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A cube is painted red on all faces. It is then cut into 27 equal small

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A cube is painted red on all faces. It is then cut into 27 equal small  [#permalink]

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New post 28 Jan 2015, 10:07
1
6
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (01:41) correct 46% (01:47) wrong based on 185 sessions

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A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces?

A. 12
B. 8
C. 6
D. 10
E. 16
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Re: A cube is painted red on all faces. It is then cut into 27 equal small  [#permalink]

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New post 28 Jan 2015, 13:05
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Hi Salvetor,

I'm going to give you a couple of hints so that you can try this question again:

1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....

While the question asks for the number of min-cubes that have paint on 2 sides, here's a critical thinking exercise (you can use the drawing to help you; remember that the cube has 6 sides and you're not allowed to count a min-cube more than once):

Which of the 27 mini-cubes have paint on just 1 side?
Which of the 27 mini-cubes have paint on 2 sides?
Which of the 27 mini-cubes have paint on 3 sides?

Final Answer
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A


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Re: A cube is painted red on all faces. It is then cut into 27 equal small  [#permalink]

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New post 28 Jan 2015, 14:47
I saw a rubik's cube on google and it's pretty clear to me now :)
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Re: A cube is painted red on all faces. It is then cut into 27 equal small  [#permalink]

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New post 29 Jan 2015, 05:16
Salvetor wrote:
A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces?

A. 12
B. 8
C. 6
D. 10
E. 16


Similar questions to practice:
the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html
if-a-4-cm-cube-is-cut-into-1-cm-cubes-then-what-is-the-107843.html
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
a-large-cube-consists-of-125-identical-small-cubes-how-110256.html
64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html
a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html

3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html

Hope it helps.
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Re: A cube is painted red on all faces. It is then cut into 27 equal small  [#permalink]

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New post 01 Feb 2015, 13:26
EMPOWERgmatRichC wrote:
Hi Salvetor,

I'm going to give you a couple of hints so that you can try this question again:

1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....

While the question asks for the number of min-cubes that have paint on 2 sides, here's a critical thinking exercise (you can use the drawing to help you; remember that the cube has 6 sides and you're not allowed to count a min-cube more than once):

Which of the 27 mini-cubes have paint on just 1 side?
Which of the 27 mini-cubes have paint on 2 sides?
Which of the 27 mini-cubes have paint on 3 sides?

Final Answer
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A


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Rich


Thanks for the taking the time to post such an elaborate explanation, Rich.
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Re: A cube is painted red on all faces. It is then cut into 27 equal small  [#permalink]

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New post 24 Jul 2017, 11:03
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Re: A cube is painted red on all faces. It is then cut into 27 equal small   [#permalink] 24 Jul 2017, 11:03
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