Gmatasap wrote:
In the diagram above, points A, O, and B lie on the diameter of the large circle and D and d are diameters of two smaller circles. If the sum of the areas of the two smaller circles is 5/8 of the large circle's area. What is the ratio of D to d?
A.3:2
B.5:3
C.2:1
D.3:1
E.4:1
We can PLUG IN THE ANSWERS, which represent the ratio of D to d.
When the correct answer choice is plugged in, (area of left inner circle + area of right inner circle)/(area of outer circle) = 5/8.
D: D/d = 3/1.
Let D=6 and d=2, with the result that the diameter of the outer circle = 6+2 = 8.
Since the radius of left inner circle = 3, the area of the left inner circle = 9Ï€.
Since the radius of right inner circle = 1, the area of the right inner circle = π.
Since the radius of the other circle = 4, the area of the outer circle = 16Ï€.
Resulting ratio:
(area of left inner circle + area of right inner circle)/(area of outer circle) = (9π + π)/16π = 10π/16π = 5/8.
Success!
The correct answer is
D.
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