# CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

###### CAT Questions | Algebra | Inequalities - Integer Solutions
CAT Questions

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

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### 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. ###### 2IIM's CAT CoursesDussehra Discount of 25% Till Oct 9CAT Online Coaching Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Oct 5th, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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