# 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. $$frac{139}{4}\\$ 2. $\frac{149}{4}\\$ 3. $\frac{129}{4}\\$ 4. $\frac{119}{4}\\$ 22. #### CAT Inequalities - Roots x4 – 4x3 + ax2 – bx = 1 = 0 has positive real roots. What is the maximum possible value of a + b? 1. 20 2. 12 3. 8 4. 10 23. #### CAT Inequalities - Range |x3 – 3x + 5| > -4. What range of x satisfies this? 1. [0,∞) 2. [-4, ∞) 3. All real values of x 4. [4,∞) 24. #### CAT Inequalities - Max and Min Values What are the maximum and minimum possible values for $\frac{|x+y|}{|x|+|y|}\\$ + $\frac{|z+y|}{|z|+|y|}\\$ + $\frac{|z+x|}{|x|+|z|}\\$? 1. 3 and 1 2. 3 and 0 3. 4 and 0 4. 4 and 1 25. ##### The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below. IPMAT Rohtak Sample Paper Mock IPMAT Indore Sample Paper Mock Please note that the explanation button will take you to the IPMAT solution page. 26. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Inequalities The set of all real numbers x for which x2 - |x + 2 |+ x > 0, is 1.$-∞, -2) ∪ (2, ∞)
2. (-∞, -√2) ∪ (√2, ∞)
3. (-∞, -1) ∪ (1, ∞)
4. (√2, ∞)

If x ∈ (a, b) satisfies the inequality $$frac{x - 3}{x^{2} + 3x + 2} \geq 1,\\$ then the largest possible value of b - a is 1. 3 2. 1 3. 2 4. No real values of x satisfies the inequality 30. #### IPMAT 2019 Question Paper - IPM Indore Quants,Inequalities If a, b, c are real numbers a2 + b2 + c2 = 1, then the set of values ab + bc + ca can take is: 1. [-1,2] 2. [-$\frac{1}{2}\\$, 2] 3. [-1,1] 4. [-$\frac{1}{2}\\$, 1] 31. #### IPMAT 2019 Question Paper - IPM Indore Quants,Inequalities The inequality $\log _{2} \frac{3x - 1}{2 - x} < 1\\$ holds true for 1. x ∈$$$frac{1}{3}\\$, 1) 2. x ∈$$$frac{1}{3}\\$, 2) 3. x ∈$0, $$frac{1}{3}\\$) ∪$1,2)
4. x ∈ (-∞, 1)

32. #### IPMAT 2019 Question Paper - IPM Indore Quants,Inequalities

The set of values of x which satisfy the inequality 0.72x2 - 3x + 4 < 0.343 is

1. ($$frac{1}{2}\\$, 1) 2.$$$frac{1}{2}\\$, ∞) 3.$-∞, $$frac{1}{2}\\$) 4.$-∞, $$frac{1}{2}\\$) ∪$1, ∞)

33. #### IPMAT 2019 Question Paper - IPM Indore Quants,Inequalities

Determine the greatest number among the following four numbers

1. 2300
2. 3200
3. 2100 + 3100
4. 4100

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

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)

2. #### CAT 2018 Question Paper Slot 2 - Number Theory | Inequalities

The smallest integer n for which 4n > 1719 holds, is closest to

1. 33
2. 39
3. 37
4. 35

3. #### CAT 2018 Question Paper Slot 2 - Polynomials | Inequalities

The smallest integer n such that n3 - 11n2 + 32n - 28 > 0 is (TITA)

4. #### 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)

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