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# P and Q are each circular regions. What is the radius of P, if the are

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Math Expert
Joined: 02 Sep 2009
Posts: 49231
P and Q are each circular regions. What is the radius of P, if the are  [#permalink]

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05 Sep 2018, 00:26
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Difficulty:

25% (medium)

Question Stats:

93% (01:32) correct 7% (03:48) wrong based on 14 sessions

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P and Q are each circular regions. What is the radius of P, if the area of P minus the area of Q is 15π and P has a circumference that is 4 times that of Q?

A. 1
B. 2
C. 4
D. 5
E. 20

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Re: P and Q are each circular regions. What is the radius of P, if the are  [#permalink]

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05 Sep 2018, 00:37
Bunuel wrote:
P and Q are each circular regions. What is the radius of P, if the area of P minus the area of Q is 15π and P has a circumference that is 4 times that of Q?

A. 1
B. 2
C. 4
D. 5
E. 20

Let p and q are the radius of circular regions P and Q respectively.
Given, area of P minus the area of Q is 15π
Or, $$p^2-q^2=15$$
Or, (p+q)(p-q)=15------------(1)

Given, P has a circumference that is 4 times that of Q
or, p=4q-------------(2)

from(1), $$(p+\frac{p}{4})(p-\frac{p}{4})=15$$
Or, $$\frac{5p}{4} * \frac{3p}{4}=15$$
Or, $$p^2=16$$
or, p=4

Ans. (C)
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Re: P and Q are each circular regions. What is the radius of P, if the are &nbs [#permalink] 05 Sep 2018, 00:37
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