Ask Questions, Discuss Approaches & No Clutter

GMAT questions involving fractions: How to solve them quickly

Open 0 Answers 248 Views Tutorial

GMAT fractions

There are some questions involving fractions that certainly seem very difficult at first glance. You need a systematic method to solve such questions.

Consider the following question from The Economist GMAT Tutor's database of practice questions:

If a is an integer and (a2)/(123) is odd, which of the following must be an odd integer?
A) a/4
B) a/12
C) a/27
D) a/36
E) a/72

Tip: try plugging in a value for ‘a’

One approach to this question is to try to work out a possible value for a and use this as a plugin. There are many things to remember as you do this.


  • You are told that (a2)/(123) is odd. Therefore, a2 must be at least as large as 123, or is possibly larger than 123, since the entire expression must be an integer. How large is 123?
  • Break 123 down into its prime factors:


= (3*4)3 
= (3*2*2)3 
= (3*22)3 
= 26 *33


  • a is an integer. Therefore, a2 is the square of an integer, or a perfect square
  • Is it possible that a2 = 26 * 33? For this to be true, the square root of 26 * 33 must be an integer. What is the square root of 26 * 33? This is 23*33/2, which is not an integer. Therefore, a2 cannot be 26 * 33. The problem lies with the fact that 3 is raised to an odd power. If we raise 3 to an even power, we will obtain an integer as the square root.
  • Let us test whether it is possible that a2 = 26 * 34. (We are now multiplying by an additional 3.) The square root of 26 * 34 = 23 * 32 = 8*9 = 72. 72 is an integer. Therefore, it is possible that a = 72.
  • Plug 72 into each of the answer choices:


A) 72/4 = 18 – an even integer
B) 72/12 = 6 – an even integer
C) 72/27 = a non-integer
D) 72/36 = 2 – an even integer
E) 72/72 = 1 – an odd integer

Therefore, E is our answer.

Note the usefulness of prime factorization in solving this question. Although there are many steps in solving such a question, as long as you know the right method, you will be able to get to the correct answer quickly enough.

The post first appeared on here

Please log in or register to answer. And you receive a free copy of GMAT Math Formula Sheet with your sign up mail.

Student Speaks

Jyotsna Mehta

Indian School of Business, Co'18

I am very thankful to Gmatxchange and would definitely recommend Gmatxchange mentors to all those students applying for MBA admissions

Your Tentative GMAT Score
Estimate your GMAT score.
The scorer helps you to determine your current level within a few questions you solve.Read More
Please log in or register to use the Scoring Feature
Confused about your profile & colleges, Get FREE profile evaluation today from over 10 consultants.
Follow us and get quick prep updates on Facebook