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What fractional part of the total surface area of cube C is [#permalink]

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22 Mar 2008, 01:57

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A

B

C

D

E

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16. What fractional part of the total surface area of cube C is red? (1) Each of 3 faces of C is exactly 1/2 red. (2) Each of 3 faces of C is entirely white.
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Jimmy Low, Frankfurt, Germany Blog: http://mytrainmaster.wordpress.com GMAT Malaysia: http://gmatmalaysia.blogspot.com

"Each of 3 faces" means that 3 faces each have exacltly 1/2 red. So we dont know anything about the other 3 faces. And the same with statement 2

E is my choice.

Sondenso, If this meaning is right, we can use following: 1. cube has 6 faces 2. a face can be white or 1/2 red (C) Therefore, C is correct. 3 faces are white and 3 other faces are 1/2 red and \(ratio=\frac{3*\frac12}{6}=\frac14\)
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"Each of 3 faces" means that 3 faces each have exacltly 1/2 red. So we dont know anything about the other 3 faces. And the same with statement 2

E is my choice.

Sondenso, If this meaning is right, we can use following: 1. cube has 6 faces 2. a face can be white or 1/2 red (C) Therefore, C is correct. 3 faces are white and 3 other faces are 1/2 red and \(ratio=\frac{3*\frac12}{6}=\frac14\)

Walker,

The 1 and the 2 combined do not say "the 3 faces...red" and "the other 3 faces...white", so we have 6 faces, how can we know what face? right?
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3 of the 6 sides are entirely white -- means definitely not red. Let's talk about the other 3 sides now. First statement says: 3 of the 6 sides are exactly 1/2 red. Means; they must be talking about the 3 sides which are not entirely white.

Now, if "a" is side:

area of 1 side is a^2. total area for 6 sides is 6*a^2 area with red will be 3*((a^2)/2). Because half the area of each of the 3 remaining faces is red. (a^2)/2 will be half the area times 3 for three sides. now, divide: [3*((a^2)/2)]/[6*a^2]=1/4. We got the answer.
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