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GMAT Online Preparation | Statistics & Averages Practice Question #13

A 600 to 650 level GMAT Statistics and Averages problem solving practice question. The question is an application of the Arithmetic Mean – Geometric Mean inequality. Specifically, it focuses on two inferences that can be drawn.

Inference 1: If the product of two positive numbers is known, their sum is maximised when the difference between the two numbers is maximised.

Inference 2: This inference is a corollary to the first one. If the product of two positive numbers is known, their sum is minimised when the difference between the two numbers is minimised. The sum is minimum when the two numbers are equal – if such a possibility exists.

Question
Area of a rectangle is 100 sq.units. If the sides are integers, what is the maximum and minimum value of the perimeter?

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