CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Inequalities - Modulus,Quadratic

The question is about an inequality that contains modulus. Our task is to find out the range of the x in the inequality. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

Question 8: (|x| - 2) (x + 5) < 0. What is the range of values x can take?


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Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : The product of two terms are negative when one of them is negative, and the other positive. If both are negative or positive, the product will be positive. When will these two terms be seperately negative?

This can be true in two scenarios.

Scenario I: (|x| - 2) < 0 and (x + 5) > 0
Or |x| < 2 and x > -5.This gives us the range (-2, 2)

Scenario II: (|x| - 2) > 0 and (x + 5) < 0
Or |x| > 2 and x < -5. This gives us the range (-∞, -5)
So, the overall range is (-∞, -5) or (-2, 2)

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

Hence the answer is "The range is (-∞, -5) or (-2, 2)"


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