# CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

###### CAT Questions | Algebra | Inequalities - Natural Numbers CAT Questions

The question is about three distinct natural numbers. Given the sum of three distinct natural numbers we need to maximize the value of 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 6: The sum of three distinct natural numbers is 25. What is the maximum value of their product?

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##### 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?

Let the three natural numbers be a, b and c. We know that a + b + c = 25.
Let us substitute some values and see where this is headed
a = 1, b = 2 c = 22, Product = 44
a = 2, b = 3 c = 20, product = 120
a = 5, b = 6 c = 14, product = 420

The numbers should be as close to each other as possible. (Just trial and error and one can figure this out). This property is an extension of the AM-GM Inequality.

$$frac{25}{3}\\$∼8 25 divided by 3 is approximately equal to 8. So, we should choose a, b, and c close enough to 8. 8 + 8 + 9 = 25. But the numbers need to be distinct. 8 * 7 * 10 come closest. The maximum product would be 560. The question is "The sum of three distinct natural numbers is 25. What is the maximum value of their product?" ##### Hence the answer is "The maximum product is 560." ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 4000/- 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, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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