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15 Sep 2014, 23:15
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: \(Percent=\frac{\text{Change}}{\text{Original}}*100=\frac{6*646*16}{6*16}*100=300%\). Answer: D
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Re: M0111
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19 Feb 2016, 11:42
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.



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25 Jul 2016, 11:25
how did you ascertain that there would be 64 smaller cubes?



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12 Sep 2016, 05:04
Hi,
How did you got below :
Each of those little cubes will have the surface area equal to 6∗1^2= 6 cm2



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29 Sep 2016, 03:58
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.



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17 Sep 2017, 06:32
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 ?



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01 Oct 2018, 02:03
Hi Bunuel,
I calculated the number of cubes through surface area. Surface area of original cube = 96 Surface area of each smaller cube =6 Total cubes = 96/6 = 16 cubes.
Although I understood how you solved the question, what is the error in my approach?



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Re: M0111
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08 Jan 2019, 06:29
Bunuel wrote: 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: \(Percent=\frac{\text{Change}}{\text{Original}}*100=\frac{6*646*16}{6*16}*100=300%\).
Answer: D Hey Bunuel, The formula you used for percentage increase does not correspond to 300% Percent Increase = Change/Original * 100% = 25696/96 * 100% = 190/96 * 100% = 166.67%. Please explain.



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08 Jan 2019, 06:32
sakshamjinsi wrote: Bunuel wrote: 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: \(Percent=\frac{\text{Change}}{\text{Original}}*100=\frac{6*646*16}{6*16}*100=300%\).
Answer: D Hey Bunuel, The formula you used for percentage increase does not correspond to 300% Percent Increase = Change/Original * 100% = 25696/96 * 100% = 190/96 * 100% = 166.67%. Please explain. 6*64 = 384, not 256
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New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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09 Jan 2019, 00:02
Bunuel wrote: 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% SA of original cube : 6s^2 = 6* 16 and vol 4^3 = 64 the cube of 64 cm^3 is being cut into 1 cm small length pieces or say 64 pieces the new SA would be 6*1^3 = 6 * 64 % change = (6*646*16)/6*16 = 300% IMO D
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