The question is about maximum possible value. Our task is to maximize the product of three integers given their range and their sum. 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 14: If a, b, c are integers such that – 50 < a, b, c < 50 and a + b + c = 30, what is the maximum possible value of abc?

- 1000
- 5000
- 4410
- 4560

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

abc will be maximum when it is positive. So, a, b, c can all be positive or two of the three can be negative and one positive.

When all are positive, max product is when the numbers are 10, 10 and 10.

When two are negative and one positive, the best–case scenario would be when two negative numbers are as low as possible (magnitudes as high as possible) so that the product can be high. Now, in order for the product to be maximum, the positive number should be as high as possible. So, let the positive number be 49. Then the sum of the two negative numbers should be –19. The best– case scenario would be when numbers are 49, –9, –10.

Product would be 4410.

The question is **"what is the maximum possible value of abc?"**

Choice C is the correct answer.

CAT 2024

Classroom Batches Starting Now! @Gopalapuram and @Anna nagar

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com