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What is the ratio of the inner circle's circumference to the outer cir

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Bunuel
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What is the ratio of the inner circle's circumference to the outer cir [#permalink] New post   14 Sep 2018, 01:23
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What is the ratio of the inner circle's circumference to the outer circle's circumference, if the inner circle's area is 80% of the outer circle's area?


A. 4 : 5

B. \(2 : \sqrt{5}\)

C. \(\sqrt{5}: 2\)

D. \(4 \pi: \sqrt{5}\)

E. It cannot be determined from the information given.

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magbot
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What is the ratio of the inner circle's circumference to the outer cir [#permalink] New post   Updated on: 14 Sep 2018, 10:46
Area Of Inner circle with radius "r" = 80/100 * Area of outer circle with radius "R"
\(\pi * r^2 = \frac{80}{100} * \pi * R^2\)
cancel pi and take square root on both sides
\(r = \sqrt\frac{8}{10} * R\)
\(\frac{r}{R} = \frac{2}{\sqrt5}\)
Multiply \(2*\pi\) in numerator and denominator of LHS to get the circumference
\(\frac{2*\pi*r}{2*\pi*R} = \frac{2}{\sqrt5}\)

Answer: B

Originally posted by magbot on 14 Sep 2018, 10:10.
Last edited by magbot on 14 Sep 2018, 10:46, edited 1 time in total.
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hibobotamuss
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Re: What is the ratio of the inner circle's circumference to the outer cir [#permalink] New post   14 Sep 2018, 10:30
I don't get r=810−−√∗Rr=810∗R
rR=25√

How did we get that value? magbot
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Re: What is the ratio of the inner circle's circumference to the outer cir [#permalink] New post   14 Sep 2018, 10:47
added some more info hibobotamuss, does this make sense
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Re: What is the ratio of the inner circle's circumference to the outer cir [#permalink] New post   14 Sep 2018, 11:39
given, the area of C1 is 80% of C2

lets put it this way,

C1/C2=80/100

thus, pi*R1*R1/pi*R2*R2= 80/100


R1square/R2square=4/5


R1/R2=2/root5


for crcmfrnc


2piR1/2piR2=2/root5


or 2/root5
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gmatclubot
Re: What is the ratio of the inner circle's circumference to the outer cir [#permalink]
14 Sep 2018, 11:39
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