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GMAT Quant Questions - Inequalities

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Inequalities is an important topic and you will get questions in inequalities in the quantitative reasoning section of the GMAT exam. Questions in inequalities appear in both variants - data sufficiency and problem solving. Inequalities, data sufficiency, indices, and absolute value is a potent combination.

A collection of GMAT practice questions in inequalities is given below. Attempt these questions and check whether you have got the correct answer. If you could not solve the question, go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

  1. If "x" is an integer, which of the following inequalities have a finite range of values of "x" satisfying them?

    1. x2 + 5x + 6 > 0
    2. |x + 2| > 4
    3. 9x - 7 < 3x + 14
    4. x2 - 4x + 3 < 0
    5. (B) and (D)
    • Correct AnswerChoice (D).
      The solution to x2 - 4x + 3 < 0 is a finite range.
      Correct answer
    • Explanatory Answer
    • Linear and Quadratic inequalities
    • Medium
  2. What values of 'x' will be the solution to the inequality 15x - 2/x > 1?

    1. x > 0.4
    2. x < 1/3
    3. -1/3 < x < 0.4, x > 15/2
    4. -1/3 < x < 0, x > 2/5
    5. x < --1/3 or x > 2/5
    • Correct AnswerChoice (D).
      The values of x that satisfy the inequality are
      -1/3 < x < 0, x > 2/5
      Correct answer
    • Explanatory Answer
    • Inequalities: Quadratic expression
    • Easy
  3. What is the smallest integer that satisfies the inequality (x - 3)/ (x^2 - 8x - 20) > 0> 0?

    1. -2
    2. 10
    3. 3
    4. -1
    5. 0
    • Correct AnswerChoice (D).
      The smallest integer that satisfies the inequality is -1.

      Correct answer
    • Explanatory Answer
    • Inequalities : Quadratic expression
    • Easy
  4. Data Sufficiency: Is a < b?

    1. ab < ba
    2. a/b > 1
    • Correct AnswerChoice (E).
      The two statements together are NOT sufficient.
      Correct answer
    • Explanatory Answer
    • Inequalities in exponents
    • Hard
  5. Is | a | > | b |?

    1. 1/(a - b) > 1/(b - a)
    2. a + b < 0
    • Correct AnswerChoice (C).
      The two statements together are SUFFICIENT to answer the question.
      Correct answer
    • Explanatory Answer
    • Inequalities in absolute value
    • Medium
  6. Is a3 > a2?

    1. 1/a> a
    2. a5 > a3
    • Correct AnswerChoice (A).
      Statement 1 alone is sufficient; statement 2 is not.
      Correct answer
    • Explanatory Answer
    • Inequalities in exponents
    • Hard
  7. Is | a | > a?

    1. a2 < a
    2. (a/2) > (2/a)
    • Correct AnswerChoice (A).
      Statement 1 alone is sufficient; statement 2 is not.
      Correct answer
    • Explanatory Answer
    • Exponents and absolute value
    • Hard
  8. Is 'a' positive?

    1. a - b > 0
    2. 2a - b > 0
    • Correct AnswerChoice (E).
      The two statements together are NOT sufficient.
      Correct answer
    • Explanatory Answer
    • Positive & negative numbers
    • Medium
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