Question 18

Note that you are not asked for the specific area of circular region A or the specific area of circular region B. Rather, you are asked, regardless of what the specific area of is of each of the regions, what is the specific ratio of the area of circular region A to the area of circular region B.

Remember the issue is not whether you can determine the ratio but rather whether it can be determined by someone.

Key vocabulary:

area of a circular region = pirr (where r is the radius of the circle)

circumference of a circular region = 2pir (where r is the radius of the circle)

Statement (1) by itself: If the ratio of the circumference of region A to the circumference of region B is 3 to 1, this means that the ratio of the radius of region A to the radius of region B is 3 to 1. If the radius of A is three times the radius of B, this means that the area of region A is 9 times the area of region B. This means that the ratio is 9 to 1. Hence the answer can be determined from (1) alone. (B), (C), and (E) can be eliminated.

If you didn't understand the above mathematical discussion, just relax. You are not required to figure any of this out. All you need know is that if one knows either the value of the radius of each circular region or the value of the ratio of the radius of circular region A to the ratio of circular region B, then somebody could determine the answer.

Statement (2) by itself: We are given the value of radius of A. If the circumference of B is 6pi, then the radius of B is 3. Since, statement (2) gives us the value of the radius of each circular region the specific area of each circular region can be determined and the specific ratio of the value of A to B can be determined. Hence, the answer can be determined from statement (2) alone.

Since, the value of the ratio can be determined from each of statements (1) and (2) alone, the answer to the question is (D).