If |x| < x^2, which of the following must be true ?
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
OAE
Source-GMATPrep EP2
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
OAE
Source-GMATPrep EP2
|x| < x² implies that x is NONZERO.NandishSS wrote:If |x| < x^2, which of the following must be true ?
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
Since x is nonzero, |x| > 0 and x² > 0.
Implication:
Both sides of the inequality are positive, allowing us to SQUARE the inequality.
(|x|)² < (x²)²
x² < x�.
Since x² > 0, we can safely DIVIDE both sides by x²:
x²/x² < x�/x²
1 < x²
x² > 1.
The correct answer is E.
