Simplifying Fractions on the GMAT
Consider the following question from The Economist GMAT Tutor:
If and are integers, and , which of the following must be true?
A) is an integer
B) is an integer
C) is an integer
D) is an integer
E) is an integer
How to simplify
Let’s rearrange the equation in the question to find an expression for :
Both sides of this latest equation must be integers, as we have been told that is an integer. For to be an integer, the in the denominator must be balanced by at least in the numerator. Let’s balance it with exactly by making :
If you look at Option C, the , which is (), will be canceled by the presence of in , leaving an integer.
C is therefore our answer.
Alternatively, find an expression for :
Again, we know both sides must be integers, as is an integer. For to be an integer, the in the denominator must be balanced by at least in the numerator. Thus, must be at least . is an integer. Using this method, we have further proof that Option C is correct.
This question really just asks you to cancel elements that are present in both numerator and denominator. As long as you do this carefully, you will be able to solve such questions quickly.
This post appeared first on the Economist GMAT Tutor blog.