CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Properties of Inequalities

The question is for finding the solution of a inequality. We need to solve the inequality which is in the form of fraction. 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 17: Solve :\\frac{(x – 4) (x+3)}{(x + 4) ( x +5)}\\) > 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 : Solve for x in the traditonal approach!!

\\frac{(x – 4) (x+3)}{(x + 4) ( x +5)}\\) > 0
Consider this as \\frac{a}{b}\\) > 0
Here both a > 0 & b > 0 or a < 0 & b < 0

Case 1: (x – 4) (x + 3) > 0 & (x + 4) ( x +5) > 0
x > 4 , x > -3, x > -4 , x > -5
Combining all we get x > 4

Case 2: (x – 4) (x + 3) < 0 & (x + 4) ( x +5) < 0
x < 4, x < -3, x < -4, x < -5
Combining all x < -5
Hence range is (-∞,-5) ∪ (4, ∞)

The question is "Solve :\\frac{(x – 4) (x + 3)}{(x + 4) ( x + 5)}\\) > 0?"

Hence the answer is "x ∊ (-∞,-1] ∪ [√3, 3)"

Choice A is the correct answer.


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