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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.
(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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24 Feb 2011, 13:59
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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 --> 1/2 of 3 faces out of 6 is red, but we know nothing about the other 3. What if some fraction of the other 3 faces is red also? For example 1/3 of the 4th face is red, 1/4th of the 5th face and 1/10th of the 6th face? Hence statement (1) is not sufficient.
(2) Each of 3 faces of C is entirely white --> 3 faces out of 6 are white, but we know nothing about the other 3. Not sufficient.
(1)+(2) Half of 3 faces is red and other 3 faces are entirely white --> fractional part which is red is 1.5/6=1/4. Sufficient.
Answer: C.
Hope it's clear.
(1) Each of 3 faces of C is exactly 1/2 red --> 1/2 of 3 faces out of 6 is red, but we know nothing about the other 3. What if some fraction of the other 3 faces is red also? For example 1/3 of the 4th face is red, 1/4th of the 5th face and 1/10th of the 6th face? Hence statement (1) is not sufficient.
(2) Each of 3 faces of C is entirely white --> 3 faces out of 6 are white, but we know nothing about the other 3. Not sufficient.
(1)+(2) Half of 3 faces is red and other 3 faces are entirely white --> fractional part which is red is 1.5/6=1/4. Sufficient.
Answer: C.
Hope it's clear.
09 May 2022, 11:42
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jaynayak
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:
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:
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:
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
Cheers,
Brent
