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Circle P is inside Circle Q, and the two circles share the same center

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Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q’s diameter and Circle P’s diameter?

A 6
B 9
C 12
D 18
E 24
[Reveal] Spoiler: OA

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Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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SajjadAhmad wrote:
Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q’s diameter and Circle P’s diameter?

A 6
B 9
C 12
D 18
E 24

This question requires us to find the diameter of larger Circle Q.

Circle P's radius is given. From that derive P's diameter and circumference, then Q's circumference and diameter.

Circle P radius = 3, so
P's diameter is \(2r = 6\)

P's circumference is \(\pi*d\)
P's circumference = \(6\pi\)

Circle Q's circumference is four times that of P.
Q's circumference: \(6\pi * 4 = 24\pi\)

Circle Q's diameter is derived from its circumference:

Q's circumference:
\(24\pi = \pi*d\)
Q's diameter, \(d = 24\)
P's diameter, \(d = 6\)

The difference between the two diameters is (24 - 6) = 18

ANSWER D

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Re: Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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SajjadAhmad wrote:
Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q’s diameter and Circle P’s diameter?

A 6
B 9
C 12
D 18
E 24


Since the radius of Circle P (the smaller circle) is 3, the diameter and circumference of Circle P are 6 and 6π, respectively. Since the circumference of Circle Q is four times the circumference of Circle P, the circumference and diameter of Circle Q are 24π and 24, respectively.

Thus, the difference between the diameters of Circles Q and P is 24 - 6 = 18.

Answer: D
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Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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New post 23 Sep 2017, 01:13
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SajjadAhmad wrote:
Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q’s diameter and Circle P’s diameter?

A 6
B 9
C 12
D 18
E 24


Perimeter of the circle is 2\(\pi\)r - where r is the radius of the circle.
According to this formula,
Perimeter of circle P is 2\(\pi\)p - assume radius of circle P is p
Perimeter of circle Q is 2\(\pi\)q - assume radius of circle Q is q
As per the question 2\(\pi\)q = 4*2\(\pi\)p ==> q=4p Since p=3 ==> q=12
Diameter of the circle is twice the radius, hence
Diameter of circle Q is 2*12 = 24 and Diameter of circle P is 2*3 = 6

Difference is 24 - 6 = 18

Hence answer is D.
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Re: Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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New post 23 Sep 2017, 02:34
Radius of Q circle =q
Radius of P Circle = p

Given : 4*(2*pi*p) = 2*pi*q => q=4p
As p=3 =>> q= 4*3=12
Diameter of p =6 and diameter of q=24
Difference q-p = 24-6=18

Answer:D

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Re: Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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New post 23 Sep 2017, 05:10
let r be small circle radius and R be the big circle radius.
then 2(pi)r = 4*2(pi) R
so R should be 3*4 = 12
Diameter of big circle should be 24
small circle diameter is 6
then difference = 24-6 = 18
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Re: Circle P is inside Circle Q, and the two circles share the same center   [#permalink] 23 Sep 2017, 05:10
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