What is the value of p³ - q³?
(1) p - q = 0
(2) p + q = 0
Target question: What is the value of p³ - q³?
IMPORTANT: This question requires us to know that we can factor a DIFFERENCE OF CUBES as follows: p³ - q³ = (p - q)(p² + pq + q²). You are
not required to know how to factor a difference of cubes (or a sum of cubes) for the GMAT. So, this would not be an official GMAT question.
That said, here's my solution (just for kicks):
First, we'll REPHRASE the target question as....
REPHRASED target question: What is the value of (p - q)(p² + pq + q²)?
Statement 1: p - q = 0
If
p - q = 0, then we can be certain that
(p - q)(p² + pq + q²) = 0
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: p + q = 0
There are several values of p and q that satisfy this condition. Here are two:
Case a: p = 1 and q = -1, in which case
p³ - q³ = 2
Case b: p = -1 and q = 1, in which case
p³ - q³ = -2
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
