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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
5
5
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (02:12) correct 44% (02:24) wrong based on 115 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

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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1
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
1
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
1
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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New post 07 Feb 2019, 05:04
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Re: Cubes with each side one inch long are glued together to form a larger   [#permalink] 07 Feb 2019, 05:04
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