CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Inequalities - Integers

The question is about maximum possible value. We need to maximize the given expression given the range of two variables. 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 19: Consider integers m, n such that -5 < m < 4 and -3 < n < 6. What is the maximum possible value of m2 - mn + n2?

  1. 65
  2. 60
  3. 50
  4. 61

2IIM : Best Online CAT Coaching


Try 5 full classes for free


Best CAT Coaching in Chennai


Batches filling fast.
Starts Sat, May 25th, 2019


Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : Simple understanding of positive and negative sign will be sufficient to solve this one!

Points to note
1. m2 and n2 are always positive
2. -mn will be maximum when m and n have opposite signs

After this, it is pretty simple. We are better off with m being negative and n positive as in this case they can take higher values. m = -4, n = 5 works best. Note that as far as absolute value is concerned maximum |m| can be is 4 and maximum |n| can be is 5. This is important, otherwise we may have a scenario where even sacrificing –mn we might be able to maximise this.

So, m = -4, n = 5 works
m2 - mn + n2 = 16 + 20 + 25 = 61.

The question is "What is the maximum possible value of m2 - mn + n2?"

Hence the answer is "61"

Choice D 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,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

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