Equation

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

Hi shibsriz,

This question is perfect for TESTing VALUES; you don't have to do any algebra beyond that to get the correct answer. Here's how:

The question asks for the value of P^3 - Q^3.

Fact 1: P - Q = 0

This means that P = Q

If P = Q = 0, then 0^3 - 0^3 = 0
If P = Q = 2, then 2^3 - 2^3 = 0
If P = Q =-3, then (-3)^3 - (-3)^3 = 0
Fact 1 is SUFFICIENT

Fact 2: P + Q = 0

This means that P and Q are opposites or are both 0

If P = Q = 0, then 0^3 - 0^3 = 0
If P = 1, Q = -1, then 1^3 - (-1)^3 = 2
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

If we're going to determine sufficiency/insufficiency by TESTING values, I think it's important to note that this strategy provides definitive results ONLY IF the statement is insufficient. If the statement is sufficient, then testing values will only give us a GENERAL FEELING that the statement is sufficient.

To illustrate the potential problems with TESTING values, consider this target question: Is positive integer k a prime number?
Statement 1: k is an odd integer.

We should recognize that statement 1 is not sufficient, but notice what happens if we don't choose good numbers to plug in. If x is odd, then here are some possible cases:
x = 3, in which case x is prime
x = 5, in which case x is prime
x = 7, in which case x is prime
Well, I've already plugged in 3 odd integers, and they all led to the same conclusion. So, x must be prime, right? No. This would be the wrong conclusion.

So, be careful when plugging in values. The only time this technique yields definitive conclusions is when the statement is not sufficient AND you're able to find plug in values that yield different answers to the target question.

For more information about this important concept, you can watch our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1101

Cheers,
Brent