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Circle 1, Circle 2 and Circle 3 have the same center

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by srk228 » Mon Nov 07, 2016 8:59 pm
Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?

(1) A2=A3

(2) A2+A3 = 2 A1





OA = C


Is this C because given both 1 & 2, we know that A1=A2=A3? I just want to be sure that my understanding of the statements together is correct. Or am I suppose to take something different away from the 2 statements together?

Thanks.
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by GMATGuruNY » Mon Nov 07, 2016 9:03 pm
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by Jay@ManhattanReview » Thu Jan 05, 2017 3:41 am
srk228 wrote:Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?

(1) A2=A3

(2) A2+A3 = 2 A1


OA = C


Is this C because given both 1 & 2, we know that A1=A2=A3? I just want to be sure that my understanding of the statements together is correct. Or am I suppose to take something different away from the 2 statements together?

Thanks.
We have to find out the unique values of A1/A2 and A2/A3.

S1: Given that A2 = A3, we get A2/A3 = 1, but we cannot get the value of A1/A2 since we have no information about A1. Insufficient.

S2: Given that A2+A3 = 2A1, we cannot get the unique values of A1/A2 and A2/A3.

If A1 = A2 = A3, we get A1/A2 = 1 and A2/A3 = 1.

However, if A2=1/2 and A3=1, then A1 = 3/4. Thus, A1/A2 = 3/2 and A2/A3 = 1/2. No unique value. Insufficient.

S1 and S2: By A2 = A3 and A2+A3 = 2A1, we get that A1 = A2 = A3, thus A1/A2 = 1 and A2/A3 = 1. Sufficient.

Answer: C

-Jay
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