Problem Solving

There are two concentric circles with radii 10 and 8. If the radius of the outer circle increased by 10% and the radius of the outer circle decreased by 50%, approximately by what percent did the area between the circles grow?
A) 140%
B) 141%
C) 190%
D) 192%
E) 292%

We have 2 concentric circles (a circle within a circle)

Area of circle = (pi)r²

So, area of circle with radius 10 = (pi)(10²) = 100pi
Area of circle with radius 8 = (pi)(8²) = 64pi

So area between the two circles = 100pi - 64pi = 36pi

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Radius of outer circle increases 10%.
So, radius increases from 10 to 11
So, new area = (pi)(11²) = 121pi

Radius of inner circle decreases 50%.
So, radius decreases from 8 to 4
So, new area = (pi)(4²) = 16pi

So area between the two new circles = 121pi - 16pi = 105pi

Percent increase = (100)(change in value)/(original value)

If the area increases from 36pi to 105pi, the percent increase = 100(105pi - 36pi)/36pi
= (100)(69pi)/(36pi)
= 6900/36
≈ [spoiler]191.7%[/spoiler]

Answer: D

Aside: On the GMAT, it's very likely that the answer choices would have been more spread apart to allow us to quickly approximate the value of 6900/36

Cheers,
Brent