What Fractional Part of the Total Surface Area of the Cube C is Red GMAT Data Sufficiency

Question: What fractional part of the total surface area of the cube C is red?

(1) Each of 3 faces of C is exactly ½ red
(2) Each of 3 faces of C is entirely white

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: C
Solution with Explanation:

Approach Solution (1):
To calculate the fraction of the whole cube that's red, we need to know what fraction of each of the six faces is red.
Statement (1) only discusses three of the faces, leaving the other three faces unknown, so it's insufficient.
Statement (2) only discusses three of the faces, leaving the other three faces unknown, so it's insufficient.
Together, the statements provide information about all six faces: three are half red, and the other three contain no red at all (they're entirely white). Thus, the two statements together are sufficient to establish the fractional part of the total surface area of cube C that is red.
Correct option: C

Approach Solution (2):
(1) Each of 3 faces of C is exactly 1/2 red.
We don’t know what fraction of other 3 faces are red
Insufficient
(2) Each of 3 faces of C is entirely white
Again we don’t know what fraction of other faces is red
Combing the two statements
Each of 3 faces of C is exactly 1/2 red.
Each of 3 faces of C is entirely white.
We know that out of 6 faces, area of exactly 3 faces is exactly 1/2 red
Fraction part = (3/2)/6 = ¼
Correct option: C

Approach Solution (3):
(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.
Correct option: C

“What fractional part of the total surface area of the cube C is red?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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