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If a cube of side length 24 units is cut into 512 smaller cubes of equ

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If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 23 May 2017, 13:25
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If a cube of side length 24 units is cut into 512 smaller cubes of equal dimensions, then what is the ratio of the combined surface area of the smaller cubes and the surface area of the original cube?


A. 1:48
B. 3:32
C. 8:1
D. 32:3
E. 48:1
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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 23 May 2017, 14:04
niteshwaghray wrote:
If a cube of side length 24 units is cut into 512 smaller cubes of equal dimensions, then what is the ratio of the combined surface area of the smaller cubes and the surface area of the original cube?


A. 1:48
B. 3:32
C. 8:1
D. 32:3
E. 48:1


512 = 8^3, which means that a side of a large cube will be divided into 8 parts giving the side lengths of smaller cubes as 24/8 = 3.

The combined surface area of the smaller cubes = 512*(6*3^2);

The surface area of the original cube = 6*24^2 (number of faces * area of a face).

\(Ratio = \frac{512*6*3^2}{6*24^2}=\frac{8^3*3^2}{6*8^2*3^2}=8\).

Answer: C.
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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 24 May 2017, 00:00
Bunuel wrote:
niteshwaghray wrote:
If a cube of side length 24 units is cut into 512 smaller cubes of equal dimensions, then what is the ratio of the combined surface area of the smaller cubes and the surface area of the original cube?


A. 1:48
B. 3:32
C. 8:1
D. 32:3
E. 48:1


512 = 8^3, which means that a side of a large cube will be divided into 8 parts giving the side lengths of smaller cubes as 24/8 = 3.

The combined surface area of the smaller cubes = 512*(6*3^2);

The surface area of the original cube = 6*24^2 (number of faces * area of a face).

\(Ratio = \frac{512*6*3^2}{6*24^2}=\frac{8^3*3^2}{6*8^2*3^2}=8\).

Answer: C.



Hi Bunuel,

I'm having a little trouble understanding the highlighted part. could you please explain that a bit ?
Thanks in advance.
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If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 24 May 2017, 00:47
1
Shruti0805 wrote:
Bunuel wrote:
niteshwaghray wrote:
If a cube of side length 24 units is cut into 512 smaller cubes of equal dimensions, then what is the ratio of the combined surface area of the smaller cubes and the surface area of the original cube?


A. 1:48
B. 3:32
C. 8:1
D. 32:3
E. 48:1


512 = 8^3, which means that a side of a large cube will be divided into 8 parts giving the side lengths of smaller cubes as 24/8 = 3.

The combined surface area of the smaller cubes = 512*(6*3^2);

The surface area of the original cube = 6*24^2 (number of faces * area of a face).

\(Ratio = \frac{512*6*3^2}{6*24^2}=\frac{8^3*3^2}{6*8^2*3^2}=8\).

Answer: C.



Hi Bunuel,

I'm having a little trouble understanding the highlighted part. could you please explain that a bit ?
Thanks in advance.


Check the image:

Image

The cube above is made of 8*8*8 = 512 little cubes. Notice that the sides of the cubes are divided by 8 equal parts.

Hope it helps.

Attachment:
cube.png
cube.png [ 280.71 KiB | Viewed 3832 times ]

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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 27 May 2017, 04:57
Bunuel wrote:
niteshwaghray wrote:
If a cube of side length 24 units is cut into 512 smaller cubes of equal dimensions, then what is the ratio of the combined surface area of the smaller cubes and the surface area of the original cube?


A. 1:48
B. 3:32
C. 8:1
D. 32:3
E. 48:1


512 = 8^3, which means that a side of a large cube will be divided into 8 parts giving the side lengths of smaller cubes as 24/8 = 3.

The combined surface area of the smaller cubes = 512*(6*3^2);

The surface area of the original cube = 6*24^2 (number of faces * area of a face).

\(Ratio = \frac{512*6*3^2}{6*24^2}=\frac{8^3*3^2}{6*8^2*3^2}=8\).

Answer: C.

Hi, can you please provide link for such examples for practice?

Sent from my XT1663 using GMAT Club Forum mobile app
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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 27 May 2017, 05:27
goalMBA1990 wrote:
Bunuel wrote:
niteshwaghray wrote:
If a cube of side length 24 units is cut into 512 smaller cubes of equal dimensions, then what is the ratio of the combined surface area of the smaller cubes and the surface area of the original cube?


A. 1:48
B. 3:32
C. 8:1
D. 32:3
E. 48:1


512 = 8^3, which means that a side of a large cube will be divided into 8 parts giving the side lengths of smaller cubes as 24/8 = 3.

The combined surface area of the smaller cubes = 512*(6*3^2);

The surface area of the original cube = 6*24^2 (number of faces * area of a face).

\(Ratio = \frac{512*6*3^2}{6*24^2}=\frac{8^3*3^2}{6*8^2*3^2}=8\).

Answer: C.

Hi, can you please provide link for such examples for practice?

Sent from my XT1663 using GMAT Club Forum mobile app


Similar questions to practice:
https://gmatclub.com/forum/m01-183522.html (GMAT Club)
https://gmatclub.com/forum/there-is-a-r ... 96312.html (Veritas Prep)
https://gmatclub.com/forum/cubes-with-e ... 93391.html
http://gmatclub.com/forum/if-a-4-cm-cub ... 07843.html (GMAT Club)
http://gmatclub.com/forum/a-large-cube- ... 10256.html
http://gmatclub.com/forum/64-small-iden ... 51009.html
http://gmatclub.com/forum/the-entire-ex ... 55955.html (Manhattan GMAT)
http://gmatclub.com/forum/a-big-cube-is ... 99424.html
http://gmatclub.com/forum/a-large-solid ... 51096.html
http://gmatclub.com/forum/a-wooden-cube ... 62570.html
https://gmatclub.com/forum/a-cube-of-si ... 48513.html
https://gmatclub.com/forum/a-certain-cl ... 67230.html (GMAT Prep)
https://gmatclub.com/forum/a-cube-has-a ... 09376.html
https://gmatclub.com/forum/a-cube-is-pa ... 80789.html (Data Sufficiency)
https://gmatclub.com/forum/a-certain-cu ... 63928.html

3-D Geometry Questions to practice: http://gmatclub.com/forum/3-d-geometry- ... 71024.html

Hope it helps.
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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 27 May 2017, 11:25
2
Shruti0805 wrote:
Bunuel wrote:
niteshwaghray wrote:
If a cube of side length 24 units is cut into 512 smaller cubes of equal dimensions, then what is the ratio of the combined surface area of the smaller cubes and the surface area of the original cube?


A. 1:48
B. 3:32
C. 8:1
D. 32:3
E. 48:1


512 = 8^3, which means that a side of a large cube will be divided into 8 parts giving the side lengths of smaller cubes as 24/8 = 3.

The combined surface area of the smaller cubes = 512*(6*3^2);

The surface area of the original cube = 6*24^2 (number of faces * area of a face).

\(Ratio = \frac{512*6*3^2}{6*24^2}=\frac{8^3*3^2}{6*8^2*3^2}=8\).

Answer: C.



Hi Bunuel,

I'm having a little trouble understanding the highlighted part. could you please explain that a bit ?
Thanks in advance.



let me explain..

24 units of each side.. so volume = 24 * 24 * 24...
divide this by 512...
24 * 24 *24/ 512 = 27...
implies volume of each cube is 3..

rest is understandable... thanks,,,
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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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New post 28 May 2017, 21:00
Awesome, understood. Thank you mohshu !
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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ   [#permalink] 08 Dec 2019, 13:36
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