How to Solve Simple Math Equations on the GMAT

Many students who take the GMAT come from backgrounds that stressed mathematics. A significant percentage of GMAT test takers come from engineering backgrounds or other fields that require strong analytical skills. However, these students often find that the GMAT quantitative section is challenging for them. This is because the GMAT tests math in a way that is unfamiliar to these students, taking them out of their comfort zones and requiring them to solve questions in new and unfamiliar ways (most glaringly, without a calculator).

Students who were never very fond of math in high school (and even kindergarten) often struggle with the math on the GMAT, but this is somewhat expected. If you never liked a topic, you probably never spent hours thinking about it or doing exercises in your leisure time (think of people who dislike cardio). However, many students who traditionally excel at math struggle just as much as the students who never cared for the subject. This frustration can be even more pronounced when it’s about a topic you’ve traditionally excelled at over your life.

Delving into the topic a little, the GMAT does not allow you to have a calculator with you during the exam because the calculator is a crutch that will end up doing the work for you. Naturally, in every conceivable real world situation, you will have a calculator with you, but finding ways to get the correct answer is an important aspect of business. When a decision needs to be made in a split second, you cannot always reach for your calculator. Worse than that, a calculator is clearly faster and more accurate than you, but we cannot (yet) be replaced by computers because computers cannot think as humans do (#Skynet). If the goal of the GMAT was to ensure that all students could perform complex mathematical calculations, you’d have a TI graphing calculator attached to your arm. The goal of the exam is to make you think, and nothing mitigates independent thinking like a calculator.

So how does the exam test math if it won’t give you complex math? Basically by giving you simple math and expecting you to solve it quickly. Simple math does not necessarily mean small numbers. In fact, large, unwieldy numbers are a great way to validate that you understand the underlying concept rather than utilize a brute force approach to solve the problem.

Let’s look at a very simple math question that helps to underline the kind of math problems you should be able to execute quickly:

What is 1,800 / 2.25?
(A) 400
(B) 500
(C) 650
(D) 800
(E) 850

On the actual GMAT, you might only see this question if you’re scoring in the bottom quintile of the test. However, you can easily have a calculation such as this to execute as part of a larger problem. Either way, getting the correct answer on a question such as this should ideally take you 30 seconds or less.

There are many ways to get the correct answer here, and the method chosen has a lot to do with personal preference. As someone who is comfortable with mental math, I would immediately attempt to approximate this equation. If it were simply 1,800 / 2, the answer would be 900. Since 2.25 is bigger than 2, the answer must be a little smaller. This narrows the choice down to likely either D or E. Rounding 2.25 to 3 would yield a division with a quotient of 3, further cementing the elimination of answer choices A and B. However between 800 and 850, the choice is pretty close, so we might need a more precise approach.

One common strategy is to convert the decimal into a fraction. Using algebraic rules, this might simplify our math quite a bit. 1,800 / 2.25 is the same as 1,800 / (9/4). This equation might seem equally daunting, but remember that division is the same thing as multiplication, and dividing by 9/4 is the same as multiplying by 4/9 (this property holds for all numerators and denominators). If I turned this into 1,800 * 4/9, I can think of it as two separate steps: (1,800 * 4) / 9, or (1,800 / 9) * 4 (commutative property). The second is clearly much easier to process, and you end up with 200 * 4, or 800. The answer must thus be D and can be seen fairly cleanly using fractions.

You can also get the answer by using reverse-engineering. Simply put, an equation of 2.25 * x = 1,800 would yield the same x, so you can think of this equation as backwards. If x were 1, the product would be 2.25, which is clearly not the right answer. How can I get closer to the actual product? Well if I set x to be 4, then the product would be 9. From 9, I might be able to see that I could set x to be 40 and then 400, giving 90 and 900 respectively. Once I’m at 900, I simply double x (from 400 to 800) and get the correct answer. This strategy can be helpful for those who dislike division and prefer to work with multiplication.

Overall, it doesn’t matter which strategy you use (in fact you may use an entirely different approach and still get the correct answer. There is no “correct” strategy on the GMAT, only the Machiavellian notion that you must get the correct answer, by algebra, deduction, induction, strategic guessing or even dumb luck. Being able to solve math questions in roughly as long as it would take to solve if you had a calculator will help you realize why the tool is not allowed on the exam. In the best case, you can turn math on its ear and appreciate the nuanced way the GMAT tests your understanding of these fundamental concepts.

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.