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Formula Sheet

Inequalities — Formula Sheet

CAT · Quantitative Aptitude

Free Inequalities formula sheet for CAT Quantitative Aptitude 2026 — all important formulas, equations, and constants for quick reference.

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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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Formula Sheet — Inequalities

Important formulas and equations from Inequalities for CAT Quantitative Aptitude.

Formulas — Inequalities

Basic Properties and Definitions

a > b means a - b > 0
If a > b, then a ± c > b ± c
If a > b and c > 0, then ac > bc
If a > b and c < 0, then ac < bc

Important Standard Inequalities

a² + b² ≥ 2ab
AM ≥ GM: (a + b)/2 ≥ √(ab)
|a + b| ≤ |a| + |b|
a/b + b/a ≥ 2

Linear Inequalities

ax + b > 0 → x > -b/a (if a > 0)
ax + b > 0 → x < -b/a (if a < 0)

Quadratic Inequalities

ax² + bx + c > 0, D = b² - 4ac
D < 0: Always same sign as 'a'
D = 0: Same sign as 'a' except at x = -b/2a
D > 0: Sign changes at roots

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Frequently Asked Questions

What topics are covered in Inequalities for CAT?
Inequalities is an important chapter in CAT Quantitative Aptitude. 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 CAT?
Inequalities is a frequently tested chapter in CAT Quantitative Aptitude. Questions from this chapter appear regularly in previous year papers. There are 53 practice questions available for this chapter.
How to prepare Inequalities for CAT?
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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