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


  • Correct Answer
    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.

Correct Answer: C. 3510

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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.