CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Inequalities - Integer Solutions

The question is about maximum possible value. Sum of three distinct number is given and our task is to maximize their product. 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 10: If a, b, c are distinct positive integers, what is the highest value a * b * c can take if a + b + c = 31?

  1. 1080
  2. 1200
  3. 1024
  4. 1056

2IIM : Best Online CAT Coaching


Try 5 full classes for free


Video Explanation


Best CAT Coaching in Chennai


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


Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : When 'a' + 'b' is given to be a constant, 'ab' has its maximum value when they are closest to each other, or if 'a' = 'b'. What happens when 'a' and 'b' are distinct?

The sum of three numbers is given; the product will be maximum if the numbers are equal.
\\frac{a + b + c}{3}\\) > ∛abc
So, if a + b + c is defined, abc will be maximum when all three terms are equal. In this instance, however, with a, b, c being distinct integers, they cannot all be equal.

So, we need to look at a, b, c to be as close to each other as possible.
a = 10, b =10, c = 11 is one possibility, but a, b, c have to be distinct. So, this can be ruled out.
The close options are,
a, b, c: 9, 10, 12; product = 1080
a, b, c: 8, 11, 12; product = 1056
Maximum product = 1080

The question is "what is the highest value a * b * c can take if a + b + c = 31?"

Hence the answer is "1080"

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