CAT Practice : Inequalities

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This is the world of inequality (we do not mean inequity). Ignore it at your own peril. You will definitely get questions from this topic, and it forms the basis for much of algebra.
  1. 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
    • Correct AnswerChoice (B).
      There are 30 integer values that 'x' can take that satisfy the inequality.
      Correct answer
    • Explanatory Answer
    • Integer Solutions
    • Medium
  2. Cubic Inequalities

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

    1. (2, ∞)
    2. ((1, 2) ∪ (2, ∞)
    3. (-∞, 1) ∪ (2, ∞)
    4. (-∞, 1)
    • Correct AnswerChoice (B).
      Within this range, the inequality remains positive, or greater than zero
      Correct answer
    • Explanatory Answer
    • Cubic Inequalities
    • Hard
  3. Quadratic Inequalities

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


    • Correct Answerx < -10 or x > 3 Correct answer
    • Explanatory Answer
    • Quadratic Inequalities
    • Easy
  4. Integer Roots - Trial and Error

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

    • Correct AnswerThere are a total of nine values Correct answer
    • Explanatory Answer
    • Integer Roots
    • Medium
  5. Modulus Inequalities

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

    • Correct Answer( -∞, -4) or (2, 4) or ( 10, ∞) Correct answer
    • Explanatory Answer
    • Modulus
    • Hard
  6. Natural Numbers

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

    • Correct AnswerThe maximum product is 560. Correct answer
    • Explanatory Answer
    • Natural Numbers
    • Easy
  7. Integers - Polynomials

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

  8. Modulus - Quadratic

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

    • Correct AnswerThe range is (-∞, -5) or (-2, 2) Correct answer
    • Explanatory Answer
    • Modulus
    • Hard
  9. 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?

    • Correct Answer(-∞, -2) or (-2, 2) Correct answer
    • Explanatory Answer
    • Quadratic Inequalities
    • Hard
  10. 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?

  11. Modulus - Tricky Question

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

  12. 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?

  13. Inequalities - Integer Solutions

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

  14. 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?

  15. Properties of Inequalities

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

    1. x
    2. x
    3. x
    4. x
    • Correct AnswerChoice (B).
      Correct answer
    • Explanatory Answer
    • Properties of Inequalities
    • Medium
  16. Properties of Inequalities

    Find range of f(x) = x2 – 6x + 14



    • Correct AnswerChoice (D).
      Correct answer
    • Explanatory Answer
    • Properties of Inequalities
    • Medium
  17. Properties of Inequalities

    Solve :

    • Correct AnswerChoice (A).
      Correct answer
    • Explanatory Answer
    • Properties of Inequalities
    • Medium
  18. Modulus - Tricky

    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. 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. 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. Inequalities - Minimum Value

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

  22. 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. 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. Inequalities - Max and Min Values

    What are the maximum and minimum possible values for

    1. 3 and 1
    2. 3 and 0
    3. 4 and 0
    4. 4 and 1
    • Correct AnswerChoice (A).
      Correct answer
    • Explanatory Answer
    • Inequalities - Max and Min Values
    • Medium

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