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

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VP
Status: Preparing for the GMAT
Joined: 02 Nov 2016
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Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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17 Sep 2017, 11:44
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Question Stats:

63% (00:51) correct 37% (00:27) wrong based on 27 sessions

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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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Director
Joined: 22 May 2016
Posts: 814

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

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17 Sep 2017, 14:01
1
KUDOS
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

Kudos [?]: 264 [1], given: 552

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

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22 Sep 2017, 11:45
1
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Expert's post
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.

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Kudos [?]: 840 [1], given: 2

Manager
Joined: 06 Aug 2017
Posts: 54

Kudos [?]: 8 [1], given: 19

GMAT 1: 610 Q48 V24
Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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23 Sep 2017, 01:13
1
KUDOS
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

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Senior Manager
Joined: 02 Jul 2017
Posts: 252

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

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23 Sep 2017, 02:34
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

Kudos [?]: 59 [0], given: 59

Manager
Joined: 07 Jun 2017
Posts: 110

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Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Re: Circle P is inside Circle Q, and the two circles share the same center [#permalink]

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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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