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GMAT Club team member V
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In the figure above, point O lies at the center of both circles. If th  [#permalink]

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Attachment: 5674.jpg [ 16.81 KiB | Viewed 316 times ]

In the figure above, point O lies at the center of both circles. If the length of OP is 6 and the length of PQ is 2, what is the ratio of the area of the smaller circle to the area of the larger circle?

(A) 3/8

(B) 7/16

(C) 1/2

(D) 9/16

(E) 5/8

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3410
Re: In the figure above, point O lies at the center of both circles. If th  [#permalink]

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2

Solution

Given
In this question, we are given that
• In the given figure, point O lies at the center of both circles.
• The length of OP is 6 and the length of PQ is 2

To find
We need to determine
• The ratio of the area of the smaller circle to the area of the larger circle

Approach and Working out
As OP = 6, the radius of the smaller circle = 6
• Hence, area of the smaller circle = $$π6^2= 36π$$

As PQ = 2, the radius of the larger circle = 6 + 2 = 8
• Hence, area of the larger circle = $$π8^2 = 64π$$

Therefore, the required ratio = $$\frac{36π}{64π} = \frac{9}{16}$$

Thus, option D is the correct answer.

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Target Test Prep Representative V
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Re: In the figure above, point O lies at the center of both circles. If th  [#permalink]

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Attachment:
5674.jpg

In the figure above, point O lies at the center of both circles. If the length of OP is 6 and the length of PQ is 2, what is the ratio of the area of the smaller circle to the area of the larger circle?

(A) 3/8

(B) 7/16

(C) 1/2

(D) 9/16

(E) 5/8

The area of the smaller circle is π x 6^2 = 36π. The area of the larger circle is π x (6 + 2)^2 = 64π. The ratio of the smaller circle to the larger circle is 36π/64π = 36/64 = 9/16.

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See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Re: In the figure above, point O lies at the center of both circles. If th   [#permalink] 29 Mar 2020, 04:04

# In the figure above, point O lies at the center of both circles. If th  