Circle problem

[gmat009]

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.

[namitrajiv]

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

[gmat009]

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

[namitrajiv]

yes gmat009 , B is sufficient too
thanks for the explanation...

it should be D

[gmat009]

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

[4meonly]

I ve got D :

[mental]

IMO D

is the source authentic?

[Looser]

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.

[wi_snow]

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

[lephuong]

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