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Geometry

by BTGmoderatorRO » Sun Jan 07, 2018 7:34 am
There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles grow?

140%
141%
190%
192%
292%

OA is D

DO I need to draw a solid shape to interpret this? Pls, an Expert contribution is needed.
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by Brent@GMATPrepNow » Sun Jan 07, 2018 7:37 am
Roland2rule wrote:There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles grow?

140%
141%
190%
192%
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

---------------------------------------

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
Brent Hanneson - Creator of GMATPrepNow.com
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