What Math Skills Are Tested on the GMAT?

Start the year off strong by diving into your GMAT math prep with vigor (or renewed vigor, as the case may be.) The Quantitative section is often the most feared, but its content is predictable and conquerable. Brush up on the specific math skills that the exam tests and pair this knowledge with solid critical thinking to be successful.

Remember, the concepts presented here are the basics of what the GMAT tests. For advanced concepts and questions, the test-makers will build on the basics and use certain variations to make these more difficult.

[ RELATED: GMAT Quantitative Strategies ]

While arithmetic is foundational in grade school (and thus requires a great deal of review for many GMAT students), you must study the fundamentals as well as the more advanced concepts. The GMAT tests your ability to do the following:

• Manipulate fractions, decimals, and ratios (as well as convert among the three).
• Understand the properties and concepts of real numbers (such as odds and evens, integers, and multiples).
  
• Work with percentages.
• Calculate and manipulate exponents and roots.
• Understand and apply descriptive statistics (mean, median, mode, standard deviation).
• Understand and apply properties of sets (such as Venn diagrams).
• Know and apply various counting methods (including permutations and combinations).
• Understand, calculate, and analyze probability.

Several Quantitative questions you’ll encounter on GMAT Test Day will require the application of more than one of these topics. In arithmetic, there are several concepts and equations you’ll have to memorize.

Generally, the algebra you’ll encounter on the GMAT does not test you above a high school level. However, it has probably been several years since high school. These are the concepts you must review for the test:

• Manipulating algebraic expressions (isolating variables and solving for a variable).
• Solving equations (linear equations with one or more unknowns and quadratic equations).
• Solving and manipulating inequalities.
• Applying and solving functions.

Since the GMAT isn’t a high school equivalency exam, the test-makers added additional concepts that borrow heavily from the items above but add a real-life dimension to the concept.  The GMAT requires that you know a few more equations and concepts. However, at the base level, this is just an additional application of the concepts above. These additional applications include the ability to calculate the following:

• Interest (both simple and compound).
• Discounts and/or profits.
• Work and combined work problems.
• Rate and measurement problems.

While this list of what you need to know for GMAT math is comprehensive, it is not sufficient by itself. Since the GMAT doesn’t require a significant amount of outside knowledge, you’ll find these concepts presented in a manner that makes them far more difficult than they seem on paper. The only way to ensure you are prepared is to practice.

While geometry was removed from the GMAT, coordinate plane geometry is actually considered algebra—so coordinate plane can still appear on the exam.

Every line on a coordinate system can be expressed in the form y = mx + b where m is the slope and b is the y-intercept (that is, the point where the line crosses the x axis).

Be sure you are comfortable with the relationships between parallel and perpendicular lines in the coordinate plane. Lines that are parallel have the same slope; they continue at the same slope to infinity and never cross. A line that is perpendicular to another line has a slope that is the negative reciprocal (change the sign and flip the fraction) of the other line’s slope.

For example, y = 23x + 4 will be parallel to all other lines that share a slope of 23. A line that is perpendicular to y = 23x + 4 would have a slope of  -(1/23), which you find by changing the positive sign to a negative and taking the reciprocal of the fraction.

How To Turn Algebra Into Arithmetic on the GMAT

Algebra and arithmetic are very similar, but algebra uses variables where arithmetic would use real numbers. On certain GMAT problems, we can take a problem in which we were given variables and use real numbers instead “ we’re turning algebra into arithmetic”.

Recognize when you can turn algebra into arithmetic

First, we need to know when we can use this technique. It’s possible to use this technique when there are variable expressions in the answers. Variable expressions do use variables but do not contain an equals sign or an inequality sign. For example, x+3 is a variable expression; x+y = 3 is not a variable expression but a variable equation.

You can sometimes pick your own numbers even when a variable isn’t given in the problem “ for example, when the answers are in the form of fractions or percentages of something. In these problems, you’d have to introduce a variable (or variables) yourself in order to solve or you could just pick a real number. For instance, I could talk about the changing price of a TV set: first it goes up by 5% and then it goes down by 10%. And I might ask: what fraction of the original price is the new price? You can tell me that without knowing any real numbers! (In fact, you can tell me just based on the info I’ve given you in this paragraph.)

If they give you variable expressions in the answers, or if the problem keeps talking about some number but never gives you a real number for it, and the answers are in the form of a fraction or percentage of the original, then you may want to turn this problem into arithmetic.

Deciding whether to turn algebra into arithmetic

After we determine that we can use this method, we next have to decide whether we want to do so on this particular problem. There isn’t a one-size-fits-all answer to this question; different students will prefer different things. The very general rule is that you use algebra on problems that are easier (for you) and you use arithmetic on problems that are harder (for you). The particular line, though, is different for every student. So how do you decide?

You figure it out while you’re studying. From now on, every time you see a problem that can be done using this method, try it both ways “ the algebra and the arithmetic. Then decide which way was easier for you on this problem and, as specifically as possible, why. And how are you going to remember that for future? (Hint: drill, baby, drill!) Then, when you see a similar future problem, you’ll already have made the decision as to which method to use.

Turning algebra into arithmetic

Okay, so let’s do it, already! First, we see how many variables we have and whether we need to pick for all of them or whether some will be determined by others. For example, if a problem talks about a cell phone plan costing x cents per minute and Jamie talked for y minutes last month, then I’m going to pick for both of the variables in the problem. If, on the other hand, the problem tells me that x+y = a, then I know I’m only going to pick for x and y; after that, a will be determined.

Picking Numbers

Next, I’m going to be smart about picking my numbers. Full disclosure: the main drawback to this turn algebra into arithmetic method is that, if I’m very unlucky, I could happen to pick some number that will work for more than one answer choice. This can’t happen on every problem, but it can happen sometimes. I can reduce the chances to almost zero, though, if I’m smart about picking my numbers.

Don’t pick zero. Don’t pick one. Don’t pick a number that already shows up in the problem. Don’t pick a number that would result in a calculation that gives you that same number again. For example, a percentage problem asks you to reduce the price of a TV set by a certain percentage and then do something with the new price relative to the amount saved off of the original price. You probably don’t want to discount that TV set by 50%, because then both the amount saved and the new price are the same number!

Other than that, though, make your life as easy as you can. Pick small integers. If you need to pick more than one, choose numbers with slightly different characteristics “ an even and an odd, for instance. If a number needs to be divided at some point, pick something that will still give you an integer after you divide.

When you’re studying, go back over what numbers really worked well or really didn’t. How could you have known, before you started solving, that picking 2 on this one was probably not a great idea? Or, conversely, that picking 2 on this other one was a great idea?

Doing the Arithmetic

Okay, now you’ve got your real number or numbers. (You’ve written them down clearly on your scrap paper, along with your variables, right?) Now, do the arithmetic. Wherever the problem says x, you now use 2, and wherever the problem say y, you now use 3. When you’re done, you’ve got a numerical answer.

GMAT Algebra Practice Question

*Before being simplified, the instructions for computing income tax in country R were to add 2 percent of one’s annual income to the average (arithmetic mean) of 100 units of country R’s currency and 1 percent of one’s annual income. Which of the following represents the simplified formula for computing the income tax, in country R’s currency, for a person in that country whose annual income is I?

(A) 50 + I/200

(B) 50 + 3I/100

(C) 50 + I/40

(D) 100 + I/50

(E) 100 + 3I/100

Key Takeaways for Turning Algebra Problems into Arithmetic Problems on the GMAT

• You can turn algebra problems into arithmetic problems. The process is straightforward, though it does take practice to become efficient.
• Know how to choose between algebra and arithmetic “ and know that this is based on your individual level. When studying, try problems both ways to determine which way is best for you in different situations.

* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.