Oh no it’s been years since you’ve thought about rate of motion! It doesn’t matter if you have an incredible intuition for math mind or if you feel a wave of dread every time you have to calculate a tip at a restaurant.
The math skills tested on the GMAT’s Quantitative section tend to be difficult for everyone. None of the math is terribly advanced, but that’s why it’s so hard. Studying for this test, you’ll undoubtedly encounter math you haven’t seen since middle or high school and you’ll go “Oh… Pythagorean theorem, I think I used to know what that is.”
The good news is that there’s a finite amount of math you really need to review in order to be prepared for the GMAT Quant section. However, since the math covered on this test is relatively low level, your real task while preparing for the test is understanding the challenging ways the GMAT asks you to apply this background knowledge.
By the time you’re done reading this article you’ll know exactly what math you have to review and get an idea of what sort of strategies you should be practicing while working through practice problems.
All the Concepts Tested on the GMAT Quantitative
Like I said, the math on the GMAT is not advanced. There’s barely any trigonometry, and there’s no calculus, stats, number theory, or anything else that you probably find intimidating. In theory, a high schooler who has completed Algebra 2 is prepared to take this test.
Memorize the following concepts and you’ll be well prepared for the Quant section. Chances are you already know most of these concepts, even if you feel like you don’t.
- Prime numbers
- Negatives: adding, subtracting, multiplying, dividing
- Fractions: adding, subtracting, multiplying, dividing
- Simplifying fractions and cross-reducing
- Number lines
Percents and probabilities
- Calculating percent change
- Calculating percent increase and decrease
- Discounts and sales tax
- Finding probability of a single case
- Finding probability of two cases
- D = RT
- Combined rate formula
- Algebraic manipulation
- Variable operations
- Perimeter and area of rectangles and squares
- Circumference and area of a circle
- Area of a triangle
- Pythagorean theorem and pythagorean triples
- Special right triangles
- Degree measures of a line, right angle, circle, semi-circle, and triangle
- Angle identities including: vertical angles, supplementary angles, interior alternate angles
- Formula for degree measure of a polygon
- Finding the slope of a line
- Identifying the (x,y) coordinates
- Identifying the y-intercept of a line
- Slope-intercept form
- Calculating length of a line segment
- Quadrants of a coordinate plane
Exponents and radicals
- Definitions of base and exponent
- Squares of 1 through 15
- Multiplying exponential numbers with the same base
- Dividing exponential numbers with the same base
- Raising a power to a power
- Negative exponents
- Exponent of 0
- Fraction exponent
- Reducing a radical to its simplest form
Problem Types on the GMAT Quantitative Section
There are two types of problems on the GMAT Quantitative section, problem solving and data sufficiencies.
Problem solving questions are the same type of multiple choice math questions you’ve seen on standardized tests your whole life. You solve the problem, find the answer choice that matches your own answer, and you’re done. We’ll come back to these later.
Dealing with Data Sufficiency Questions
Data sufficiencies are unique to the GMAT. Paradoxically, you should not solve data sufficiency questions. What in the world does that mean?
Well, your task with data sufficiency questions is to figure out if you have enough information to answer the question should you really want to In particular, there are only 2 types of DS questions – those that ask you a yes/no question, such as ‘is p a prime integer?’ . and those that ask you a numerical question, such as ‘What is Bill’s age?’ In both cases, if the information given is sufficient to answer the question, you can mark ‘sufficient’ without bothering to actually calculate!
DS questions always have the same 5 answer choices.
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
In order to complete the data sufficiency questions you first want to evaluate Statements 1 and 2 individually. When you’re evaluating if there’s enough information to make a judgement about Statement 1, ignore that Statement 2 exists. When you’re evaluating if there’s enough information to make a judgement about Statement 2, ignore that Statement 1 exists
Next, eliminate answer choices based on this evaluation. If Statement 1 alone is not sufficient, eliminate A and D (since they can’t each be alone sufficient if A isn’t sufficient, right?).
If you have eliminated A, B, and D, see if Statements 1 and 2 are sufficient together. If they are, C is your answer. If they are not, eliminate C and choose E.
And hopefully this much is obvious but memorize what all of the answer choices mean for data sufficiency questions. They will always be exactly the same, so you’ll be wasting a lot of time and mental energy constantly reminding yourself what the answer choices mean when you’re completing these problems. The best way to memorize them is to practice!
Key Strategies for the Quantitative Section
Since the GMAT is really testing critical thinking and problem solving capabilities, memorizing all of the the formulas and concepts that apply is only going to get you so far.
You’ll do a lot better on the GMAT going in with an arsenal of strategies, so let’s talk about the most popular (and trusty) ones that you can pick up.
As always — sorry to sound like a broken record here — the only way to make these strategies second nature is to practice them a ton.
The Mother of All Strategies: Plugging in Numbers
You will mainly be confronted with algebra on this test. One of the keys to success on the GMAT is realizing that if an equation is true, it is true for any number you plug into it. When you see the variable X it’s not just some abstract concept, it’s something that has a constant value.
For instance, if you have a problem solving question that says a TV is on sale for 40% off and you have to pay 5% sales tax, and the question doesn’t provide a price for the TV, just pick a price. If I say the TV costs $100, then I know it’s on sale for $60 and will cost $63 after tax. That’s pretty easy.
Generally 100 is a good number to pick for percent problems, but the general idea is to pick numbers that are easy to work with.
Plugging in numbers is a very useful way to evaluate data sufficiency problems. For those, you may want to try multiple numbers. For instance, if the question is asking if x will be negative, then make sure to try both a positive and a negative number.
Work Backwards (Plugging in Answer Choices)
This is similar to the last strategy, but only works on problem solving questions. If you ever have a question which basically asks “which of the following would be a solution to this problem,” just plug in the answer choices until you find the one that works.
There are countless opportunities to estimate on the GMAT, and that’s intentional. Part of critical thinking is knowing when and how to take shortcuts, so the people who write the GMAT rewards test takers who know when to estimate.
If you’re about to do some complex calculation, always ask yourself if there’s a simpler way. For example, it’s pretty hard to find 37% of some number, but 33% is basically a third, so you know that your new number will be roughly a third of the original, but a little higher.
Estimate as often as possible, since it will often save precious time and brain power that you would have spent crunching numbers. You’ll need all of the spare seconds and energy you can get to really plunge into the questions where you can’t estimate, so save yourself a little effort early on.
Use the Distributive Property
Remember this old thing? You probably learned it in 5th grade or so.
The idea here is that you can solve pretty complex arithmetic by breaking numbers down into chunks that are easier for you to calculate quickly. I always calculate a 15% tip by finding 10% of my dinner bill and then cutting that amount in half, then adding the two amounts together. So if my dinner cost me $22, then 10% of that is $2.20, 5% is $1.10, and therefore 15% is $3.30.
Let’s see an example of the distributive property in action on a harder problem. What’s 197 times 54? Well 197 is really 200 – 3, so we can just calculate 3 times 54 and subtract it from 200 times 54, which is much easier than calculating 197 times 54. (Btw this is 10,800 minus 162, or 10,638).
Getting in the Math Mindset
Well, those are all tips for what you can do on test day, but what can you do to get yourself in the right frame of mind of all of this stuff to start making sense? Since you’re probably not used to thinking in a mathematical way, put in some work to get into that headspace.
Work Out the Right Side of Your Brain
Knowing math cold is what your left brain is for. That’s the one that does all of your analytical thinking and rule following. What you’ll need is to do is get creative.
The GMAT Quant section rewards creative approaches to these problems. Often times, you’ll find that if you dive right into a problem and start applying a formula, you’ll do a ton of work and still not get an answer.
What can you to work out the right side of your brain? Read literature, listen to music and pick out what your favorite instruments are doing, play logic games like chess or sudoku, improvise some ingredients while cooking dinner, and so on. Do things that take some creativity and are fun. You’ll find yourself picking up on the patterns in the test questions a lot easier soon enough.
Keep a Journal of Math Questions with Alternate Solutions
As you’re working through prep books like the official GMAT guide, you’ll be reading through answer explanations and will constantly see explanations that give two ways to do a problem.
Take some notes about each of these questions, regardless about whether you got them right or wrong. The more time you spend meditating on new ways to do problems, the easier it will come to you.
And once you have a journal full of them, circle back to some earlier questions and see if the alternate way of finding a solution is one you see quicker now. Hopefully after focusing on those alternate solutions enough, you’ll start completing problems in those creative ways yourself.