CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Inequalities - Modulus Integer Solutions

The question is about maximum possible value. Our task is to maximize the given modulus that is tricky. 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 11: a, b, c are distinct natural numbers less than 25. What is the maximum possible value of |a – b| + |b – c| – |c – a|?

  1. 44
  2. 46
  3. 23
  4. 21

Rs. 2500 off on 2IIM Ultimate DI LR Course for CAT 2019. Offer valid till March 24th.

Signup to sample the Best CAT Online Coaching

Video Explanation

Best CAT Coaching in Chennai

Starts Sat, Mar 23, 2019

Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : Visualising the terms in a number line would be heplful!

CAT : Algebra: Inequalities
For any two points M, N on the number line representing numbers m, n the distance MN = | m - n|.
So, for three points, P, Q and R on the number line |p – q|, |q – r|, |r – p| are distances between three pairs of points on the number line.

In this case, we are trying to find maximum value of |a – b| + |b – c| – |c – a|. If b lies between a and c, the above value would be zero. So, b should not be between a and c.
The best case scenario would be if a, c were very close to each other and far from b. Let us try b = 24, a = 1, c = 2.
In this case |a – b| + |b – c| – |c – a| = 23 + 22 – 1 = 44. This is the maximum possible value.

We could also have b = 1, a = 24, c = 23,
|a – b| + |b – c| – |c – a| = 23 + 22 – 1 = 44.

The question is "What is the maximum possible value of |a – b| + |b – c| – |c – a|?"

Hence the answer is "44"

Choice A is the correct answer.

Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Mar 23rd, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo

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