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# M01 #11

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