GMAT Tip: Mastering Inequality Problems

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This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep.

Of all the types of math that appear on GMAT data-sufficiency problems, the type that tends to give students the greatest trouble is the inequality question, which makes use of  ”greater than” or “less than” signs.  Fortunately, three core pieces of knowledge can help you to attack inequality problems with a lot less difficulty.

Rule No. 1: When you multiply or divide by a negative, you must flip the sign.

Say that x > 4. This means that possible values of x include 5, 10, and 100. That means that possible values of -1(x) would include -5, -10, and -100—all numbers that are less than -4. As this demonstrates, if you multiply or divide by a negative, you must flip the sign.

Rule No. 2: When you’re asked to multiply or divide by a variable, you can’t do it unless you know whether you have to flip the sign.

This is the classic data-sufficiency application of the above. Most test-takers understand that they need to flip the sign when multiplying by a negative, but the test traps them by not indicating whether a variable is positive or negative. So if a statement tells you that a/b > 1, you don’t know that a > b. To determine if a > b, you multiply both sides by b. But if b were negative, you’d have to flip that “greater than” sign when you multiplied by b, resulting in “less than b.” When you see an inequality and a variable, your guard should immediately go up—the GMAT loves to trap people by tempting them to multiply or divide by a variable.

Rule No. 3: When you see multiple variables and an inequality, you should look to do some algebra.

Many test-takers approach inequality problems by thinking conceptually first, but a lot of inequality problems simply don’t lend themselves to that kind of thinking—there are just too many potential values to consider. So remember this handy technique: As long as the signs are pointed in the same direction, you can add inequalities together to eliminate a variable. For example, if you’re given:

x + 3y > 10

y – x > 2

You can add the inequalities together, which eliminates the x and –x terms, giving you:

4y > 12

y > 3

These questions can be extremely difficult to solve conceptually, but for those who know to employ algebra, the answers come much more readily.

Keep these principles in mind when you see GMAT inequality questions, and your score is much more likely to be greater than it is now.

Brian Galvin has studied the GMAT full time since 2006 as the director of academic programs for Veritas Prep. He received a Masters in Education from the University of Michigan and is the proud owner of a 99th percentile GMAT score.

For more GMAT advice from Veritas Prep, read “Mastering Inequality Questions on the GMAT”

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