Surface Area

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Surface Area

by knight247 » Wed Dec 21, 2011 1:46 am
What fraction 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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by rijul007 » Wed Dec 21, 2011 3:35 am

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by [email protected] » Wed Dec 21, 2011 4:27 am
knight247 wrote:What fraction 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.
(1) Each of 3 faces of C is exactly 1/2 red but nothing has been said about the other 3 faces, some fraction of the other 3 faces may be red, about which we are not sure; NOT sufficient.

(2) Each of 3 faces of C is entirely white but again nothing has been said about the other 3 faces; NOT sufficient.

Combining (1) and (2), we clearly know that 1/2 of 3 faces is red while the other 3 faces are entirely white, so fractional part of the total surface area of cube C, which is red = 1.5/6 = 1/4; SUFFICIENT.

The correct answer is C.
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Re: Surface Area

by [email protected] » Mon May 09, 2022 10:42 am
knight247 wrote:
Wed Dec 21, 2011 1:46 am
What fraction 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.
Target question: What fractional part of the total surface area of cube C is red

Statement 1: Each of 3 faces of C is exactly 1/2 red
Since we have no information about the other three faces, statement 1 is NOT SUFFICIENT
Consider these two counterexamples showing all six faces of the cube:
Image
In the top example, the fraction of the total surface area that is red = (0.5 + 0.5 + 0.5 + 1)/6 = 2.5/6
In the bottom example, the fraction of the total surface area that is red = (0.5 + 0.5 + 0.5)/6 = 1.5/6
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of 3 faces of C is entirely white
Since we have no information about the other three faces, statement 2 is NOT SUFFICIENT
Consider these two counterexamples showing all six faces of the cube:
Image
In the top example, the fraction of the total surface area that is red = (0.5 + 0.5 + 0.5)/6 = 1.5/6
In the bottom example, the fraction of the total surface area that is red = 0/6
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine both statements, we know exactly what the six faces look like:
Image
So, the fraction of the total surface area that is red = (0.5 + 0.5 + 0.5)/6 = 1.5/6
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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