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# If three times the circumference of circle P is double the circumferen

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Joined: 02 Sep 2009
Posts: 52390
If three times the circumference of circle P is double the circumferen  [#permalink]

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29 Sep 2016, 03:43
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:21) correct 42% (01:27) wrong based on 100 sessions

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If three times the circumference of circle P is double the circumference of circle Q, then the diameter of circle Q is how many times the radius of circle P?

A. 6
B. 3
C. 1.5
D. 4/3
E. 2/3

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Re: If three times the circumference of circle P is double the circumferen  [#permalink]

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29 Sep 2016, 03:51
B
let r1 be the radius of circle P and r2 be the radius of circle Q
3(2*pi*r1)=2(2*pi*r2)
simplifying you get r1/r2= 2/3
now question asks dia of Q is how many times the radius of P.
so d1/d2=2/3
d2=1.5d1
so dia of circle Q= 3 times radius of circle P
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Re: If three times the circumference of circle P is double the circumferen  [#permalink]

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30 Sep 2016, 02:57
This is a great GMAT question. Answer is 3. But a lot of us (including me) will choose 1.5 in the exam

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Re: If three times the circumference of circle P is double the circumferen  [#permalink]

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30 Sep 2016, 08:46
Bunuel wrote:
If three times the circumference of circle P is double the circumference of circle Q, then the diameter of circle Q is how many times the radius of circle P?

A. 6
B. 3
C. 1.5
D. 4/3
E. 2/3

Assume the radius of circle P = p and radius of circle Q = q
Given:
3*(2*pi*p) = 2*(2*pi*q)
3p = 2q Or q = (3/2)*p

Hence diameter of Q = 2*(3/2)*p = 3p
Correct Option: B
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Re: If three times the circumference of circle P is double the circumferen  [#permalink]

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27 Feb 2017, 04:26
let the radius of circle P bep1 and Q be q. According to the question:
3*(2*pi*p) = 2* (2*pi*q)
Or q/p = 3/2
Since the ratio of diameter is the ratio of radius, therefore the answer will be 1.5. Option C
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Re: If three times the circumference of circle P is double the circumferen  [#permalink]

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01 Mar 2017, 17:10
Bunuel wrote:
If three times the circumference of circle P is double the circumference of circle Q, then the diameter of circle Q is how many times the radius of circle P?

A. 6
B. 3
C. 1.5
D. 4/3
E. 2/3

We can let the diameter of circle P = p and the diameter of circle Q = q. Using the formula circumference = Π(diameter), we have:

3(pΠ) = 2(qΠ)

3p = 2q

(3/2)p = q

Now we can let the radius of circle P = r. Since the diameter of a circle is always twice the radius, we have p = 2r. Substituting this in the last equation, we have:

(3/2)(2r) = q

3r = q

We see that the diameter of circle Q is 3 times the radius of circle P.

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Re: If three times the circumference of circle P is double the circumferen &nbs [#permalink] 01 Mar 2017, 17:10
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