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What is the area of the larger of two circular regions, D and E?

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What is the area of the larger of two circular regions, D and E?  [#permalink]

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New post 04 Sep 2018, 22:53
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A
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Question Stats:

86% (00:34) correct 14% (00:25) wrong based on 14 sessions

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What is the area of the larger of two circular regions, D and E?

(1) The smaller circular region has a circumference one-fourth that of the larger circular region.
(2) The radius of D and E together is equal to 25.

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Re: What is the area of the larger of two circular regions, D and E?  [#permalink]

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New post 04 Sep 2018, 23:01
What is the area of the larger of two circular regions, D and E?

(1) The smaller circular region has a circumference one-fourth that of the larger circular region.
The circumference is \(2\pi*r\), so the relation in circumference is the same as relation in radius.
so \(R_s=\frac{R_l}{4}........R_l=4*R_s\)
but no numeric value
insufficient

(2) The radius of D and E together is equal to 25.
so \(R_l+R_s=25\)
but which circle has what radius is not known
insufficient

combined
\(R_l+R_s=25...........4*R_s+R_s=25................R_s=5\)
so \(R_l=20\) and thus area = \(\pi*20^2=400|pi\)
sufficient

C
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Re: What is the area of the larger of two circular regions, D and E?  [#permalink]

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New post 04 Sep 2018, 23:03
Let smaller circle have radius r1 and larger radius be r2
Then circumfrence will be
2*pi*r1 and 2*pi*r2 respectively
From stat 1:r1/r2 =1/4 so 4r1-r2=0...(1) not suff
From stat 2: r1+r2=25...(2)
Not suff
Together the above eqs can be solved to get the radius..so C should be the correct choice
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Re: What is the area of the larger of two circular regions, D and E? &nbs [#permalink] 04 Sep 2018, 23:03
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What is the area of the larger of two circular regions, D and E?

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