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# If P and Q are circular regions such that the area of one is 4 times

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
If P and Q are circular regions such that the area of one is 4 times  [#permalink]

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07 Sep 2018, 00:37
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:28) correct 33% (01:34) wrong based on 15 sessions

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If P and Q are circular regions such that the area of one is 4 times the area of the other, what is the radius of the larger circle?

(1) The sum of the radii is 45.
(2) The sum of their areas is 1125π.

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Re: If P and Q are circular regions such that the area of one is 4 times  [#permalink]

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07 Sep 2018, 01:21
Bunuel wrote:
If P and Q are circular regions such that the area of one is 4 times the area of the other, what is the radius of the larger circle?

(1) The sum of the radii is 45.
(2) The sum of their areas is 1125π.

Question: what is the radius of the larger circle?

Ratio of Area of two similar figures = Square of Ratio of corresponding sides
Ratio of Areas of two circles $$= (r_1/r_2)^2$$
i.e. $$4/1= (r_1/r_2)^2$$
i.e. $$2/1= (r_1/r_2)$$

Statement 1: The sum of the radii is 45.
i.e. $$45= (r_1+r_2)$$
one radius will be 15 and other will be 30
Two equations in two variables hence

SUFFICIENT

Statement 2: The sum of their areas is 1125π
i.e. $$π(r_1^2 + r_2^2) = 1125π$$ where $$2/1= (r_1/r_2)$$

Two equations in two variables hence

SUFFICIENT

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Re: If P and Q are circular regions such that the area of one is 4 times   [#permalink] 07 Sep 2018, 01:21
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