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16 Sep 2014, 00:16
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The radii of two concentric circles are 10 and 8 units, respectively. If the radius of the outer circle is increased by 10% and the radius of the inner circle is decreased by 50%, what is the approximate percentage increase in the area between the circles? (The area of a circle is \(\pi r^2\) and concentric circles are circles with common center.)
A. 140%
B. 141%
C. 190%
D. 192%
E. 292%
A. 140%
B. 141%
C. 190%
D. 192%
E. 292%
16 Sep 2014, 00:16
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Bookmarks
Official Solution:
The radii of two concentric circles are 10 and 8 units, respectively. If the radius of the outer circle is increased by 10% and the radius of the inner circle is decreased by 50%, what is the approximate percentage increase in the area between the circles? (The area of a circle is \(\pi r^2\) and concentric circles are circles with common center.)
A. 140%
B. 141%
C. 190%
D. 192%
E. 292%
The area between the circles is the difference between their areas: \(\pi R^2 - \pi r^2\).
Initially, the difference in areas is \(\pi 10^2 - \pi 8^2 = 36\pi\).
After resizing, the difference in areas is \(\pi 11^2 - \pi 4^2 = 105\pi\).
To find the approximate percentage increase in the area between the circles, we can use the formula: \(\frac{change}{original}*100 = \)
\(=\frac{105\pi - 36\pi}{36\pi} *100 = \)
\(= \frac{23}{12}*100 = \)
\(= (2 - \frac{1}{12}) *100 \approx\)
\(\approx 200 - 8 = 192\%\)
Therefore, the area between the circles has approximately increased by 192%.
Note: The area of a square, rectangle, the volume of a cube or a rectangular solid, and the Pythagorean theorem are not considered by the GMAT as specific geometry knowledge and can still be tested on the exam. There are several questions involving this in the GMAT Prep Focus mocks. Thus, the question above is not about geometry; it's rather on precents.
Answer: D
The radii of two concentric circles are 10 and 8 units, respectively. If the radius of the outer circle is increased by 10% and the radius of the inner circle is decreased by 50%, what is the approximate percentage increase in the area between the circles? (The area of a circle is \(\pi r^2\) and concentric circles are circles with common center.)
A. 140%
B. 141%
C. 190%
D. 192%
E. 292%
The area between the circles is the difference between their areas: \(\pi R^2 - \pi r^2\).
Initially, the difference in areas is \(\pi 10^2 - \pi 8^2 = 36\pi\).
After resizing, the difference in areas is \(\pi 11^2 - \pi 4^2 = 105\pi\).
To find the approximate percentage increase in the area between the circles, we can use the formula: \(\frac{change}{original}*100 = \)
\(=\frac{105\pi - 36\pi}{36\pi} *100 = \)
\(= \frac{23}{12}*100 = \)
\(= (2 - \frac{1}{12}) *100 \approx\)
\(\approx 200 - 8 = 192\%\)
Therefore, the area between the circles has approximately increased by 192%.
Note: The area of a square, rectangle, the volume of a cube or a rectangular solid, and the Pythagorean theorem are not considered by the GMAT as specific geometry knowledge and can still be tested on the exam. There are several questions involving this in the GMAT Prep Focus mocks. Thus, the question above is not about geometry; it's rather on precents.
Answer: D
19 Feb 2016, 12:53
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Change in big circle: 10^2-8^2 = 36
Change in small circle: 11^2-4^2 = 105
105 is barely less than 3 times bigger. 3 times bigger is 200% increase so D is the closest.
Change in small circle: 11^2-4^2 = 105
105 is barely less than 3 times bigger. 3 times bigger is 200% increase so D is the closest.
