Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE PS – In the figure shown, if the area of the shaded region…

In the figure shown, if the area of the shaded region…

Solution:

We are given the diagram of a shaded portion of a circular ring. Let’s sketch and label the diagram. As seen below, we can also use a specific formula for area of the shaded region in a ring.

To determine the area of the shaded ring we can use the formula, where a = radius of the smaller circle and b = radius of the larger circle:

Area of shaded ring = π(b^2 – a^2)

In this particular problem we are given that the area of the shaded ring is 3 times the area of the smaller circular region. We know that the area of the smaller region is πa^2, so we can create the following equation:

π(b^2 – a^2) = 3πa^2

b^2 – a^2 = 3a^2

b^2 = 4a^2

b = 2a

Since the radius of the larger circle is twice the radius of the smaller circle, the circumference of the larger circle is also twice the circumference of the smaller circle.

Answer: C 

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