Data Sufficiency - 32

What is the value of x?

1) (-x)^3 = -x^3
2) (-x)^2 = -x^2


Answer: B

From statement (1):

if x = 0 both sides are equal
if x = 1 both sides are again equal {(-1)^3 = -1 & -1^3 = 1}
=> x = 0 or x = 1
Hence insufficient

From statement (2):

x can only be zero because the square of a number other than zero cannot be negative
{(-1)^2 = 1 which is not equal to -(1)^2)}
=> from above it is sufficient to say that x = 0
Hence sufficient