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题库 / GMATLA-DS-18
In the 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
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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(2) CD = 1 and DE = 4 --> CD+DE=CE=R=5CD+DE=CE=R=5. Next, AD+DE=AE=DIAMETER=2R=10AD+DE=AE=DIAMETER=2R=10, and since AD=2rAD=2r, then 2r+DE=102r+DE=10 --> 2r+4=102r+4=10 --> r=3r=3. Sufficient.
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