Manipulating GMAT Equations

by on November 8th, 2010

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.

Cardinal Rule of Equations

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.

Tips for Minimizing 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 canceled out.

Same Expressions Written Differently

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.

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