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

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VP
Joined: 14 May 2006
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A large cube 10 cm on a side is composed of cubes 1 cm on a [#permalink]  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
Manager
Joined: 25 May 2006
Posts: 227
Followers: 1

Kudos [?]: 19 [0], given: 0

Donâ€™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-
_________________

Who is John Galt?

Manager
Joined: 04 Jul 2006
Posts: 57
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Kudos [?]: 2 [0], given: 0

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).
VP
Joined: 25 Nov 2004
Posts: 1495
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Kudos [?]: 38 [0], given: 0

Re: PS: Cube probability [#permalink]  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.
Senior Manager
Joined: 07 Jul 2005
Posts: 406
Location: Sunnyvale, CA
Followers: 2

Kudos [?]: 4 [0], given: 0

yep. (E) it is.
same methods as used by MA and gameover.
CEO
Joined: 15 Aug 2003
Posts: 3470
Followers: 61

Kudos [?]: 697 [0], given: 781

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
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 110 [0], given: 0

Now solve this one:

http://www.gmatclub.com/phpbb/viewtopic.php?t=31924
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

VP
Joined: 14 May 2006
Posts: 1418
Followers: 4

Kudos [?]: 57 [0], given: 0

OA is E as seen in the other thred
Director
Joined: 28 Dec 2005
Posts: 758
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: PS: Cube probability [#permalink]  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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