Manipulating equations is one of the most important skills for success on the GMAT quantitative section . You can be assured that you will see many problems on test day that require you to work with equations. While these problems can, at times, be solved using alternative strategies such as picking numbers and backsolving, you will also see problems in which the fastest path to the correct answer is to work through the algebra.

When dealing with algebra, always remember the cardinal rule of equations: what you do to one side you must do to the other. As long as you follow this rule you will always end up with mathematically true statements, even if they do not take you in the direction of the right answer. Thus, you can always backtrack through your steps and try another path. Just be careful with your math and make sure not to make any careless errors.

In order to minimize such errors, it is always a good idea to remove any fractions early on, because you will have an easier time working with integers. For the same reason, you should keep numbers positive when possible and always keep a look out for numbers that can be factored or cancelled out.

Lastly, if you arrive at an algebraic expression as an answer, but it does not match any if the choices, check to see if any of the options are the same expression written in a different way. This is most common when the result has a radical in the denominator. In these situations, multiply your answer by 1, writing 1 in a way that would eliminate the radical. For example, if you end up with 3/√3 multiply it by √3/√3, to arrive at (3√3)/3, if that helps you match an answer choice.

For more on this topic, including examples, see our Kaplan GMAT video on Equations.

Basic math content knowledge, such as the formula for the area of a triangle or the equation for calculating an average, is often the wolf in sheep’s clothing on the GMAT – test takers who lack proficiency in the basics find it very challenging to strategically approach questions in the Quantitative section.

In working with GMAT students, I have seen that learning the basic quantitative content areas and practicing how and when to apply them to test questions frees test takers to tackle Data Sufficiency and Problem Solving questions with greater confidence and speed. The best way to practice foundational math content is through drills and practice, first working basic problems that get you back in the habit of mathematical operations such as using the distributive property, dealing with fractions properly, and applying the rules of exponents and radicals. Even if you feel that you have a good understanding of one of these math content areas, it still pays to practice with it until the use of operations and rules becomes second nature.

As I always tell my students, you should practice, practice, practice, and then practice some more! Once you have refreshed your basic skills, you will be better primed to approach the complicated verbiage and the multi-step calculations that can create obstacles on the GMAT Quantitative section. Moving forward to test questions, you can flip through your mental files more quickly and pull up the math knowledge that you have practiced extensively and etched into your brain. It’s amazing how much faster a Data Sufficiency question goes when you recognize properties of systems of linear equations and can determine, aha!, if you have two distinct linear equations, you have enough to solve for the value of the two variables presented in the question stem! If the very phrase ‘linear equation’ makes your eyes cross, you are definitely a candidate for a refresher on the math content areas that the GMAT focuses on – Arithmetic, Algebra, and Geometry.

In this series of articles, we’ll cover the three main “pillars” of GMAT prep necessary for success on test day.  The first pillar is content, which encompasses the math and verbal skills necessary to answer the questions given to you on Test Day.  This is the factual stuff you HAVE to know when you walk in the door for the GMAT.  For example, a question like

“What is the area of a right triangle whose legs have lengths 3 and 4?”

Is literally unanswerable if you don’t know the formula for a triangle’s area (one-half base times height, for the record).  Other vital content areas tested on the GMAT include, organized by section:

Quantitative content areas:

Algebra (including Isolating a Variable, Systems of Equations, FOIL, etc.)
Geometry (including Triangles, Quadrilaterals, and Circles, with a little bit of solids and coordinate geometry)
Number Properties (including Positives/Negatives, Odds/Evens, Prime Numbers, Integers, etc)
Arithmetic  & Proportions (including Ratios, Rates, Percents,  Averages, etc)

Verbal content areas:

Grammar (for Sentence Correction)
Argument Analysis (for Critical Reasoning)

One of the first steps of successful GMAT prep is to assess your strengths and weaknesses in terms of content.  Maybe there’s a lot of writing required at your job, so your grammar is strong, or you have fond memories of geometry formulas but don’t know the first thing about argument analysis.  After identifying your current status with regard to GMAT content, you then must follow through and be willing to confront those areas that are a little rustier, or that you never learned in the first place.

But it is not enough to merely work your weaknesses tirelessly until Test Day.  As an illustration of this principle, the subject of probability comes to mind.  In my experience, a great many students are nervous about their ability to answer probability questions quickly and accurately, and rightfully so: the subject can be tested in many ways, and some of the GMAT’s hardest questions test knowledge of probability content.  However, I do not advise these students to concentrate many precious hours of study time to brushing up on probability, beyond gaining a general knowledge of the principles at hand.  Why?  Because however difficult it may be, even the highest-scoring test takers will not likely run into no more than 2 or 3 probability questions on Test Day, and so time is better spent mastering higher-yield topics, such as Algebra or Number Properties.

Thus, in terms of content, to really maximize your score, you have to find yourself an individual or organization who knows the GMAT inside and out to help you prepare and to use your preparation time efficiently.  Having someone over your shoulder, guiding you on what to cover next and how to allocate your prep time can really make a difference in the score you ultimately receive.

Stay tuned for Pillar #2: Strategy.