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A large cube 10 cm on a side is composed of cubes 1 cm on a

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A large cube 10 cm on a side is composed of cubes 1 cm on a [#permalink] New post 14 Jul 2006, 14:09
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A large cube 10 cm on a side is composed of cubes 1 cm on a side. The outside of the large cube is painted red and then all of the individual cubes are mixed in a drum. If one cube is selected randomly, which of the following is the approximate probability that the cube will have at least one red face?

A) 1:6

B) 1:5

C) 1:4

D) 1:3

E) 1:2

again... fastest way to solve this :?:
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 [#permalink] New post 14 Jul 2006, 16:23
Don’t know if it's the fastest way but it work for me.

Total 1cm cubes = 10x10x10=1000
Total 1cm cubes with only one face painted red=8x10x6=480
Total 1cm cubes that are painted on three sides to be consider=4+4=8

Probability = 488/1000 is close to 1/2 -E-

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 [#permalink] New post 14 Jul 2006, 16:35
Maybe it is a faster way to consider the interior of the large cube.

We know that we have 10*10*10=1000 small cubes.
(10-2)*(10-2)*(10-2)=8*8*8=512 of the small cubes are in the interior of the large cube.
(1000-512)/1000=488/1000 is approximately equal to 1/2.

Hence (E).
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Re: PS: Cube probability [#permalink] New post 14 Jul 2006, 16:51
u2lover wrote:
A large cube 10 cm on a side is composed of cubes 1 cm on a side. The outside of the large cube is painted red and then all of the individual cubes are mixed in a drum. If one cube is selected randomly, which of the following is the approximate probability that the cube will have at least one red face?

A) 1:6
B) 1:5
C) 1:4
D) 1:3
E) 1:2

again... fastest way to solve this :?:


totoal = 10^3 = 1000
small inside cubs that are not painted = 8^3=512
so the prob = (1000-512)/1000 = 488/1000 i.e approx 1:2.
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 [#permalink] New post 14 Jul 2006, 17:01
yep. (E) it is.
same methods as used by MA and gameover.
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 [#permalink] New post 14 Jul 2006, 17:40
Sorry for posting links here..

http://www.gmatclub.com/phpbb/viewtopic ... light=drum

P(atleast one red face) = 1 - P(no red face)

The unpainted "area of the cube" is 8*8*8

the total area = 10* 10*10

P(No reds) = 512/1000

P(atleast one red face) = 488/1000

Approximately 1:2


Another one:
http://www.gmatclub.com/phpbb/viewtopic ... light=drum
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 [#permalink] New post 14 Jul 2006, 23:20

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 [#permalink] New post 22 Jul 2006, 19:11
OA is E as seen in the other thred
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Re: PS: Cube probability [#permalink] New post 22 Jul 2006, 19:31
u2lover wrote:
A large cube 10 cm on a side is composed of cubes 1 cm on a side. The outside of the large cube is painted red and then all of the individual cubes are mixed in a drum. If one cube is selected randomly, which of the following is the approximate probability that the cube will have at least one red face?

A) 1:6

B) 1:5

C) 1:4

D) 1:3

E) 1:2

again... fastest way to solve this :?:


E it can only be :)
Re: PS: Cube probability   [#permalink] 22 Jul 2006, 19:31
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