GMAT Diagnostic Test Question 33

BELOW IS REVISED VERSION OF THIS QUESTION.

A circle is inscribed right in the middle of a semicircle with a diameter of \(\pi\) as shown below. What is the ratio of the area of the semicircle to the area not covered by the inscribed circle?

A. 4:1
B. 3:2
C. 3:1
D. 4:3
E. 2:1

Since the radius of the big circle (\(\frac{\pi}{2}\)) is twice the radius of the inscribed circle (\(\frac{\pi}{4}\)) then its area is 4 times greater then the area of the inscribed circle (because in the area formula the radius is squared. For example the area of a circle with radius of 2 is \(4\pi\), which is 4 times greater than the radius of a circle with the radius of 1, which is \(\pi\)).

Thus the are of the semicircle is 4/2=2 times greater than the area of the inscribed circle: so, the area of the semicircle is 2 units, the area of the inscribed circle is 1 unit, and the area of the semicircle not covered by the inscribed circle is also 1 unit. Ratio: 2/1.

Answer: E.

Hope it's clear.