# CAT Questions | CAT Algebra Questions

###### CAT Quantitative Aptitude | CAT Algebra: Inequalities Questions

A CAT Algebra question from Inequalities that appears in the Quantitative Aptitude section of the CAT Exam consists of concepts: Range of Inequalities, Modulus functions, Possible solutions and so on. The topic also involves linear and quadratic equations, finding roots, polynomials, functions and more. Inequalities is a crucial topic for CAT. Having a good foundation in this subject can help a student tackle questions in Coordinate Geometry, Functions. In CAT Exam, one can generally expect to get 2~3 questions from Inequalities. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. #### CAT Inequalities - Integer Solutions

How many positive integer values can x take that satisfy the inequality (x - 8) (x - 10) (x - 12).......(x - 100) < 0?

1. 25
2. 30
3. 35
4. 40

2. #### CAT Inequalities - Cubic Inequalities

Solve the inequality: x3 – 5x2 + 8x – 4 > 0?

1. (2, ∞)
2. (1, 2) ∪ (2, ∞)
3. (-∞, 1) ∪ (2, ∞)
4. (-∞, 1)

3. #### CAT Inequalities - Quadratic Inequalities

Find the range of x for which (x + 2) (x + 5) > 40?

4. #### CAT Inequalities - Integer Roots, Trial and Error

How many integer values of x satisfy the inequality x( x + 2)(x + 4)(x + 6) < 200?

5. #### CAT Inequalities - Modulus Inequalities

Find the range of x where ||x - 3| - 4| > 3?

6. #### CAT Inequalities - Natural Numbers

The sum of three distinct natural numbers is 25. What is the maximum value of their product?

7. #### CAT Inequalities - Integers, Polynomials

If x (x + 3) (x + 5) (x + 8) < 250, how many integer values can x take?

8. #### CAT Inequalities - Modulus, Quadratic

(|x| - 2) (x + 5) < 0. What is the range of values x can take?

9. #### CAT Inequalities and Quadratic Inequalities

a and b are roots of the equation x2 - px + 12 = 0. If the difference between the roots is at least 12, what is the range of values p can take?

10. #### CAT Inequalities - Integer Solutions

If a, b, c are distinct positive integers, what is the highest value a × b × c can take if a + b + c = 31?

1. 1080
2. 1200
3. 1024
4. 1056

11. #### CAT Inequalities - Modulus

a, b, c are distinct natural numbers less than 25. What is the maximum possible value of |a – b| + |b – c| – |c – a|?

1. 44
2. 46
3. 23
4. 21

12. #### CAT Inequalities - Maximum Possible Value

Consider integers p, q such that – 3 < p < 4, – 8 < q < 7, what is the maximum possible value of p2 + pq + q2?

1. 60
2. 67
3. 93
4. 84

13. #### CAT Inequalities - Integer Solutions

For how many integer values does the following inequality hold good? (x + 2) (x + 4) (x + 6)........(x + 100) < 0?

1. 25
2. 50
3. 49
4. 47

14. #### CAT Inequalities - Maximum possible value

If a, b, c are integers such that – 50 < a, b, c < 50 and a + b + c = 30, what is the maximum possible value of abc?

1. 1000
2. 5000
3. 4410
4. 4560

15. #### CAT Inequalities - Properties of Inequalities

Solve x2 - |x + 3| + x > 0?

1. x ∊ (-∞,-1] ∪ [√3, 3)
2. x ∊ (-∞,-√3) ∪ (√3, ∞)
3. x ∊ (-4,-3) ∪ (4, ∞)
4. x ∊ (-8,-3] ∪ [2, ∞)

16. #### CAT Inequalities - Properties of Inequalities

Find range of f(x) = x2 – 6x + 14?

1. (-∞, 8)
2. (-∞, 100)
3. (-∞, 45)
4. (5, ∞)

17. #### CAT Inequalities - Properties of Inequalities

Solve :$$frac{$x – 4$ (x+3)}{(x + 4) ( x +5)}$ > 0? 1. x ∊$-∞,-5) ∪ (-4 , -3) ∪ (4, ∞)
2. x ∊ (-∞,-5) ∪ (4, ∞)
3. x ∊ (-4,-3) ∪ (4, ∞)
4. x ∊ (-5,-3] ∪ [4, ∞)

18. #### CAT Inequalities and Modulus

Consider three distinct positive integers a, b, c all less than 100. If |a - b| + |b - c| = |c – a|, what is the maximum value possible for b?

1. 98
2. 99
3. 50
4. 100

19. #### CAT Inequalities - Integers

Consider integers m, n such that -5 < m < 4 and -3 < n < 6. What is the maximum possible value of m2 - mn + n2?

1. 65
2. 60
3. 50
4. 61

20. #### CAT Inequalities - Integers

Consider integers p, q, r such that |p| < |q| < |r| < 40. P + q + r = 20. What is the maximum possible value of pqr?

1. 3600
2. 3610
3. 3510
4. 3500

21. #### CAT Inequalities - Minimum Value

What is the minimum value of f(x) = x2 – 5x + 41?

1. #### CAT 2018 Question Paper Slot 2 - Inequalities

If a and b are integers such that 2x2 - ax + 2 ＞ 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b is (TITA)

1. #### CAT 2017 Question Paper Slot 1 - Inequalities

For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied? (TITA)

The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.

1. #### XAT 2018 Question Paper - QADI

If 2 ≤ |x – 1|×|y + 3| ≤ 5 and both x and y are negative integers, find the number of possible combinations of x and y.

1. 4
2. 5
3. 6
4. 8
5. 10

The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.

1. #### IPMAT 2020 Question Paper - IPM Indore Quants

Consider the following statements:
(i) When 0 < x < 1, then $$frac{1}{1+x}$ < 1 - x + x2$ii) When 0 < x < 1, then $$frac{1}{1+x}$ > 1 - x + x2$iii) When -1 < x < 0, then $$frac{1}{1+x}$ < 1 - x + x2$iv) When -1 < x < 0, then $$frac{1}{1+x}$ > 1 - x + x2 Then the correct statements are 1.$i) and (ii)
2. (ii) and (iv)
3. (i) and (iv)
4. (ii) and (iii)

2. #### IPMAT 2019 Question Paper - IPM Indore Quants

If x ∈ (a, b) satisfies the inequality $$frac{x - 3}{x^{2} + 3x + 2} \geq 1,\\$ then the largest possible value of b - a is 1. 3 2. 1 3. 2 4. No real values of x satisfies the inequality ###### Prepare for CAT 2022 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2022 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Preparation | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Inequalities Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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