# CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

###### CAT Questions | Algebra | Quadratic Inequalities CAT Questions

The question is about a quadratic inequality. Our task is to find the range of the given 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 3: Find the range of x for which (x + 2) (x + 5) > 40?

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2021Online Batches Available Now!

##### Method of solving this CAT Question from Algebra - Inequalities : We know how to solve the inequality if its greater or lesser than zero. But what happens when its greater or lesser than some non zero value? Can you reduce it to a familiar form?

There are two ways of trying this one. We can expand and simplify this algebraically.
x2 + 7x + 10 > 40 or x2 + 7x - 30 > 0
(x + 10) (x - 3) > 0
The roots are -10 and +3.
=> x should lie outside the roots.

Now, what is this based on?
There is a simple thumb rule for solving quadratic inequality

For any quadratic inequality ax2 + bx + c < 0
Factorize it as a(x - p) ( x - q) < 0

Whenever a is greater than 0, the above inequality will hold good if x lies between p and q.
a(x - p) (x - q) will be greater than 0, whenever x does not lie between p and q. In other words x should lie in the range ( -∞, p) or (q, ∞).

Now, coming back to the question (x + 10) (x - 3) > 0 Or, x < -10 or x > 3

Second method:
5 * 8 = 40, -8 * -5 = 40
So, if x + 2 > 5 this will hold good => x > 3
If x + 2 is less than -8 also, this will hold good => x < -10.
The first method is far more robust.

The question is "Find the range of x for which (x + 2) (x + 5) > 40?"

##### Hence the answer is "x < -10 or x > 3"

###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/-

Online Classroom Batches Starting Now!

###### Best CAT Coaching in ChennaiPrices slashed by Rs 4000/-

Attend a Demo Class

## CAT Online Preparation | CAT Algebra Videos On YouTube

#### Other useful sources for Algebra Questions | Inequalities Sample Questions

##### 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