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Circle problem

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by gmat009 » Tue Oct 07, 2008 11:56 am
In the figure[attached figure], 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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |

by namitrajiv » Tue Oct 07, 2008 12:04 pm
A It is ,

AB=3 i.e. radius of the smaller circle

BC= 2 AC =5 radius of the larger circle ,

we find the difference in area
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by gmat009 » Tue Oct 07, 2008 12:17 pm
namitrajiv wrote:A It is ,

AB=3 i.e. radius of the smaller circle

BC= 2 AC =5 radius of the larger circle ,

we find the difference in area
Why is B not sufficient
CD=1, DE=4
Therefore CE=5 , so CA =5 (radius of larger circle)
If CA=5 and CD=1 then AD=6 (diameter of smaller circle)
Therefore AB=3(radius of smaller circle)

We find difference and B is sufficient too......

Is something wrong with my logic
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by namitrajiv » Tue Oct 07, 2008 12:24 pm
yes gmat009 , B is sufficient too
thanks for the explanation...

it should be D
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by gmat009 » Tue Oct 07, 2008 12:26 pm
namitrajiv wrote:yes gmat009 , B is sufficient too
thanks for the explanation...

it should be D
OA is A, that's the problem.

Can someone plz. help
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by 4meonly » Fri Oct 17, 2008 8:32 am
I ve got D :?:
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by mental » Fri Oct 17, 2008 9:24 am
IMO D

is the source authentic?
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by Looser » Sat Nov 15, 2008 7:26 pm
I answered D at first also, but if you remember that figures may not be drawn to scale, B may not be correct.

Imagine a situation when small circle is so small that point D actually lies before C. In this case, the diameter of the large circle will be 8, therefore the diameter of small circle will be 8-(DC+CE), or 3.

If on the other hand, point D lies after point C on the line, the diameter of the small circle will be 6 as mentioned in the posts above.

We have two possible answers, therefore B is insufficient.
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The answer should be D

by wi_snow » Sat Aug 22, 2009 1:49 am
I agree with the opinion that when the circle is very small,the answer B is insufficient,however,the question showed words that "in the figure",so I think B is also right in this figure.
So my answer is D
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by lephuong » Mon Feb 13, 2012 12:36 am
Looser wrote:I answered D at first also, but if you remember that figures may not be drawn to scale, B may not be correct.

Imagine a situation when small circle is so small that point D actually lies before C. In this case, the diameter of the large circle will be 8, therefore the diameter of small circle will be 8-(DC+CE), or 3.

If on the other hand, point D lies after point C on the line, the diameter of the small circle will be 6 as mentioned in the posts above.

We have two possible answers, therefore B is insufficient.
Actually, even in that case, B is sufficient.

We will have all the points in this order: A, B, D, C, E.

Radius of the larger circle is: AC = DE = DE - DC = 4 - 1 = 3
Radius of the smaller circle is: AB = BD = 1/2 (AC - DC)= 1
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