Ease Into Prep with a GMAT^® Question of the Day

The amount of paint needed to cover a circular sign is determined by the area of that sign. The formula for the area of a circle is a = πr². The problem establishes that the radius of the larger sign is 2 times the radius of the smaller sign. The question asks for the relative change in size from the smaller sign to the larger one—how many times larger is the larger one?

Since no real numbers are stated in the problem, you can choose your own; this strategy is called Choosing Smart Numbers. Call the radius of the smaller sign 2 and the radius of the larger sign 4.
Area smaller = π(2)² = 4π
Area larger = π(4)² = 16π
What's the relative difference between these two areas? The smaller one is 4π and the larger is 16π, so the area of the larger one is 4 times the area of the smaller one. Therefore, it will take 4 times as much paint to cover the larger one.

The correct answer is (C).