CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

The question is about range. This is really interesting. We need to find out the range of an inequality which contains modulus. 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 23: |x³ – 3x + 5| > -4. What range of x satisfies this?

1. [0,∞)
2. [-4, ∞)
3. All real values of x
4. [4,∞)

Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : At times we just need common sense to solve some problems!

It may be late in the night when you solve this question. Overload of details might have dulled your senses. Mathematical ideas might be playing games with you. But that does not mean you should stare a gift horse in the mouth.

Modulus of something > - 4. When can this not happen?

Who said CAT Preparation cannot be fun ?

This can never happen.

All real values of x satisfy the above inequality.

The question is "|x³ – 3x + 5| > -4. What range of x satisfies this?"

Hence the answer is "All real values of x"

Choice C is the correct answer.