# Fractions in GRE math: An overview

It is important on the GRE to know how to solve questions involving fractions. The good news is that there are simple methods to help us.

Consider the following question from our question bank:

*A used car salesman receives an annual bonus if he meets a certain quota. This year, the salesman has so far sold 1/5 of last year's quota. If this year's quota is reduced by 25 percent, the quantity that he still needs to sell this year in order to receive the annual bonus is what fraction of the preceding year's car quota?*

*A) 4/15B) 4/20C) 3/4D) 11/20E) 9/20*

You should immediately realise that the simplest way to solve this question is by plugging in numbers. However, which numbers should you choose? Look at the numbers in the question. We have 1/5 and 25%. 25% could be written as 1/4. The number you should choose will be divisible by 4 and 5. Let’s take 20.

Last year’s quota is therefore 20.

A simple table may help:

Last Year | This Year |

20 | 15 |

To obtain this year’s quota, we know that this year’s quota is reduced by 25%, so (1/4)(20) = 5 and 20 - 5 = 15, so 15 is this year’s quota.

We are told that the salesman has sold 1/5 of last year’s quota:

1/5 x 20 = 4. So he still needs to sell 15 - 4 = 11 to reach this year’s quota.

Now be careful with the wording of the question:

“The quantity that he still needs to sell this year in order to receive the annual bonus is what fraction of the preceding year's car quota?” The quantity that he still needs to sell is 11. The preceding year’s car quota is 20. Expressed as a fraction this is 11/20. Answer choice D is correct.

Now let’s consider a question involving fractions and inequalities. This is also from our question bank.

If 2 ≤ x ≤ 7 and 6 ≤ y ≤ 15, which of the following CANNOT be a value of x / y?

A) 1/3

B) 2/7

C) 1/5

D) 2/13

E) 1/8

The easiest way to solve this question is to set up limits for x/y. Work out the smallest possible fraction for x/y and the largest possible fraction for x/y.

The smallest possible fraction comes when the numerator is as small as possible and the denominator is as large as possible. In our case this will be when x/y = 2/15.

The largest fraction comes when the numerator is as large a possible and the denominator is as small as possible. In this case, this will be when x/y = 7/6.

So our answer must be between 2/15 and 7/6. The only fraction among the answer choices that lies outside this range is 1/8. Answer choice E is correct.

There are a number of questions involving fractions. Here we have just looked at two. However, if you remember these useful strategies, you will be well on the way to solving many questions. Remember plugging in and establishing upper and lower limits.