Inequalities on the GMAT should be approached in the same way as regular equations. We can manipulate inequalities the same way that you can manipulate equations. As with equations on the GMAT, you first must simplify the equation in order to answer the question presented.
The title of this post is: Flipping the sign to inequalities. The only difference to simplifying inequalities compared to normal equations is the times when we have to flip the sign. There are two consistent times when we must always flip the sign:
- When we multiple by a negative number.
- When we divide by a negative number.
While these situations may seem straight forward, the GMAT has found fun ways to increase the difficulty. Let’s look at an advanced Data Sufficiency question:
1. Is ?
2) . If we calculate the equation, we see the answer is – which is mathematically correct. If we drop the base without flipping the sign, the inequality reads , which isn’t mathematically accurate.)
Thus, Statement 1 simplifies to: . Since , it is also greater than -4: Sufficient.
Let’s look at statement 2: Quadratics and inequalities are difficult when combined – the squared variable results in two possible solutions. For this example, a savvy test takers notices we can factor out from the equation. Translating this to and and . If we solve for in this situation, we get the outcome of . Is this possible? Yes! We can re-write this as and x< 0[/latex]) – don’t forget that binomials usually have two solutions!
Good luck as you practice with inequalities. This was a complicated post! Don’t worry if it doesn’t set in immediately. Print out this screen and read it a couple times – you’ll get it. This is just one of the advanced math topics included among the Kaplan GMAT math material in the newly revised course. If you’ve gotten beyond the intermediate questions and algebra topics, you may be ready to work through advanced topics like this in preparation for the toughest questions on test day.