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

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Manager
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Location: India
GMAT 1: 700 Q45 V40
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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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23 May 2017, 13:25
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67% (02:58) correct 33% (02:37) wrong based on 83 sessions

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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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Joined: 02 Sep 2009
Posts: 60647
Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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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).

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

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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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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).

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

Hi Bunuel,

I'm having a little trouble understanding the highlighted part. could you please explain that a bit ?
Math Expert
Joined: 02 Sep 2009
Posts: 60647
If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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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).

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

Hi Bunuel,

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

Check the 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 [ 280.71 KiB | Viewed 3866 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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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).

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

Sent from my XT1663 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 60647
Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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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).

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

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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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).

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

Hi Bunuel,

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

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,,,
Manager
Joined: 24 Dec 2016
Posts: 95
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
Re: If a cube of side length 24 units is cut into 512 smaller cubes of equ  [#permalink]

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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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08 Dec 2019, 13:36
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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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