Modulus Function Practice Questions for CAT 2026 — Set 1 with Solutions

Introduction

Tackling the Common Admission Test (CAT) can be an intimidating endeavor, particularly when it involves mastering quantitative aptitude. A crucial concept that often appears in the exam is the modulus function. Grasping how to handle modulus questions is vital for achieving a high score in this section.

Modulus Function Questions for CAT 2026

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Frequently Asked Questions — Modulus Function for CAT 2026

What is the modulus (absolute value) function?

|x| = x if x >= 0, and |x| = -x if x < 0. For example, |5| = 5 and |-3| = 3. The modulus function always gives a non-negative output regardless of the sign of the input.

How is the modulus function tested in CAT 2026?

CAT tests modulus in equations like |x-3| = 5 (split into two cases), inequalities like |2x+1| < 7, and modulus of expressions like |x²-4|. Questions often require careful case analysis for each sign change point.

How many case splits do I need when solving modulus equations?

Each modulus expression |f(x)| requires splitting at f(x)=0. A question with two modulus terms like |x-2| + |x+3| = 7 requires 3 intervals: x<-3, -3<=x<2, and x>=2. Check each interval and verify solutions.

What is the triangle inequality for modulus?

|a+b| <= |a| + |b|. This is called the triangle inequality and appears in advanced CAT questions involving optimization or range of modulus expressions. Equality holds when a and b have the same sign.

How do I solve |ax + b| < c type inequalities?

For |ax+b| < c (where c>0): solve -c < ax+b < c, which gives (-c-b)/a < x < (c-b)/a (adjust inequality direction if a<0). For |ax+b| > c: solve ax+b > c OR ax+b < -c separately.

What are the most common mistakes when solving modulus questions?

Common mistakes: forgetting to check which interval a solution belongs to, not verifying solutions in the original equation, missing cases when the expression inside the modulus is negative, and incorrect sign flipping when a<0.

How many modulus questions typically appear in CAT?

CAT typically has 1–2 modulus questions per year in the QA section. They are considered medium-to-hard difficulty. However, modulus also appears implicitly in functions and inequalities, making it a high-value topic to master.

How should I practice modulus questions for CAT?

Master the case-split method first. Practice 10 basic modulus equations, then 10 modulus inequalities, then 10 combined problems. Focus on questions with two or more modulus terms, as these are most common in CAT.

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Frequently Asked Questions — Modulus Function for CAT 2026

What is the modulus (absolute value) function?

|x| = x if x >= 0, and |x| = -x if x < 0. For example, |5| = 5 and |-3| = 3. The modulus function always gives a non-negative output regardless of the sign of the input.

How is the modulus function tested in CAT 2026?

CAT tests modulus in equations like |x-3| = 5 (split into two cases), inequalities like |2x+1| < 7, and modulus of expressions like |x²-4|. Questions often require careful case analysis for each sign change point.

How many case splits do I need when solving modulus equations?

Each modulus expression |f(x)| requires splitting at f(x)=0. A question with two modulus terms like |x-2| + |x+3| = 7 requires 3 intervals: x<-3, -3<=x<2, and x>=2. Check each interval and verify solutions.

What is the triangle inequality for modulus?

|a+b| <= |a| + |b|. This is called the triangle inequality and appears in advanced CAT questions involving optimization or range of modulus expressions. Equality holds when a and b have the same sign.

How do I solve |ax + b| < c type inequalities?

For |ax+b| < c (where c>0): solve -c < ax+b < c, which gives (-c-b)/a < x < (c-b)/a (adjust inequality direction if a<0). For |ax+b| > c: solve ax+b > c OR ax+b < -c separately.

What are the most common mistakes when solving modulus questions?

Common mistakes: forgetting to check which interval a solution belongs to, not verifying solutions in the original equation, missing cases when the expression inside the modulus is negative, and incorrect sign flipping when a<0.

How many modulus questions typically appear in CAT?

CAT typically has 1–2 modulus questions per year in the QA section. They are considered medium-to-hard difficulty. However, modulus also appears implicitly in functions and inequalities, making it a high-value topic to master.

How should I practice modulus questions for CAT?

Master the case-split method first. Practice 10 basic modulus equations, then 10 modulus inequalities, then 10 combined problems. Focus on questions with two or more modulus terms, as these are most common in CAT.