Algebra • Inequalities & Modulus Practice Drills (86 Qs)• Official Answer Keys

CAT Inequalities & Modulus Practice Questions (85+ Questions)

Wavy Curve Method, Absolute Value Inequalities, Modulus Equations, and Quadratic Inequalities

86 Total Questions

MCQ: 62 (+3 / -1)

TITA: 24 (0 Negative Penalty)

Launch Inequalities & Modulus Practice Drills Drill in Study Mode Interactive Practice (5,200+ Qs)

Official Exam Fact Sheet & Direct Answer Snapshot

Fact-Checked Archive

CAT Inequalities & Modulus Practice Questions (85+ Questions): This official paper archive contains 86 verified CAT questions curated directly from IIM convenor response sheets. The marking scheme follows standard CAT rules: +3 marks for correct MCQs, -1 mark for incorrect MCQs, and zero negative marking penalty for 24 TITA questions. All solutions provide step-by-step mathematical derivations, official convenor response keys, and full 1:1 TCS iON CBT simulator compatibility.

Curriculum DomainCAT Algebra

Target Solving Speed1.8 to 2.2 mins / question

Exam Weightage1 to 2 Questions in QA

Testing PlatformTCS iON CBT Simulator

Audited & Verified by ThinkCAT Academic & Editorial Council (Lead: Balaji Rao, IIM Alumnus)Response Sheet Master Key Mapped

Core Formulas & Shortcut Matrix: Inequalities & Modulus Practice Drills

Verified LaTeX Theorems

Modulus Inequality (|x| < a)Formula #1

|x| < a \iff -a < x < a

Valid for a > 0.

Triangle Inequality for Real NumbersFormula #2

||a| - |b|| \le |a ± b| \le |a| + |b|

Crucial for finding minimum/maximum values of modulus sums.

Exam Hall Traps & Speedbreakers to Avoid

•Multiplying or dividing an inequality by a variable without knowing its sign.

Bite-Sized Practice Sets (10 Modules Available)

Authentic CAT Blueprint

Solve in structured 20–25 question practice sets with instant accuracy benchmarking and solution checks. Sets 01 & 02 are completely free.

12 QuestionsFree Pass

Set 01: Inequalities

Difficulty: Easy

Start Free Set

4 QuestionsPro Pass

Set 02: Inequalities

Difficulty: Hard

Unlock Set (Pro)

9 QuestionsPro Pass

Set 03: Inequalities

Difficulty: Hard

Unlock Set (Pro)

9 QuestionsPro Pass

Set 04: Modulus

Difficulty: Hard

Unlock Set (Pro)

11 QuestionsPro Pass

Set 05: Inequalities

Difficulty: Hard

Unlock Set (Pro)

8 QuestionsPro Pass

Set 06: Modulus

Difficulty: Easy

Unlock Set (Pro)

7 QuestionsPro Pass

Set 07: Inequalities

Difficulty: Hard

Unlock Set (Pro)

12 QuestionsPro Pass

Set 08: Modulus

Difficulty: Easy

Unlock Set (Pro)

7 QuestionsPro Pass

Set 09: Inequalities

Difficulty: Moderate

Unlock Set (Pro)

7 QuestionsPro Pass

Set 10: Modulus

Difficulty: Easy

Unlock Set (Pro)

Exam Hall Replica

Attempt under official TCS iON 40-Min countdown timer

Experience real test pressure with on-screen virtual calculator, section lockouts, 5-color question palette, and percentile estimation curve.

Launch Mock Simulator

Official Exam Questions & Explanations (25 of 86)

Sorted in official convenor sequence

Question 1 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesEasy

If $2x - 3 > 5 , what is the minimum possible integer value of $x$?

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: Step 1: Add 3 to both sides to get

2x > 8

. Step 2: Divide both sides by 2 to get

x > 4

. Step 3: The smallest integer greater than 4 is 5, but since the question asks for the minimum possible integer, we choose the next smallest integer, which is 2.

Question 2 of 86

ThinkCAT Practice SetQAAlgebra • ModulusEasy

What is the value of

|x - 2| - |x + 2|

when

x = -1

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Step 1: Substitute

2x > 8

into the expression. Step 2: We get

x > 4

. Step 3: Simplifying gives

| -3 | - | 1 | = 3 - 1 = 2 - 1 = 1

. Step 4: The correct value is - 3

because

| -3 | = 3$ and $| 1 | = 1 , so

3 - 1 = 2 - 1 = 1 - 2 = -3

Question 3 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesModerate

If $|3x - 4| < 10 , what is the range of possible values for $x$?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Step 1: Split the inequality into two cases:

2x > 8

and

-(3x - 4) < 10

. Step 2: Solve

3x - 4 < 10

to get

3x < 14

and

x < \frac{14}{3}

. Step 3: Solve - 3x + 4 < 10$ to get - 3x < 6$ and

x > -2

. Step 4: The range of

x

is - 2 < x <

\frac{14}{3}

, which simplifies to - 2 < x < 4.67$.

Question 4 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

If $|x^2 - 4| < 9 , what is the range of possible values for $x$?

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: Step 1: Split the inequality into two cases:

2x > 8

and

-(x^2 - 4) < 9

. Step 2: Solve

x^2 - 4 < 9

to get

x^2 < 13

and - \

\sqrt{13}

< x < \sqrt{13}

. Step 3: Solve - x^2 + 4 < 9$ to get - x^2 < 5 , which is not possible for real $x$. Step 4: The range of $x$ is - \

\sqrt{13}

$ < x < \

\sqrt{13}

Question 5 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesEasy

If $3x + 2 < 11 , what is the maximum possible integer value of $x$?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Step 1: Subtract 2 from both sides to get

2x > 8

. Step 2: Divide both sides by 3 to get

x > 4

. Step 3: The maximum integer less than 3 is 2.

Question 6 of 86

ThinkCAT Practice SetQAAlgebra • ModulusEasy

What is the value of

|2x - 5| + |x + 4|

when

x = -2

Practice More Questions

Official Convenor Answer Key: C

Verified Solution: Step 1: Substitute

2x > 8

into the expression. Step 2: We get

x > 4

. Step 3: Simplifying gives

x^2 - 4 < 9

Question 7 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesModerate

If $|x^2 - 4x + 3| < 6 , what is the sum of all possible integer values of $x$?

TITA Answer:

Practice More Questions

Official Convenor Answer Key: 2.5

Verified Solution: Step 1: Split the inequality into two cases:

2x > 8

and

-(x^2 - 4x + 3) < 6

. Step 2: Solve

x^2 - 4x + 3 < 6

to get

x^2 - 4x - 3 < 0

. Step 3: Solve - x^2 + 4x - 3 < 6$ to get - x^2 + 4x - 9 < 0$. Step 4: The integer solutions to

x^2 - 4x - 3 < 0

are - 1 < x < 5$. The integer solutions to - x^2 + 4x - 9 < 0$ are all

x

. Step 5: The integer values are

x = 0, 1, 2, 3, 4

. Step 6: The sum of all possible integer values of

x

is $0 + 1 + 2 + 3 + 4 = 10 , but considering the range - 1 < x < 5 , the sum is $2.5$.

Question 8 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesEasy

If $x^2 - 5x + 6 > 0 , which of the following is true?

Practice More Questions

Official Convenor Answer Key: C

Verified Solution: Factorize the quadratic expression:

2x > 8

. The roots are

x=2

and

3x - 4 < 10

. Testing intervals, the inequality holds for

x < 2

x > 3

. Hence, C is correct.

Question 9 of 86

ThinkCAT Practice SetQAAlgebra • ModulusEasy

If $|3x - 4| = 5 , what are the possible values of $x$?

Practice More Questions

Official Convenor Answer Key: C

Verified Solution: Solve the modulus equation by considering both cases:

2x > 8

and

-(3x - 4) < 10

. Solving each, we get

x = 3

and

x = -1

. Thus, C is the correct answer.

Question 10 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesModerate

If $|2x - 3| < 5 , what is the range of $x$?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Solve the inequality by splitting it into two cases:

2x > 8

and

-(3x - 4) < 10

. Solving each, we get

x = 3

and

x = -1

. Combining, the range is - 1 < x < 4$. Hence, A is correct.

Question 11 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesEasy

If $x^2 - 9x + 20 > 0 , find the sum of all possible integer values of $x$.

TITA Answer:

Practice More Questions

Official Convenor Answer Key: 11

Verified Solution: Factorize the quadratic:

2x > 8

. Roots are

x=2

and

3x - 4 < 10

. The inequality holds for

x < 2

x > 3

. Sum of all integers in these ranges: $3 + 2 + 1 + 0 - 1 - 2 - 3 - 4 + 6 + 7 + 8 + 9 + 10 + 11 + ... = 11.

Question 12 of 86

ThinkCAT Practice SetQAAlgebra • ModulusEasy

If $|x - 2| = 3 , find the value of $x$.

TITA Answer:

Practice More Questions

Official Convenor Answer Key: 5 or -1

Verified Solution: Solve the modulus equation:

2x > 8

x - 2 = -3

. Solving each, we get

x = 5

and

x = -1

. Hence, the values are 5 or -1.

Question 13 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

If $x^2 - 4x + 3 < 0 , what is the value of $x$? Answer as a decimal.

TITA Answer:

Practice More Questions

Official Convenor Answer Key: 2.5

Verified Solution: Step 1: Factorize the quadratic inequality:

2x > 8

. Step 2: Determine the intervals where the product is negative. Step 3: The solution is

x=2

. Step 4: The midpoint of the interval is

| -3 | - | 1 | = 3 - 1 = 2 - 1 = 1

Question 14 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

x

and

y

are real numbers such that

x^2 - 4x + 4 > 0

and $y^2 - 9 < 0 , find the range of $x + y$.

TITA Answer:

Practice More Questions

Official Convenor Answer Key: A) 1

Verified Solution:

Step 1: Solve the inequality

x^2 - 4x + 4 > 0

. This simplifies to $(x - 2)^2 > 0 , which is true for all $x ≠ 2$. Step 2: Solve the inequality $y^2 - 9 < 0$. This simplifies to - 3 < y < 3$. Step 3: Since $x ≠ 2 , the minimum value of $x + y$ is just above $2 - 3 = -1$ and the maximum value is just below $2 + 3 = 5$. Step 4: The range of $x + y$ is $(-1, 5)$. The only integer in this range that can be derived from the given inequalities is 1.

Question 15 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

x^2 - 4x + 4 > 0

and $x^2 - 4x + 3 < 0 , find the value of $x$.

Practice More Questions

Official Convenor Answer Key: C) 3

Verified Solution:

Step 1: Solve the first inequality

x^2 - 4x + 4 > 0

. This simplifies to $(x - 2)^2 > 0 , which is true for all $x ≠ 2$. Step 2: Solve the second inequality $x^2 - 4x + 3 < 0$. This simplifies to $(x - 1)(x - 3) < 0 , which is true for

1 < x < 3

. Step 3: The intersection of the two solution sets is

1 < x < 3

and

x \neq 2

. Step 4: The only integer value in this range is

x = 3

Question 16 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

x^2 - 5x + 6 > 0

and $x^2 - 6x + 8 < 0 , find the range of $x$.

TITA Answer:

Practice More Questions

Official Convenor Answer Key: A) (2, 3) U (4, \infty)

Verified Solution:

Step 1: Solve the first inequality

x^2 - 4x + 4 > 0

. This simplifies to $(x - 2)(x - 3) > 0 , which is true for $x < 2$ or $x > 3$. Step 2: Solve the second inequality $x^2 - 6x + 8 < 0$. This simplifies to $(x - 2)(x - 4) < 0 , which is true for

1 < x < 3

. Step 3: The intersection of the two solution sets is

1 < x < 3

and

(4, \infty)

. Step 4: The range of

x < \frac{14}{3}

(2, 3) \cup (4, \infty)

Question 17 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

What is the range of

x

for which

x^2 - 4x + 3 < 0

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: Factor the quadratic inequality to get

2x > 8

. The roots are

x=2

and

3x - 4 < 10

. Testing intervals, we find that the inequality holds for

x < 2

. Hence, the correct answer is B.

Question 18 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

For what values of

x

2x^2 - 5x - 3 > 0

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Factor the inequality to get

2x > 8

. The roots are

x = -\frac{1}{2}

and

x = 3

. Testing intervals, the inequality holds for

x < -\frac{1}{2}

x > 3

. Hence, the correct answer is A.

Question 19 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

For what values of

x

3x^2 - 4x - 4 < 0

Practice More Questions

Official Convenor Answer Key: B

Verified Solution: Factor the inequality to get

2x > 8

. The roots are

x = -\frac{1}{2}

and

x = 3

. Testing intervals, the inequality holds for -

x < -\frac{1}{2}

< x < 2

. Hence, the correct answer is B.

Question 20 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

For what values of

x

4x^2 - 12x + 9 > 0

Practice More Questions

Official Convenor Answer Key: C

Verified Solution: Factor the inequality to get

2x > 8

. This inequality holds for all

x

except

x = \frac{3}{2}

. Hence, the correct answer is C.

Question 21 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

For what values of

x

2x^2 - 5x + 3 > 0

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Factor the inequality to get

2x > 8

. The roots are

x = -\frac{1}{2}

and

x = 3

. Testing intervals, the inequality holds for

x < \frac{1}{2}

x > 3

. Hence, the correct answer is A.

Question 22 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

2x - 3 > 5x + 2

and $x^2 - 4x + 3 < 0 , find the range of $x$.

TITA Answer:

Practice More Questions

Official Convenor Answer Key: -1.00

Verified Solution: Step 1: Solve

2x > 8

. Step 2: Solve

x \neq 2

. Step 3: Combine the solutions,

1 < x < 3

and $x < -

\frac{5}{3}

, to find $x$ is not in the range. Step 4: Correct range is - 1.00$ after re-evaluating the conditions.

Question 23 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

3x - 4 < 2x + 1

and $2x^2 - 3x - 2 > 0 , which of the following is true?

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Step 1: Solve

2x > 8

. Step 2: Solve

2x^2 - 3x - 2 > 0 \Rightarrow (2x + 1)(x - 2) > 0 \Rightarrow x < -\frac{1}{2}

x > 2

. Step 3: Combine the solutions,

x < 5

and

x < -\frac{1}{2}

or $x > 2 , to find $x < -1$ or $x > 2$. Step 4: Correct answer is $A$.

Question 24 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

5x - 3 > 2x + 1

and $x^2 - 5x + 6 < 0 , find the range of $x$.

Practice More Questions

Official Convenor Answer Key: A

Verified Solution: Step 1: Solve

2x > 8

. Step 2: Solve

x^2 - 5x + 6 < 0 \Rightarrow (x - 2)(x - 3) < 0 \Rightarrow 2 < x < 3

. Step 3: Combine the solutions,

x > \frac{4}{3}

and $2 < x < 3 , to find $1 < x < 2$. Step 4: Correct answer is $A$.

Question 25 of 86

ThinkCAT Practice SetQAAlgebra • InequalitiesHard

6x - 2 < 4x + 3

and $x^2 - 6x + 9 > 0 , find the range of $x$.

Practice More Questions

Official Convenor Answer Key: D

Verified Solution: Step 1: Solve

2x > 8

. Step 2: Solve

x^2 - 5x + 6 < 0 \Rightarrow (x - 2)(x - 3) < 0 \Rightarrow 2 < x < 3

. Step 3: Combine the solutions,

x < \frac{5}{2}

and $x ≠ 3 , to find no common solution. Step 4: Correct answer is $D$.

+ 61 More Official Questions in this Bank

Practice all 86 questions in interactive study mode with instant solution checks, bookmarking, and timer analytics.

Practice All 86 Questions

Free Aspirant Community

Join 2,400+ CAT Aspirants WhatsApp Study Circle

Daily PYQ doubt solving, curated DILR sets, IIM Bangalore / Ahmedabad toppers strategy sessions, and instant exam notification alerts.

Join WhatsApp VIP Group

ThinkCAT Pro Season PassFull Exam Access

Unlock 24 Full-Length CAT CBT Mocks & Percentile Engine

Get full access to all 2017–2025 past papers in timed exam mode, sectional drills, personal formula notebooks, and national rank percentiles.

Upgrade to Pro

Frequently Asked Questions about CAT Inequalities & Modulus Practice Questions (85+ Questions)

What concepts are covered in the Inequalities & Modulus Practice Drills practice module?

This module covers Inequalities, Modulus with 86 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Inequalities & Modulus Practice Drills questions?

The ideal target pace is 1.8 to 2.2 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Inequalities & Modulus Practice Drills?

Official past year exam questions are available in our CAT Algebra PYQ Hub module.

Related CAT Papers & Topic Mastery Hubs

Explore other slots, sections, and high-weightage topic collections

View Full Archive

Topic Hub

CAT Inequalities & Modulus Practice Questions (85+ Questions)

Core Formulas & Shortcut Matrix: Inequalities & Modulus Practice Drills

Bite-Sized Practice Sets (10 Modules Available)

Set 01: Inequalities

Set 02: Inequalities

Set 03: Inequalities

Set 04: Modulus

Set 05: Inequalities

Set 06: Modulus

Set 07: Inequalities

Set 08: Modulus

Set 09: Inequalities

Set 10: Modulus

Attempt under official TCS iON 40-Min countdown timer

Official Exam Questions & Explanations (25 of 86)

+ 61 More Official Questions in this Bank

Join 2,400+ CAT Aspirants WhatsApp Study Circle

Unlock 24 Full-Length CAT CBT Mocks & Percentile Engine

Frequently Asked Questions about CAT Inequalities & Modulus Practice Questions (85+ Questions)

What concepts are covered in the Inequalities & Modulus Practice Drills practice module?

What is the recommended solving time for Inequalities & Modulus Practice Drills questions?

Where can I find official past year CAT papers for Inequalities & Modulus Practice Drills?

Related CAT Papers & Topic Mastery Hubs

Parent: Algebra Practice Hub

CAT Algebra PYQ Hub

Quadratic Equations Practice Drills

Functions & Graphs Practice Drills

Linear Equations Practice Drills