I think what you're missing is this:
In #2, q = -p, or the opposite of p. So p + q = 0, then if p = 2, then q = -2. So that 2 + -2 = 0. Works. Now apply this to \(p^3 - q^3\)
First try p = 2 and q = -2: \(2^3 - (-2)^3 = 8 - - 8 = 16\)
Now try p = -2 and q = 2: \((-2)^3 - 2^3 = -8 - 8 = -16\)
In both situations, p + q = 0, but when used in the equation given in the stem, we get different values so the statement cannot be sufficient, and therefore, A must be the answer since B is insufficient.
x-ALI-x wrote:
DS Question, I don't buy the answer.
Question:
What is the value of \(p^3 - q^3\) ?
1. \(p - q = 0\)
2. \(p + q = 0\)
I answered D. Reasoning:
\(p^3 - q^3\) = (p - q) (p + q) (p - q)
statement 1: (p-q) = 0, then \(p^3 - q^3 = 0\)
statement 2: (p+q) = 0, then \(p^3 - q^3 = 0\)
Am I missing something?
OA is A.
OE: From statement (1) it is clear that \(p=q\) , so the initial difference is 0. Absolutely enough. Statement (2) doesn't give any additional information. So, the answer is A