Data Sufficiency

sana.noor wrote:what is the value of x?
a) x^3-x^2 = 0
b) (-x)^2 = -x^2

Statement 1: x³ - x² = 0 --> x²(x - 1) = 0
Hence, either x² = 0 or (x - 1) = 0
Hence, either x = 0 or x = 1

As we cannot uniquely determine the value of x, statement 1 alone is not sufficient

Statement 2: (-x)² = -x²
As (-x)² cannot be negative and -x² cannot be positive, the must be equal to zero only.
Hence, x = 0

As we can uniquely determine the value of x, statement 2 alone is sufficient

The correct answer is B.

sana.noor wrote:I was doing this question as
x^3-x^2 = 0
X^3 - x^2 + x^2 = 0 + x^2
x^3 = x^2
and the only solution of x is +1...therefore i thought that the answer must be D.

1. The first red line is redundant, as from the given equation itself we can deduce that x³ = x².
2. x = 1 as well as x = 0 both satisfy the equation.

sana.noor wrote:I was doing this question as
x^3-x^2 = 0
X^3 - x^2 + x^2 = 0 + x^2
x^3 = x^2
and the only solution of x is +1...therefore i thought that the answer must be D.

I think it's helpful in this case to think conceptually, rather than algebraically. If x^3 - x^2 = 0, then x^3 and x^2 must have the same value. For what numbers are the square and the cube equal? For 0 and 1.

When you're thinking about exponent behavior, you want to think about the categories of numbers that behave differently: 0, 1, -1, positives greater than 1, negatives less than -1, positive fractions, and negative fractions. Make sure you don't forget about 0!