EMPOWERgmatRichC wrote:
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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This question is part of the Quant 4-Pack seriesScroll Down For Official Explanation 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