If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
I. ab < 1
III. a/b < 1
Select:
A) I only
B) II only
C) III only
D) I and II only
E) I and III only
MANHATTAN GMATOFFICIAL SOLUTION:   You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:   1 &gt; 1 - ab &gt; 0   0 &gt; -a b &gt; -1 Subtract 1 from all three terms.   0 &lt; ab &lt; 1 Multiply all three terms by -1 and flip the inequality signs.   Therefore you know that 0 &lt; ab &lt; 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b &lt; 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.   Therefore, the correct answer is (I and II only).
<result>D</result>
If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
I. ab < 1
III. a/b < 1