# CAT Practice : Inequalities

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We need 9 units of common sense and 1 unit of math to solve this.

## Inequalities - Integers

Q.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

Choice C. 3510

## Detailed Solution

We need to maximise pqr. So,w e 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.

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## More questions from Inequalities

Inequalities are crucial to understand many topics that are tested in the CAT. Having a good foundation in this subject will make us tackling questions in Coordinate Geometry, Functions, and most importantly in Algebra much more comfortable.