Magoosh is the leader in GMAT prep, helping millions of students study since 2010. Our affordable self-study plans include 800+ practice questions, full-length practice tests, and a 70 point score improvement guarantee.

Essential GMAT Algebra Formulas and Practice Questions

Mike MᶜGarry

June 5, 2024

GMAT Algebra

This post was updated in 2024 for the new GMAT.

What are the most essential topics of algebra that you need to know to succeed in GMAT math? How many formulas and equations do you have to memorize? Why must we be tortured by all this math???

The good news is that it doesn’t take a huge amount of time or energy to master the basics. Most likely, you already have the fundamentals down.

Of course, it never hurts to review, so you might want to check out these first: Introduction to Algebra and FOIL on the GMAT: Simplifying and Expanding.

This post is intended to help you gain the edge if you already have a solid foundation. By recognizing and taking advantage of some common algebraic expressions or patterns, and by remembering rather than memorizing.

Three Essential Formulas for GMAT Algebra
GMAT Algebra Practice Problems
- Problem Solving Questions
Three Essential Formulas for GMAT Algebra

Here are two algebraic equations and one formula that you should remember for the GMAT Quant section.
1. Difference of Two Squares: \(a^2 – b^2 = (a-b)(a+b) \)
2. Squaring a Binomial: \((a \pm b)^2 = a^2 \pm 2ab + b^2 \)
3. The Discriminant: \(D = b^2 – 4ac \)
There is a common theme among the three items. In one way or another, they all have something to do with quadratic expressions. These tend to be more difficult to work with than linear equations, simply because the tools look more complicated.

Using the Patterns

The first two items in the list pertain to factoring—you can check out this post for more on that topic: Algebra on the GMAT: How to Factor.

The idea is that you can replace the expression on the left of the equals sign by the one on the right, and vice versa. This technique is often used in simplifying algebraic expressions. The practice problems below will also help you to understand when to use this strategy. The third item, the discriminant, is a powerful tool to help analyze the roots of quadratic equations without ever having to find the roots explicitly.

To see these concepts in action, check out our lesson videos on Factoring – Rational Expressions and Quadratic Equations.

GMAT Algebra Practice Problem

Now let’s see if we can apply what we learned to the following GMAT Quant question!

Problem Solving Questions
1. What is the largest integral value of \(m \) such that the quadratic equation \(x^2 – 10x + m \) will have two unique solutions?
A. \(23 \)
B. \(24 \)
C. \(25 \)
D. \(26 \)
E. \(27 \)

Click here for the answer

B.

This question is made for the discriminant! You won’t have to guess and check if you know how to use the formula appropriately. To find \(D \), plug in the following to the formula:

\(a = 1 \)
\(b = -10 \)
\(c = m \)

\(D =\) \(b^2\)\( – 4\)\(a\)\(c\)
\(D =\) \((-10)^2\) \(- 4\)\((1)\)\((m)\) \(= 100 – 4m \)

Now, we know that we’re looking for two real solutions, so we want \(D = 100 – 4m > 0 \).

\(100 – 4m > 0 \implies 100 > 4m \implies 25 > m \)

So, we get \(m < 25 \). Be careful NOT to choose 25 as your answer! The largest integer that is less than 25 would be 24.
Final Thoughts

GMAT algebra questions do not have to be intimidating. Linear and quadratic expressions and their close relatives make up the bulk of the material that you need to know. By mastering the three essential formulas mentioned above, you will be well on your way to Complete GMAT Domination!

If you’re looking for more GMAT algebra practice, check out our FREE GMAT practice test with accurate score prediction and subject-by-subject performance breakdown. You can practice a single section like Math, Data Insights, or Verbal for 45 minutes or take the whole assessment for 2 hours and 15 minutes. Give it a try!
Author
- Mike MᶜGarry
  
  Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as “member of the month” for over two years at GMAT Club. Mike holds an A.B. in Physics (graduating magna cum laude) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike’s Youtube video explanations and resources like What is a Good GMAT Score? and the GMAT Diagnostic Test.
  
  View all posts
More from Magoosh
Share
Tweet
Pin

Please leave any questions or suggestions in the comments, we try our best to respond within a few days!
Your email address will not be published.

10 responses to “Essential GMAT Algebra Formulas and Practice Questions”

Hannah

November 8, 2018

The answer to Question 3 doesn’t make sense to me. Isn’t OC equal to OD since it’s a circle and O is in the center?

Reply
1. Magoosh Test Prep Expert
  
  November 13, 2018
  
  Hi Hannah!
  
  This is a great question. 🙂 Remember – Data Sufficiency diagrams aren’t drawn to scale. Because the length is not explicitly stated, we can’t assume anything about the length of OD even though we have a circle and O is in the center. Therefore, we can’t say that OC is equal to OD. 😀
  
  Reply
Chayce

December 7, 2017

I’m probably missing something here, but before I looked up the answer to problem 1, I worked the problem a different way…probably incorrectly, but I’m not sure why yet.

If we change the first binomial to equal c^2 = 117 – b^2, and then we use that new value to plug into the second given binomial (a^2 + c^2), we get a^2 + (117 – b^2) = 0. So continuing, we move over the “117” to the other side:

a^2 – b^2 = -117

which, factored, looks like:

(a + b)(a – b) = -117

But even before factoring, it looks like the answer to the question is “-117”, without using either of the prompts; obviously, I must be breaking some rule here…maybe setting the equation equal to “0”.

Anyhow, assuming that I must move on the prompts, the first one provide helpful info:

a – b = 3

We can plug this into our factored equation:

(a + b)3 = -117 Divide both sides by 3

a + b = -39 Use prompt one equation to solve for b: (a = 3 + b)

(3+b) + b = -39 Simplify

b = -18 Use to Solve for a

a = -15

Obviously, these don’t satisfy our given given equations, but could you help me figure out where I’ve gone wrong? I assume it has to do with 1) using the stated info : a, b, c are not negative numbers, and 2) trying to combine the given binomials in the way that I did, setting them equal 0.

Any help would be most appreciated; and thanks for all y’all do!

Reply
1. Magoosh Test Prep Expert
  
  December 8, 2017
  
  Hi Chayce,
  
  You hit the nail on the head here–the issue with your response is the fact that you set the equation equal to “0”. We can’t make assumptions like this on the GMAT. We don’t know what this expression is equal to ‘0’ (which is why we set a^2+c^2 equal to X, an unknown variable, in our explanation for this question). It looks like your other problems-solving instincts are OK in methodology (at least, I don’t see anything else strictly ‘illegal’ in your calculations), though as you pointed out they don’t provide you with an answer to the question. It’s difficult to be able to ‘see’ the path forward in questions like this, which is why it’s useful to really study the answers that we give for difficult DS questions–they can help you to understand how to manipulate these questions in a useful (and legal) way 🙂
  
  Reply
Chris

December 6, 2015

Hello,

In the first practice problem we have b^2 + c^2=17.
If we combine the two statements we end up with two equations: a-b=3 and a+b=21. Instead of finding the difference of two squares formula we can use the strategy of elimination(or linear combination) for the aforementioned equations. Thus, a=12 and b=9.
If we substitute b in the initial equation b^2 + c^2=17 => c^2= -64. Nothing on the number line can be squared to yield a negative number. Am i wrong?

Reply
1. Phuong
  
  October 19, 2016
  
  I’ve got the same result. c is impossible here since it is stated that a, b, and c are positive integers. So since we are not able to find out c, E should be the correct answer.
  
  Still, the method makes it seems like we have the right answer.
  
  Reply
  1. Magoosh Test Prep Expert
    
    October 20, 2016
    
    Chris and Phoung, it looks like you’re both right that c is an impossible value, which would make E the correct answer after all. However, a “hidden trick question” where the final answer is incalculable due to a negative square is not the sort of thing that you’d see on a real GMAT data sufficiency question. So Mike’s proposed strategy for this question is basically right, in the sense that it would work on the GMAT itself. But the format of the question and the answer to the question are indeed wrong. Thanks for bringing this to our attention, Chris and Phuong. I’ll mention this error to our Content Improvement Team, so they can update the post with a better, more correct initial practice problem.
    
    Reply
Brittany

August 15, 2013

Hello,

Just wondering if there are supposed to be multiple choice answers for all the practice problems? In the solutions section, with the Answer = A, etc, seems to indicate this, but as far as I can see, the only question that has multiple choice answers is #4. Am I missing something here?

Thanks.

Reply
1. Mike
  
  August 16, 2013
  
  Brittany,
  Yes, you are missing something big, in terms of GMAT math. Questions #1-3 are what are called Data Sufficiency questions, which comprise approximately half of the questions on the GMAT Quant section. I’ll recommend these two links to start:
  https://magoosh.com/gmat/2012/introduction-to-gmat-data-sufficiency/
  https://magoosh.com/gmat/2013/gmat-data-sufficiency-tips/
  I don’t know how far along you are in your GMAT prep, but in addition to learning all the math, it is crucial for success on the GMAT to master the Data Sufficiency question format.
  Does this make sense?
  Mike 🙂
  
  Reply
  1. Daniel
    
    September 16, 2015
    
    Hello,
    
    I think the issue is that those people who are practicing the GRE get linked to here and then the answers aren’t provided in the same format which confuses us. For the GRE it’s usually multiple choice or fill in the blank after all.
    
    Reply

Essential GMAT Algebra Formulas and Practice Questions

Table of Contents

Three Essential Formulas for GMAT Algebra

Using the Patterns

GMAT Algebra Practice Problem

Problem Solving Questions

Final Thoughts

Author

Leave a Comment

Leave a Reply Cancel reply

10 responses to “Essential GMAT Algebra Formulas and Practice Questions”

Essential GMAT Algebra Formulas and Practice Questions

Table of Contents

Three Essential Formulas for GMAT Algebra

Using the Patterns

GMAT Algebra Practice Problem

Problem Solving Questions

Final Thoughts

Author

More from Magoosh

Leave a Comment

Leave a Reply Cancel reply

10 responses to “Essential GMAT Algebra Formulas and Practice Questions”