Problem solving

Brent@GMATPrepNow wrote:

Roland2rule wrote:If x is less than 2, which of the following statements are always true?
I. x is negative
II. x is positive.
III. 2x is greater than or equal to x
IV. x² is greater than or equal to x.

A) III only
B) IV only
C) I and III only
D) I, III, and IV only
E) none of the statements

Key words: always true
So, if we can show that a statement could be false, we can eliminate that statement.

I. x is negative
If x < 2, then x COULD equal 1, in which case this statement need not be true
ELIMINATE C and D

II. x is positive.
If x < 2, then x COULD equal -1, in which case this statement need not be true

III. 2x is greater than or equal to x
If x < 2, then x COULD equal -1, in which case 2x = -2
In this case, 2x is NOT greater than x
ELIMINATE A

IV. x² is greater than or equal to x.
If x < 2, then x COULD equal 1/2, in which case x² = 1/4
So, x² is NOT greater than or equal to x.
ELIMINATE B

Answer: E

Cheers,
Brent