Concentric Circles

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19 Sep 2012
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Concentric Circles

Post Wed Jan 08, 2014 4:47 am
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    Where am I going wrong in this?

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    Post Wed Jan 08, 2014 6:57 am
    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


    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

    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


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