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

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Math Expert
Joined: 02 Sep 2009
Posts: 52917
What is the area of the larger of two circular regions, D and E?  [#permalink]

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04 Sep 2018, 22:53
00:00

Difficulty:

25% (medium)

Question Stats:

88% (00:48) correct 13% (00:25) wrong based on 19 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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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: What is the area of the larger of two circular regions, D and E?  [#permalink]

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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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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: What is the area of the larger of two circular regions, D and E?  [#permalink]

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04 Sep 2018, 23:03
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?   [#permalink] 04 Sep 2018, 23:03
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