Solve Gmat Inequalities “Comparisons” questions confidently with this framework

GMAT Inequalities comparisons powers of x

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, x2, x3, x4, 1/x, 1/x2 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.

GMAT question Remember the ranges: (x<-1, -1<x<0, 0<x<1 & x>1)

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.


  1. Lay out the four critical ranges
    • x < -1
    • -1 < x < 0
    • 0 < x < 1
    • x > 1
  2. Observe which ranges apply to the question. If it is not clearly given, use all
  3. 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.
  4. If you do not recall the relationships or are short of time, just take values in the ranges above.
  5. Apply the relationships to solve the question.

GMAT question

Tip: The relationship amongst the terms such as x, x2, x3, x4, 1/x, 1/x2 remains the same between the ranges. Rather than deriving the relationships again and again – Remember them.

The final relationship:

GMAT Inequalities Challenge Question:

QI2. Is 1/x4 > 1/x2 ?

a) 1/x > 1/x2

b) x2 > 7

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This is a DS question. Standard DS answer choices apply. Contact us if you have questions.

Read more on Inequalities

GMAT Inequalities: Practice Questions:

The two questions in the video: Q1 and Q2.

Other practice questions:

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