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GMAT Inequalities

by ejkiv


July 18, 2015


In many ways, GMAT inequalities are exactly like equations. However, before we go into solving for inequalities, let’s make sure we understand what exactly all of the symbols mean.

When looking at solving for inequalities, you can basically treat the inequality as an equal sign in all but 1 case, which we will cover shortly.

So, the following example can be solved exactly as you would before:

The one instance that you cannot solve as you would with an equation is when you are multiplying or dividing by -1. Here is the reason why: 3 < 4, but when multiplied by -1 you would get the expression -3 < -4, which is not true. In order to do this properly, you must flip the sign in the other direction. So, 3 < 4 would become -3 > -4.

This is how it would work when solving for x:

This most often will come around when you are dealing with variables in data sufficiency questions. While it may be tempting to cancel out variables, this can cause problems if you are not diligent. Take the following example:

ab > ac

You cannot simply cancel out the a, because the inequality will behave in a different manner depending on if a is positive or negative.

If a > 0, then b > c

but if a < 0, then b < c

This means all we know about a and c is that they are not equal. Be aware of these nuances when you are going through data sufficiency problems.

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