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If 7 white cubes and 20 red cubes, all of equal size, are fastened tog

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If 7 white cubes and 20 red cubes, all of equal size, are fastened tog  [#permalink]

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New post 30 Nov 2017, 23:58
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  55% (hard)

Question Stats:

44% (01:23) correct 56% (01:50) wrong based on 26 sessions

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If 7 white cubes and 20 red cubes, all of equal size, are fastened together to form one large cube as shown above, what is the smallest fractional part of the surface area of the large cube that could be white?

(A) 1/9
(B) 7/54
(C) 4/27
(D) 1/6
(E) 7/27

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If 7 white cubes and 20 red cubes, all of equal size, are fastened tog  [#permalink]

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New post 01 Dec 2017, 00:23
A

Let each side of the small cube be 1m.
The surface area of the large cube is 6*(3*3)=54.

Now one white cube can be placed at the centre of the large cube so that the white cube is invisible. The remaining 6 white cubes can be placed at the center of each face (we have 6 faces) to minimise the white area. Hence the surface area of the large cube that could be white is 6*(1*1)=6.

So the fraction is 6/54=1/9


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Re: If 7 white cubes and 20 red cubes, all of equal size, are fastened tog  [#permalink]

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New post 01 Dec 2017, 07:23
I think the answer is 1/6
Let the side of each cube be 1 .
Then the surface area of the large cube is 6a^2=6*9=54
Now there are 7 white cubes ans we need minimum area of these cubes so we have to place them in the middle line .
So there are 9 faces of area 1 square units each that are visible so 9/54=1/6

Please correct if i am wrong
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Re: If 7 white cubes and 20 red cubes, all of equal size, are fastened tog  [#permalink]

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New post 01 Dec 2017, 07:39
arvind910619 wrote:
I think the answer is 1/6
Let the side of each cube be 1 .
Then the surface area of the large cube is 6a^2=6*9=54
Now there are 7 white cubes ans we need minimum area of these cubes so we have to place them in the middle line .
So there are 9 faces of area 1 square units each that are visible so 9/54=1/6

Please correct if i am wrong


You can reduce the area further by placing one white cube at the core of the big cube. If u place the remaining 6 cubes at the center of each face of the big cube u have only white area as 6 which is lesser than 9


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Re: If 7 white cubes and 20 red cubes, all of equal size, are fastened tog &nbs [#permalink] 01 Dec 2017, 07:39
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