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Cubes with each side one inch long are glued together to form a larger

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Cubes with each side one inch long are glued together to form a larger [#permalink]

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New post Updated on: 18 Feb 2015, 03:25
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Question Stats:

60% (01:53) correct 40% (02:01) wrong based on 116 sessions

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Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 27 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?

A.. 64
B. 72
C. 86
D. 98
E. 112
[Reveal] Spoiler: OA

Originally posted by Turkish on 18 Feb 2015, 02:29.
Last edited by Bunuel on 18 Feb 2015, 03:25, edited 1 time in total.
Edited the question.
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Re: Cubes with each side one inch long are glued together to form a larger [#permalink]

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New post 18 Feb 2015, 03:37
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Turkish wrote:
Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 27 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?

A.. 64
B. 72
C. 86
D. 98
E. 112


27 = 3^3 cubes have no paint on them. Hence those 27 cubes are inside the bigger cube, which makes the side of the bigger cube equal to 3 + 1 + 1 = 5 smaller cubes. So, the total number of small cubes in bigger cube is 5^3 = 125. Since 27 cubes have no paint on them, then 125 - 27 = 98 cubes have at least one side painted.

Answer: D.

Or: let the number of cubes with no paint on them be x, then x + 27 must be a perfect cube. Only D fits.

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Re: Cubes with each side one inch long are glued together to form a larger [#permalink]

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New post 30 Oct 2015, 02:46
Use the options.
The options which after getting added to 27 shows a cube of a number could be right.

Here
64+27 = 91
72+27 = 99
86+27 = 113
98+27=125 ---(5*5*5)
112+27 = 139

So we have 98 as the answe!
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Re: Cubes with each side one inch long are glued together to form a larger [#permalink]

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New post 25 Nov 2016, 09:39
I think the question is written poorly.
all the faces were colored? or just one? it is singular though...
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Re: Cubes with each side one inch long are glued together to form a larger [#permalink]

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Re: Cubes with each side one inch long are glued together to form a larger   [#permalink] 04 Dec 2017, 11:23
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