In each of the inequalities below, test the following list of values:Is x negative?
(1) At least one of x and x^2 is greater than x^3.
(2) At least one of x^2 and x^3 is greater than x.
-2, -1, -1/2, 0, 1/2, 1, 2.
Statement 1: x > x³ or x² > x³ (or both)
Testing the list of values above, we get:
x > x³ is satisfied by -2 and 1/2.
x² > x³ is satisfied by -2, -1, -1/2, and 1/2.
Since can be negative or positive, INSUFFICIENT.
Statement 2: x² > x or x³ > x (or both)
Testing the list of values above, we get:
x² > x is satisfied by -2, -1, -1/2, and 2.
x³ > x is satisfied by -1/2 and 2.
Since x can be negative or positive, INSUFFICIENT.
Statements combined:
The values in red satisfy both statements.
All of the values in red are negative.
Implication:
To satisfy both statements, x must be negative.
SUFFICIENT.
The correct answer is C.
