jaynayak wrote:
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.
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 =
2.5/6In the bottom example, the fraction of the total surface area that is red = (0.5 + 0.5 + 0.5)/6 =
1.5/6Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Each of 3 faces of C is entirely whiteSince 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 =
1.5/6In the bottom example, the fraction of the total surface area that is red =
0/6Since 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 =
1.5/6Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: CCheers,
Brent