<p>If a and b are positive numbers and (a/b) > ab, which of the following must be true?
I. a>1
II. b<1
III. b<a</p>
<p>So I automatically found a counterexample for I but I couldn’t find them for II or III. How was I supposed to have logiced through this?</p>
<p>Rearrange the question and you get
a > ab^2
1 > b^2
-1 < b < 1</p>
<p>So II. seems to be true.</p>
<p>For III., let a = 1/4 and b = 1/2.
(1/4)/(1/2) > (1/4)(1/2)^2
1/2 > 1/16</p>
<p>The statement checks out here when a < b, so III. doesn’t have to be true.</p>