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Updated on: 27 May 2013, 03:28
Originally posted by gmatquant25 on 27 May 2013, 03:11.
Last edited by gmatquant25 on 27 May 2013, 03:28, edited 2 times in total.
Last edited by gmatquant25 on 27 May 2013, 03:28, edited 2 times in total.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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60% (01:24) correct
40%
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The area of a circle is increased by 800%. By what percent has the diameter of the circle increased?
(A) 100%
(B) 200%
(C) 300%
(D) 600%
(E) 800%
(A) 100%
(B) 200%
(C) 300%
(D) 600%
(E) 800%
27 May 2013, 03:21
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gmatquant25
The area of a circle is increased by 800%. By what percent has the diameter of the circle increased?
(A) 100%
(B) 200%
(C) 300%
(D) 600%
(A) 100%
(B) 200%
(C) 300%
(D) 600%
The area of the circle is increased by 800%, thus the area is increased 9 times.
The area of a circle it proportional to the square of the diameter (\(area=\pi{\frac{d^2}{4}}\)), therefore the diameter must increase 3 times (diameter increase 3 times = area increase 9 times), which is increase by 200%.
Answer: B.
Similar questions to practice:
at-a-certain-pizza-parlor-the-diameter-140460.html
the-weight-of-a-hollow-sphere-is-directly-dependent-on-its-142327.html
Hope it helps.
21 Nov 2013, 16:07
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Another approach. Firstly, given that area increased by 800%. It means that if we take initial area as 100% then final area is (100%+800%=)900%. Now, make two equations:\(pi(R^2)=100\)-----> R=10/\(\sqrt{pi}\). Likewise, \(pi(r^2)=900\)---->r=30/\(\sqrt{pi}\). Answer is \(\frac{(r-R}{R)}\)*100=200%.
