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What is the value of x?

(1) x^3 - x^2 = 0 --> \(x^2(x-1)=0\) --> \(x=0\) or \(x=1\). Not sufficient.

(2) (-x)^2 = -x^2 --> \(x^2=-x^2\) --> \(2x^2=0\) --> \(x=0\). Sufficient.

Answer: B.
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jsphcal
What is the value of x?

(1) x³ - x² = 0
(2) (-x)² = -x²

Target question: What is the value of x?

Statement 1: x³ - x² = 0
Factor to get: x²(x - 1) = 0
So, EITHER x = 0 OR x = 1
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (-x)² = -x²
ASIDE: Some students will assume that (-x)² and -x² are equivalent, but they are not.
(-x)² tells us to multiply x by -1, and then square the result.
-x² tells us to square x, and then multiply the result by -1.

In other words, (-x)² = [(-1)(x)]² and -x² = (-1)(x²)

So, we can rewrite the given equation as follows: [(-1)(x)]² = -x²
Rewrite the left side as follows: (-1)²(x)² = -x²
Simplify the left side: (1)(x²) = -x²
Add x² to both sides: 2x² = 0, which means x = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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Hello from the GMAT Club BumpBot!

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