Problem Solving Pack 2, Question 3 The total circumference of two...

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.

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.

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:

GMAT assassins aren't born, they're made,
Rich

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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