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, ∞)

🎉 Ace XAT 2025 with 2IIM's Crash Course - Enrol now


Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

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

Anything in side the modulus can be +ve, -ve or 0.

Case i) x + 3 is positive
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 the range is (-3, -√3) ∪ (√3 , ∞)

Case ii) x + 3 is negative
If x + 3 < 0 ⇒ x < -3
Then equation is in the form x2 + x + 3 + x > 0
⇒ x2 + 2x + 3 > 0

For any value of x < -3, x2 will be positive and geater than 2x even if x is negative.
So, x2 + 2x + 3 > 0, will be satisfied for all the values of x < -3,
The range is (-∞, -3)

Case iii) x + 3 is 0
⇒ x = -3
Then the equation x2 - |x + 3| + x, becomes (-3)2 - |-3 + 3| + (-3) = 9 - 3 = 6.

Hence at x = -3, x2 - |x + 3| + x > will be satisfied
Combining all 3 x ∊ (-3, -√3) ∪ (√3 , ∞) ∪ -3 ∪ (-∞, -3)
which becomes, x ∊ (-∞,-√3) ∪ (√3, ∞)

The question is "Solve x2 - |x + 3| + x > 0?"

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

Choice B is the correct answer.


CAT Online Preparation | CAT Algebra Videos On YouTube


Other useful sources for Algebra Questions | Inequalities Sample Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com