Order of Operations: The Key to GMAT Arithmetic

March 14, 2011
Bret Ruber

When a straightforward arithmetic problem appears on the GMAT, many test-takers treat it as a break from the more complicated problems that are on the GMAT.  While arithmetic problems are often not as complicated as many of the other problems on the test, you should still be careful not to make careless math errors.  The most common cause of such errors is a mistake in the order of operations.

PEMDAS

Operations in an arithmetic problem need to be completed in a specific order.  The best way to remember is via the acronym PEMDAS, which stands for parentheses, exponents, multiplication, division, addition and subtraction.  Regardless of the actual order of the operations listed in the problem, they should always be completed in this order.

PEMDAS in Action

To see why order of operations is so important, let’s consider the following two expressions:

(5 – 3) + 4 x 6 ,

and

5 – (3 + 4) x 6.

 

Simplifying the first yields:  (5 – 3) + 4 x 6 = 2 + 4 x 6 = 2 + 24 = 26

Simplifying the second yields:  5 – (3 + 4) x 6 = 5 – 7 x 6 = 5 – 42 = -37

Notice that all that changes between these two problems is the placement of the parentheses, but the results are completely different.  The wrong answer choices on the GMAT will often be based on mistakes in order of operations, so it is essential to always follow the correct order in order to achieve the highest possible score.


Bret Ruber Bret has been teaching for Kaplan since 2005, and has helped over 1000 students with their GMAT preparation. He spent three years teaching in Manhattan, where he served as an Elite Teacher and a full-time instructor, before moving to London, where he is now the GMAT Master Teacher for Kaplan’s London Center. As the GMAT Master Teacher, Bret trains, observes and mentors teachers, in addition to continuing his own teaching and tutoring, and has taught courses across Europe, including Italy, Ireland, and Germany. Bret contributes to Kaplan’s GMAT curriculum on an on-going basis, and was also a contributor to Kaplan's 2010 GMAT course.



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