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.
How many positive integer values can x take that satisfy the inequality (x - 8) (x - 10) (x - 12).......(x - 100) < 0?
A. 25
B. 30
C. 35
D. 40
Choice B
30
Solve the inequality: x3 – 5x2 + 8x – 4 > 0?
A. (2, ∞)
B. (1, 2) ∪ (2, ∞)
C. (-∞, 1) ∪ (2, ∞)
D. (-∞, 1)
Choice B
(1, 2) ∪ (2, ∞)
Find the range of x for which (x + 2) (x + 5) > 40?
x < -10 or x > 3
How many integer values of x satisfy the inequality x(x + 2)(x + 4)(x + 6) < 200?
There are a total of nine values
Find the range of x where ||x - 3| - 4| > 3?
( -∞, -4) or (2, 4) or ( 10, ∞)
The sum of three distinct natural numbers is 25. What is the maximum value of their product?
The maximum product is 560.
If x (x + 3) (x + 5) (x + 8) < 250, how many integer values can x take?
11 values
(|x| - 2) (x + 5) < 0. What is the range of values x can take?
The range is (-∞, -5) or (-2, 2)
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?
(-∞, -2) or (-2, 2)
If a, b, c are distinct positive integers, what is the highest value a × b × c can take if a + b + c = 31?
A. 1080
B. 1200
C. 1024
D. 1056
Choice A
1080
a, b, c are distinct natural numbers less than 25. What is the maximum possible value of |a – b| + |b – c| – |c – a|?
A. 44
B. 46
C. 23
D. 21
Choice A
44
Consider integers p, q such that – 3 < p < 4, – 8 < q < 7, what is the maximum possible value of p2 + pq + q2?
A. 60
B. 67
C. 93
D. 84
Choice B
67
For how many integer values does the following inequality hold good? (x + 2) (x + 4) (x + 6)........(x + 100) < 0?
A. 25
B. 50
C. 49
D. 47
Choice A
25
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?
A. 1000
B. 5000
C. 4410
D. 4560
Choice C
4410
Solve x2 - |x + 3| + x > 0?
A. x ∊ (-∞,-1] ∪ [√3, 3)
B. x ∊ (-∞,-3] ∪ [√3, ∞)
C. x ∊ (-4,-3) ∪ (4, ∞)
D. x ∊ (-8,-3] ∪ [2, ∞)
Choice B
x ∊ (-∞,-3] ∪ [√3, ∞)
Find range of f(x) = x2 – 6x + 14?
A. (-∞, 8)
B. (-∞, 100)
C. (-∞, 45)
D. (5, ∞)
Choice D
(5, ∞)
Solve :
A. x ∊ (-∞,-1] ∪ [√3, 3)
B. x ∊ (-∞,-3] ∪ [√3, ∞)
C. x ∊ (-4,-3) ∪ (4, ∞)
D. x ∊ (-8,-3] ∪ [2, ∞)
Choice A
x ∊ (-∞,-1] ∪ [√3, 3)
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?
A. 98
B. 99
C. 50
D. 100
Choice A
98
Consider integers m, n such that -5 < m < 4 and -3 < n < 6. What is the maximum possible value of m2 - mn + n2?
A. 65
B. 60
C. 50
D. 61
Choice D
61
Consider integers p, q, r such that |p| < |q| < |r| < 40. P + q + r = 20. What is the maximum possible value of pqr?
A. 3600
B. 3610
C. 3510
D. 3500
Choice C
3510
What is the minimum value of f(x) = x2 – 5x + 41?
A.
B.
C.
D.
Choice A
139⁄4
x4 – 4x3 + ax2 – bx = 1 = 0 has positive real roots. What is the maximum possible value of a + b?
A. 20
B. 12
C. 8
D. 10
Choice D
10
|x3 – 3x + 5| > -4. What range of x satisfies this?
A. [0,∞)
B. [-4, ∞)
C. All real values of x
D. [4,∞)
Choice C
All real values of x
What are the maximum and minimum possible values for
A. 3 and 1
B. 3 and 0
C. 4 and 0
D. 4 and 1
Choice A
3 and 1
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