CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Properties of Inequalities

The question is about solving an inequality. We need to solve an inequality which have both modulus and power two term. 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 15: Solve x2 - |x + 3| + x > 0?

  1. x ∊ (-∞,-1] ∪ [√3, 3)
  2. x ∊ (-∞,-3] ∪ [√3, ∞)
  3. x ∊ (-4,-3) ∪ (4, ∞)
  4. x ∊ (-8,-3] ∪ [2, ∞)

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Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : This is an excellent inequality question comprising of both quadratic and modulus!!

x2 - |x + 3| + x > 0
If x + 3 > 0 ⇒ x > -3
Then equation is in the form x2 - x - 3+ x > 0 i.e., x2 -3 > 0
x2 > 3 ⇒ x < -√3 and x > √3

But x > -3, thus x > √3
Now if x + 3 > 0 ⇒ x < -3
Then equation is in the form x2 + x + 3 + x > 0 ⇒ x2 + 2x + 3 > 0

Discriminant < 0 ⇒ a > 0 and iequality > 0 exist for all value of x.
But x < -3 , thus range will be x < -3

Combining both x ∊ (-∞,-3] ∪ [√3, ∞)

The question is "what is the maximum possible value of abc?"

Hence the answer is "x ∊ (-∞,-3] ∪ [√3, ∞) "

Choice B is the correct answer.

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