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

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

Solution

Given:
• P and Q are each circular region
• The area of P minus the area of Q is 15π and
• P has a circumference that is 4 times that of Q

To find:

Approach and Working Out:
• The radius of P = 4 times the radius of Q (since, P has a circumference that is 4 times that of Q)
• $$p^2 – q^2 = 15$$, where p is the radius of P and q is the radius of Q
o $$16q^2 – q^2 = 15$$
o Implies, q = 1

• Therefore, p = 4

Hence, the correct answer is Option C.

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

We can let the radius of Q = q and the radius of P = p. Since the circumference of P is 4 times that of Q, we have:

4 * 2πq = 2πp

8πq = 2πp

4q = p

SInce the area of P minus the area of Q is 15π, we have:

p^2π - q^2π = 15π

p^2 - q^2 = 15

Substituting, we have:

(4q)^2 = q^2 = 15

16q^2 - q^2 = 15

15q^2 = 15

q^2 = 1

q = 1

Since p = 4q, p = 4.