aislam3 wrote:what is the value of x?
1. x^3-x^2=0
2. (-x)^2= -x^2

i feel the correct answer is A, and x is either 1 or 0, could someone please explain this to me.

Target question: What is the value of x?

You're absolutely correct in concluding that, from statement 1, we know that x could equal either 1 or 0. However, this is not enough information to answer the target question with certainty.

There are two types of Data Sufficiency questions.
1) Yes/No questions (e.g., Is x odd?)
2) Specific value questions (what is the value of x?)
Aside: This is covered to a greater extent in our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1098

Here the target question is a specific value question. For these questions, for a statement to be sufficient, there must be only one possible value. So, concluding that x equals either 1 or 0 is not enough to answer the target question.

Cheers,
Brent

aislam3 wrote:what is the value of x?
1. x^3-x^2=0
2. (-x)^2= -x^2

Target question: What is the value of x?

Statement 1: x^3 - x^2 = 0
Factor to get (x^2)(x-1) = 0
There are two possible cases;
case a: x^2 = 0, which means x = 0
case b: x - 1 = 0, which means x = 1
Since statement 1 yields conflicting answers to the target question, it is NOT SUFFICIENT

Statement 2: (-x)^2 = -x^2
Rewrite: (-1x)^2 = -(x^2)
Simplify: x^2 = -(x^2)
Add x^2 to both sides: 2x^2 = 0
Divide both sides by 2: x^2 = 0
From this, we can conclude that x must equal 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent