CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Inequalities - Modulus

The question is about maximum possible value. We need to maximize a value which is given in a tricky modulus. 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 18: Consider three distinct positive integers a, b, c all less than 100. If |a - b| + |b - c| = |c – a|, what is the maximum value possible for b?

  1. 98
  2. 99
  3. 50
  4. 100

2IIM : Best Online CAT Coaching


3000 off on Quants Online Course
till Aug 25th


Best CAT Coaching in Chennai


Crash course - CAT 2019
Intakes Closing Soon!
Starts Sat, August 24th, 2019


Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : Can we relate this to a number line?

|q – p| is the distance between p and q on the number line. |p –q| is the same as |q –p| to begin with.

So, in this case we are told |a -b| + |b -c| = |c – a|. Think about this. What does this mean? There are three points on the number line. We are talking about 3 distances on the number line here. We know that sum of some two of the distances is equal to the third. What does this tell us?

This tells us that the point b has to be in between a and c. With this we are done. We can have a or c to be 99 and b to be 98.

Maximum value b can take is 98. Classic question.

The question is "If |a - b| + |b - c| = |c – a|, what is the maximum value possible for b?"

Hence the answer is "98"

Choice A 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