2012-03-14 09:00:33

If xy < 0, which of the following must be negative?

A) x³
B) (xy)²
C) xy²
D) x²y³
E) x³y³

The correct answer is E

Explanation: The product of a positive number and a negative one is negative. Thus, if xy is negative, then x and y are opposite signs (i.e. x is negative and y positive or x is positive and y negative). A negative number raised to an odd power (e.g. 3) will be negative. This means that either x³ or y³ will be negative, and the other will be positive. The product of a negative number and a positive number is negative, so choice E will be negative. This can be confirmed by picking numbers too: let x = -2 and y = 1. Then, xy would be (-2)(1), or -2, which is less than 0. (-2)³ = -8 and 1³ = - 1. -8 • 1 = -8. This holds true if y = -2 and x = 1 too.