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by Stuart@KaplanGMAT » Tue Jan 08, 2008 7:20 pm
How about reasoning it out without solving formulas?

If the area of the shaded region is 3 times as much as that of the non-shaded region, then the ratio of the area of the big circle to that of the small circle is 4:1.

Area is based off of the square of the radius... so if the big circle has 4 times the area, it will have root 4 = 2 times the radius.

Since circumference is linear, if the big circle has twice the radius, it will also have twice the circumference.
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by II » Thu Jan 10, 2008 5:13 pm
Stuart Kovinsky wrote:How about reasoning it out without solving formulas?

If the area of the shaded region is 3 times as much as that of the non-shaded region, then the ratio of the area of the big circle to that of the small circle is 4:1.

Area is based off of the square of the radius... so if the big circle has 4 times the area, it will have root 4 = 2 times the radius.

Since circumference is linear, if the big circle has twice the radius, it will also have twice the circumference.
A very good point ... and a different way of looking at this ! :-)
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