# CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

###### CAT Questions | Algebra | Inequalities - Integers

The question is about product of three integers. Our task is to maximize the product of three integers given the sum of them and their range. 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 20: Consider integers p, q, r such that |p| < |q| < |r| < 40. P + q + r = 20. What is the maximum possible value of pqr?

1. 3600
2. 3610
3. 3510
4. 3500

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##### Method of solving this CAT Question from Algebra - Inequalities : We need 9 units of common sense and 1 unit of math to solve this.

We need to maximise pqr. So, we should shoot for either all three positive or two negative and one positive. Given p + q + r = 20, two positive and one negative works better. Let us say we choose p, q to be negative and r to be positive. Maximum value r can take is 39. p + q now becomes -19.

P = -9, q = -10 and r = 39 works best.

So, the product should be -9 * -10 * 39 = 3510.

The question is "What is the maximum possible value of pqr?"

##### Hence the answer is "3510"

Choice C is the correct answer.

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