gmattesttaker2 wrote: ↑

Tue May 14, 2013 7:30 pm

Hello,

Can you please assist with the following? This is from OG 13 (Qn. 122). Sorry, I tried to draw the diagram but it was not coming accurately. So I am not uploading it.

122)
In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1) AB = 3 and BC = 2
(2) CD = 1 and DE = 4

OA: D

Solution:

Question Stem Analysis:

We are given a large circle that wholly contains a smaller circle. the area outside the small circle that is inside the large circle. If we can determine either the radius or the diameter of each circle, we will be able to determine the area inside the large circle that is outside the small circle.

Statement One Alone:

From statement one, we see that the radius AB of the small circle is 3. And since BC = 2, we add this to the length of AB= 3 to get AC = 2 + 3 = 5, the radius of the larger circle.

Statement one alone is sufficient.

Statement Two Alone:

We know that CE is the radius of the larger circle, Since CD = 1 and DE = 4, we see that CE = 1 + 4 = 5.

We know that CE = AC = 5 since C is the center of the larger circle. We are given that CD = 1, and we know that AC + CD = AD is the diameter of the smaller circle. Thus, by substitution, we know that AD = 5 + 1 = 6, and this is the diameter of the smaller circle.

Statement two is also sufficient.

Answer: D