To answer this question, you could "pick numbers" (e.g. a = 0.5 and b = 2) go through each option to determine which expression has the greatest value. That might take you 60 seconds or even longer, because that would be a time consuming and tedious method.

But, if you had a solid understanding of number properties (possibly one of the most important set of rules to know by heart for the GRE!), you could answer this question without doing any calculations.

1) recognise that always: big/small > small/big
2) see that a is small and b is big
3) recognise that a is a positive fraction, e.g. 0.5 (or 1/2)
4) if a<1, then ab<b (in this case, where b is a positive number greater than 1)
5) (a^2) < a
6) (b^2) > b

(raising a number greater than 1 will always make it greater. Therefore (b^2) > b. But, if (a) was raised, because (a) is a positive fraction, that would make a even smaller (e.g. 0.5 * 0.5 = 0.25), so (a^2) < a )

Then quickly look at the answer choices to see which expression is the greatest:

1) ab < b
2) a/b < b
3) b/a > b

so now we know that choices (A) and (B) are eliminated. (C) is the greatest value so far.

4) a/(b^2) < (b^2)/a (i.e. small/very big < very big/small) - so we can eliminate (D).

finally, compare (C) to (D):

5) (b^2)/a > b/a (very big/small > big/small), so (E) must be the right answer.

The Ultimate GRE Cheat Sheet has an exceptional chapter on number properties. You really need to know each one of these rules off by heart. You could have solved this question in 30 seconds with a solid understanding of the number properties above.

Go to Ultimate Tuition to find out more!