Important CAT Inequalities Questions and Answers [Download Free PDF]

Overview: Practice 25+ important CAT inequalities questions with solutions. Strengthen your basics and boost your score in Quant with these CAT-level inequality questions.

Mastering inequalities CAT questions is essential for cracking the Quantitative Aptitude section in the CAT exam. These questions assess your ability to analyze numerical relationships, solve compound inequalities, and interpret expressions involving variables.

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Whether it’s simple inequality rules or advanced CAT-level traps, having a strong grip on this topic can give you a competitive edge.

So, to help you out, we bring you a curated list of 25+ CAT Inequalities Questions with detailed solutions and answer keys. Read on to know and practice these questions!

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What Are CAT Inequalities Questions 2025?

Inequalities in the CAT exam test your understanding of mathematical expressions that involve comparisons using symbols such as >, <, ≥, and ≤. These questions may appear in standalone form or be embedded in data sufficiency or logical reasoning questions.

Solving CAT Inequalities Questions requires not just formula-based knowledge, but also logical sequencing, analytical thinking, and time management skills. These questions evaluate how quickly and accurately you can handle quantitative comparisons under pressure.

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25+ CAT Inequalities Questions with Answers

Q1. If x>3x > 3, which of the following must be true?

A. x2>9x^2 > 9
B. x−2>1x - 2 > 1
C. x+1<3x + 1 < 3
D. x−3<0x - 3 < 0

Correct Answer: B

Q2. Solve for x:
2x−3<52x - 3 < 5

A. x<4x < 4
B. x>4x > 4
C. x<1x < 1
D. x>1x > 1

Correct Answer: A

Q3. Which of the following is always true for any positive real number x?

A. x<x2x < x^2
B. x>x2x > x^2
C. x=x2x = x^2
D. x+1<x + 1 < x

Correct Answer: A

Q4. If x<yx < y, then:

−x<−y-x < -y
B. −x>−y-x > -y
C. x2<y2x^2 < y^2
D. 1x>1y\frac{1}{x} > \frac{1}{y}

Correct Answer: B

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Q5. Solve: 3x+2<2x+63x + 2 < 2x + 6

A. x<4x < 4
B. x>4x > 4
C. x<−4x < -4
D. x>−4x > -4

Correct Answer: A

Q6. If 4x−7>5x+24x 7 > 5x + 2, what is the solution?

A. x<−9x < -9
B. x>−9x > -9
C. x<9x < 9
D. x>9x > 9

Correct Answer: A

Q7. For what values of x is x2−4x<0x^2 - 4x < 0?

A. x<0x < 0 or x>4x > 4
B. 0<x<40 < x < 4
C. x>2x > 2
D. x<2x < 2

Q8. Solve:x−1x+2<0\frac{x - 1}{x + 2} < 0

A. x<−2x < -2 or x>1x > 1
B. −2<x<1-2 < x < 1
C. x>−2x > -2
D. x<1x < 1

Correct Answer: B

Easy Level CAT Inequalities Questions and Answers

Q9. Find the range of values satisfying: x2−5x+6≥0x^2 - 5x + 6 \geq 0

A. x≤2x \leq 2 or x≥3x \geq 3
B. 2<x<32 < x < 3
C. x<3x < 3
D. x≥2x \geq 2

Correct Answer: A

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Q10. If x>yx > y, then which of the following must be true?

A. x2>y2x^2 > y^2
B. x+y>2yx + y > 2y
C. x−y<0x - y < 0
D. xy<1\frac{x}{y} < 1

Correct Answer: B

Q11. Solve for x: x−3x+1>2\frac{x - 3}{x + 1} > 2

A. x<−1x < -1 or x>5x > 5
B. x>−1x > -1
C. x>5x > 5
D. x<−1x < -1

Correct Answer: C

Q12. Find the range of values for x satisfying: ∣x−2∣<x+1|x - 2| < x + 1

A. x>12x > \frac{1}{2}
B. x<12x < \frac{1}{2}
C. x>−3x > -3
D. x>−1x > -1

Correct Answer: A

Q13. Solve the inequality:
x2−1x−2<0\frac{x^2 - 1}{x - 2} < 0

A. −1<x<1-1 < x < 1
B. 1<x<21 < x < 2
C. x<−1x < -1 or x>2x > 2
D. x>−1x > -1

Correct Answer: B

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Q14. If a>b>0a > b > 0, which of the following is necessarily true?

A. 1a>1b\frac{1}{a} > \frac{1}{b}
B. 1a<1b\frac{1}{a} < \frac{1}{b}
C. log⁡a<log⁡b\log a < \log b
D. a2<b2a^2 < b^2

Correct Answer: B

Q15. Find the solution:
x2−6x+8≤0x^2 - 6x + 8 \leq 0

A. x≤2x \leq 2 or x≥4x \geq 4
B. 2≤x≤42 \leq x \leq 4
C. x<2x < 2
D. x>4x > 4

Correct Answer: B

Medium Level CAT Inequalities Question and Answers

Q16. A number x satisfies the inequality x2−4x+3x2−5x+6<1\frac{x^2 - 4x + 3}{x^2 - 5x + 6} < 1. Which of the following is the correct range of values for xx?

A. x<1∪x>3x < 1 \cup x > 3
B. 1<x<2∪3<x<41 < x < 2 \cup 3 < x < 4
C. x<2∪x>3x < 2 \cup x > 3
D. 2<x<32 < x < 3

Correct Answer: D

Q17. Let x be a real number such that ∣3x−4x−2∣<2\left| \frac{3x 4}{x - 2} \right| < 2. Find the range of values for x.

A. x<1∪x>3x < 1 \cup x > 3
B. x<2∪x>4x < 2 \cup x > 4
C. 1<x<2∪2<x<41 < x < 2 \cup 2 < x < 4
D. x>1x > 1

Correct Answer: C

Know More: CAT Exam Quantitative Aptitude Questions

Q 18. Suppose x∈Rx \in \mathbb{R} satisfies the inequality x2−6x+8≥0x^2 - 6x + 8 \geq 0. Then, which of the following intervals contains all the values of x that satisfy the inequality?

A. x≤2x \leq 2 or x≥4x \geq 4
B. x≤4x \leq 4
C. 2<x<42 < x < 4
D. x<2∪x>4x < 2 \cup x > 4

Correct Answer: A

Q19. A function is defined as f(x)=x−5x2−1f(x) = \frac{x - 5}{x^2 - 1}. For what values of x is f(x)>0f(x) > 0?

A. x<−1∪x>1,x≠5x < -1 \cup x > 1, x \ne 5
B. x<−1∪1<x<5x < -1 \cup 1 < x < 5
C. x<−1∪x>5x < -1 \cup x > 5
D. −1<x<1∪x>5-1 < x < 1 \cup x > 5

Correct Answer: B

Q20. Solve the inequality: (x−1)2x+3<1\frac{(x-1)^2}{x + 3} < 1. Which of the following correctly represents the solution set?

A. −3<x<2-3 < x < 2
B. x<−3∪x>2x < -3 \cup x > 2
C. x>−3x > -3
D. x<−1∪x>2x < -1 \cup x > 2

Correct Answer: A

Q21. Find the range of real values of x for which the inequality x2−6x+8x−2≥0\frac{x^2 - 6x + 8}{x - 2} \geq 0

holds true.

A. x≤2∪x≥4x \leq 2 \cup x \geq 4
B. x∈(−∞,2)∪[4,∞)x \in (-\infty, 2) \cup [4, \infty)
C. x∈(2,4]x \in (2, 4]
D. x∈(−∞,2)∪(4,∞)x \in (-\infty, 2) \cup (4, \infty)

Correct Answer: A

Q22. For what values of x does the inequality x+1x−2>2\frac{x + 1}{x - 2} > 2 hold true?

A. x<2x < 2
B. x<2,x≠−1x < 2, x \ne -1
C. x<−4∪x>3x < -4 \cup x > 3
D. x<−1∪x>3x < -1 \cup x > 3

Correct Answer: D

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Q23. Let x∈Rx \in \mathbb{R}. For which values of X does the inequality ∣2x−5∣<3x−1|2x - 5| < 3x - 1 hold?

A. x>2x > 2
B. x<1∪x>2x < 1 \cup x > 2
C. x>65x > \frac{6}{5}
D. x<65x < \frac{6}{5}

Correct Answer: C

Q24. Suppose x2−4x+4<0x^2 - 4x + 4 < 0. Which of the following is true?

A. No solution exists
B. x=2x = 2
C. x<2x < 2
D. x>2x > 2

Correct Answer: A

Difficult Level CAT Inequalities Questions 2025

Q25. Let x be a real number such that x2−9x−3<4\frac{x^2 - 9}{x - 3} < 4 . Then the solution set is:

A. x<3∪x>6x < 3 \cup x > 6
B. x<3∪3<x<6x < 3 \cup 3 < x < 6
C. x>3x > 3
D. x<6x < 6

Correct Answer: B

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Why Are CAT Inequalities Questions Important?

CAT is known for its unpredictable patterns. Yet, CAT 2025 Inequalities Questions are a recurring theme in QA and LRDI sections. Their importance lies in:

• High Scoring Potential: Once concepts are clear, you can solve them rapidly.
• Conceptual Testing: They check your fundamental understanding of algebra and logic.
• Application in Other Topics: Inequalities also appear in profit-loss, functions, and number system questions.

Read more: Mixture and Aligation CAT questions

Being adept at CAT Inequalities Questions gives you an upper hand in other related topics too.

Conclusion

Inequalities play a crucial role in CAT Quant and appear frequently in both direct and disguised forms.

As seen in the CAT Inequalities Questions above, mastering them requires not just formula memorization but also logical thinking and case-based analysis.

Practice these inequality questions CAT consistently to strengthen your foundation and avoid silly mistakes in the exam. Keep solving, keep analyzing, and you’ll definitely ace this section with confidence!