Among the GMAT questions, inequalities make a really tricky set of questions. Whether you get the inequality concept as a Problem Solving (PS) or a Data Sufficiency (DS) question, the standard of the question is usually very high and the potential to make a mistake is high as well.

Often, there is a category of gmat inequalities questions that revolves around the powers of x. Specifically, the question is looking for some sort of comparison between the exponents and fractions of x. For example: x, x^{2}, x^{3}, x^{4}, 1/x, 1/x^{2} and so on. This article focuses on providing an approach to solve these kinds of problems. With practice this framework will become easier to implement.

After you have read through the tutorial and the framework, do not miss out on the challenge question.

The below video discusses the framework in detail with two solved examples for your practice. We have added some additional links for further gmat inequalities practice at the end of the post.

Framework:

Lay out the four critical ranges

x < -1

-1 < x < 0

0 < x < 1

x > 1

Observe which ranges apply to the question. If it is not clearly given, use all

The relationships amongst the terms are always the same within the ranges. To save time on questions, instead of deriving them again and again, practice and remember.

If you do not recall the relationships or are short of time, just take values in the ranges above.

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