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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% Source: GMAT Club Tests  hardest GMAT questions SOLUTION IS HERE: m017073120.html#p1202018
Last edited by Bunuel on 12 Dec 2013, 02:33, edited 2 times in total.
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Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]
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25 Sep 2008, 14:44
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m01Q11.....explanation not clear...help please [#permalink]
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02 Oct 2008, 12:53
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.
The correct answer is D.
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: m01Q11.....explanation not clear...help please [#permalink]
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03 Oct 2008, 10:10
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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: A 4 cm cube is cut into 1 cm cubes. [#permalink]
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09 Oct 2008, 04:03
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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 Please update Thanks



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Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]
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09 Oct 2008, 04:20
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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 Please update Thanks
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Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]
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09 Oct 2008, 04:50
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O ya.. its % precent incrase problem man these small stupid mistakes are bugging me



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Re: Cube's Surface Area [#permalink]
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29 Oct 2008, 10:32
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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= (beforeafter)/before = (288/96)*100 = 300%.
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Re: Cube's Surface Area [#permalink]
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29 Oct 2008, 10:37
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]
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30 Mar 2009, 23:23
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 = (6416)/16 * 100 = 300%
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Re: PS: Cubes GMAT Test m01 [#permalink]
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31 Mar 2009, 00:13
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Agreed. SA of bigger cube = 6l^2 SA of smaller cubes = 64*(6*(l/4)^2) = 24l^2 %increase = 246/6 *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 = (6416)/16 * 100 = 300%



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Re: PS: Cubes GMAT Test m01 [#permalink]
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17 Apr 2009, 04:35
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 = (6416)/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 3dim 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]
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19 Mar 2010, 07:41
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% Source: GMAT Club Tests  hardest GMAT questions please provide detailed explanation. 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]
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18 Mar 2011, 07:32
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 % Answer : D
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Re: M01 #11 [#permalink]
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18 Mar 2011, 12:59
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]
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18 Mar 2011, 16:51
Total surface area of initial cube = 6(4^2) = 96 Total surface area of final cube = 64 * 6 *(1^2)
% change = ((final cube areainitial cube area) / initial cube area)*100 = 300%



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Re: M01 #11 [#permalink]
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22 Mar 2012, 13:22
I got answer D 300%
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]
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26 Mar 2012, 01:28
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]
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26 Mar 2012, 07:07
a tricky one...i had failed....i will go with D(300%) after the explanations
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Re: M01 #11 [#permalink]
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26 Mar 2012, 07:41
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% Source: GMAT Club Tests  hardest GMAT questions please provide detailed explanation. 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. Answer: D. Or: general formula for percent increase or decrease, (percent change): \(Percent=\frac{Change}{Original}*100\) So the percent increase will be: \(Percent=\frac{Change}{Original}*100=\frac{6*646*16}{6*16}*100=300%\). Answer: D.
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