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# A cube of side 7 cm is coloured on pair of opposite faces by

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Manager
Joined: 25 Sep 2012
Posts: 228
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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04 Nov 2013, 22:31
1
13
00:00

Difficulty:

65% (hard)

Question Stats:

61% (02:19) correct 39% (02:20) wrong based on 264 sessions

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A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

A) 150
B) 125
C) 60
D) 49
E) 40
Math Expert
Joined: 02 Sep 2009
Posts: 59586
Re: A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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05 Nov 2013, 00:45
5
2
b2bt wrote:
A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

A) 150
B) 125
C) 60
D) 49
E) 40

Look at the figure below:
Attachment:

Untitled.png [ 67.67 KiB | Viewed 5104 times ]
Only the edge cubes marked with dots will have exactly two colored faces. 5 cubes per edge * 12 edges = 60 cubes.

Hope it's clear.

P.S. A cube has 12 edges. There are 4 edges on the top square, 4 on the bottom square and 4 more that connect the 2 squares.
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Intern
Joined: 24 Jul 2017
Posts: 43
Location: India
WE: Information Technology (Computer Software)
Re: A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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09 Sep 2017, 07:47
5
3
Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks
##### General Discussion
Intern
Joined: 09 Oct 2017
Posts: 14
Location: Viet Nam
GMAT 1: 530 Q35 V28
GPA: 3.1
A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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30 Sep 2019, 19:51
devanshu92 wrote:
Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks

Hi devanshu92 and bunuel, can you please elaborate more on the above formula? What does n stand for? Is that n= length of side?
Intern
Joined: 13 May 2018
Posts: 19
Re: A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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22 Nov 2019, 16:37
hanvd1990 wrote:
devanshu92 wrote:
Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks

Hi devanshu92 and bunuel, can you please elaborate more on the above formula? What does n stand for? Is that n= length of side?

hanvd1990 nstands for the number of cubes formed . In this case the side is 7 and the cube is cut into unit cubes hence n=7
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Re: A cube of side 7 cm is coloured on pair of opposite faces by   [#permalink] 22 Nov 2019, 16:37
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