We are dealing with two circles that have the same centre, however, one circle is larger than the other, let us denote the radius of the larger / outer circle as r2 and the radius of the inner / smaller circle as r1

The shaded area is simply the difference between the area of the larger circle and the area of the smaller circle, this can be expressed as:

pi*(r2)^2 - pi*(r1)^2 , which is just the difference in their areas expressed mathematically

We are told that the shaded area is three times the area of the smaller circle

This means that the above expression is 3*pi*(r1)^2 , where r1 is the radius of the smaller circle as explained earlier

Putting this all together, we know that: pi*(r2)^2 - pi*(r1)^2 = 3*pi*(r1)^2

Re-arranging the above equation we get: pi*(r2)^2 = 4*pi*(r1)^2

Divide both sides by pi: (r2)^2 = 4*(r1)^2

Now root both sides: r2 = 2*r1 - this is telling us that the ratio of the radius of the larger circle to the radius of the smaller circle is such that r2/r1 = 2

Therefore the diameter of the larger circle is double that of the smaller circle, and as C=pi*d, the circumference of the larger circle must be twice as large

Answer (C)

This is a classic GMAT question where the area of the shaded region is the subtraction of other two areas.

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