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Inequalities — Revision Notes

XAT · Quantitative Ability & Data Interpretation

Free Inequalities revision notes for XAT Quantitative Ability & Data Interpretation 2026 — key concepts, formulas, and definitions for quick revision.

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An infographic illustrating the different inequality symbols (>, <, ≥, ≤) and classifying them into 'strict' and 'slack' inequalities, along with examples of each.
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Revision Notes — Inequalities

Key concepts, formulas, and definitions from Inequalities for XAT Quantitative Ability & Data Interpretation preparation.

Key Topics to Revise

1

Basic Concepts and Definitions

  • Two real numbers or algebraic expressions related by >, <, ≥, or ≤ form an inequality
  • Strict inequalities use > or < signs, while slack inequalities use ≥ or ≤ signs
  • For any two real numbers a and b: either a = b, a > b, or a < b (only one can be true)
2

Properties and Transformations of Inequalities

  • Addition and subtraction of the same constant preserves inequality direction
  • Multiplication or division by positive constants preserves inequality direction
  • Multiplication or division by negative constants reverses inequality direction
3

Important Standard Inequalities

  • a² + b² ≥ 2ab (AM-GM for squares)
  • |a + b| ≤ |a| + |b| (Triangle inequality)
  • |a - b| ≥ ||a| - |b|| (Reverse triangle inequality)
4

Linear Inequalities

  • Linear inequalities have the form ax + b ⋈ 0 where ⋈ represents any inequality symbol
  • Solutions are ranges of values, not specific points
  • Graph solutions on number lines using open/closed circles

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Key Concepts

Inequalities use symbols > (greater than)Key rules includeInequalities of the form ax+b>0 (orInequalities of form ax²+bx+c>0 where solutionKey inequalities include

Frequently Asked Questions

What topics are covered in Inequalities for XAT?
Inequalities is an important chapter in XAT Quantitative Ability & Data Interpretation. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Concepts and Definitions, Properties and Transformations of Inequalities, Important Standard Inequalities, Linear Inequalities.
How important is Inequalities for XAT?
Inequalities is a frequently tested chapter in XAT Quantitative Ability & Data Interpretation. Questions from this chapter appear regularly in previous year papers. There are 53 practice questions available for this chapter.
How to prepare Inequalities for XAT?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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