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605-655 Level|   Geometry|      
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EMPOWERgmatRichC
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The total circumference of two circles is 36. If the first circle has 29 Oct 2015, 19:25
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45% (medium)

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69% (02:01) correct 31% (01:47) wrong based on 166 sessions

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The total circumference of two circles is 36. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?

A) 5.7
B) 6.0
C) 6.7
D) 9.7
E) 18.0


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QUANT 4-PACK SERIES Problem Solving Pack 2 Question 3 The total circumference of two...

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A
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The total circumference of two circles is 36. If the first circle has 29 Oct 2015, 22:51
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Quote:
The total circumference of two circles is 36. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
A) 5.7
B) 6.0
C) 6.7
D) 9.7
E) 18.0
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Given that first circle has a circumference that is exactly twice the circumference of the second circle.
So, the 1st circumference is 24 and 2nd circumference is 12 [as sum of both is 36]

Question asks for approximate sum of the two radii.

Radius of 1st Circle :
2πr = 24
πr = 12
r = 12 / 3.14 = approximately less than 4.

Radius of 2nd Circle :
2πr = 12
πr = 6
r = 6 / 3.14 = approximately less than 2.

So, sum of both radi is less than 6.

Thus only option (A) wins.
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The total circumference of two circles is 36. If the first circle has 30 Oct 2015, 04:02
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EMPOWERgmatRichC
QUANT 4-PACK SERIES Problem Solving Pack 2 Question 3 The total circumference of two...


A) 5.7
B) 6.0
C) 6.7
D) 9.7
E) 18.0


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Let r= Radius of smaller circle. Let R = Radius of larger circle

Therefore:

2πr + 2πR = 36

where 2r = R

Thus:

2πr + 4πr = 36
6πr = 36
r = approx 1.9


πR + 2Rπ = 36
3πR = 36
R = approx 3.8

r + R = approx 5.7

Answer is (A) 5.7
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The total circumference of two circles is 36. If the first circle has 30 Oct 2015, 04:15
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EMPOWERgmatRichC
QUANT 4-PACK SERIES Problem Solving Pack 2 Question 3 The total circumference of two...

The total circumference of two circles is 36. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?

A) 5.7
B) 6.0
C) 6.7
D) 9.7
E) 18.0


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Let C1 and C2 stand for the 2 circumferences.

C1+C2=36 and C1=2C2 --->C1=24 and C2=12


\(2 \pi r_1 = 24\) --->\(r_1 = 24/(2*\pi)\)

Similarly, \(r_2 = 12/(2*\pi)\)

\(r_1+r_2 = 36/(2\pi)\)

\(2\pi\) is a bit more than 6 and hence \(36/(2\pi)\) will be slightly less than 6 making A the correct answer.
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The total circumference of two circles is 36. If the first circle has 30 Oct 2015, 05:28
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Answer is A. c1+c2=36
c2=2c1 this gives us c1=12

Accordingly the values approximate to less than 6 with only A feasible in the range.
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The total circumference of two circles is 36. If the first circle has 01 Nov 2015, 17:08
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EMPOWERgmatRichC
QUANT 4-PACK SERIES Problem Solving Pack 2 Question 3 The total circumference of two...

The total circumference of two circles is 36. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?

A) 5.7
B) 6.0
C) 6.7
D) 9.7
E) 18.0


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Hi All,

GMAT questions sometimes include 'quirks' that are meant to test your overall understanding of a concept. Normally, when dealing with "circle" questions, the pi sign (π) is included (as part of the prompt and answer choices). Here though, it's not - but you STILL have to account for pi when doing your calculations.

We're told that the sum of the two circumferences is 36 and that the larger circumference is twice the smaller circumference.

X = smaller circumference
2X = larger circumference

X + 2X = 36
3X = 36
X = 12

So the two circles have circumferences of 12 and 24, respectively.

To find the APPROXIMATE sum of their two radii, we don't have to be hyper-accurate, but we do have to account for how we might make a 'rounding' error.

Circumference = 2(pi)(radius)

For the smaller circle, the circumference =
2(pi)(radius) = 12
radius = 12/2pi
radius = 6/pi

Since pi = approximately 3.14, 6/pi is a little LESS than 2.

With the larger circle, we double the circumference, so we double the radius. Thus, the larger circle's radius is a little LESS than 4.

(a little less than 2) + (a little less than 4) = (a little less than 6). Only one answer 'fits' that description...

Final Answer:
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A

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The total circumference of two circles is 36. If the first circle has 27 Dec 2015, 14:44
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well, it can be easily solved, if we use approximations.
we know that C1+C2=36. C1=2C2. so we have 3C2=36, or C2=12. C1=24.

Circumference is 2*pi*R.
we know C1=24. 24=2*pi*R, or 12=pi*R => R = 12/pi.
C2=12. 12=2*pi*r or 6=pi*r => r=6/pi.
the sum is 12/pi + 6/pi = 18/pi.
now, pi can be rewritten as 22/7.
18*7/22 = 9*7/11 = 63/11.
this is slightly less than 6.
the only answer choice that is less than 6 is A.
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The total circumference of two circles is 36. If the first circle has 26 Jun 2024, 10:02
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