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What is the area of the shaded region? (1) Radius of circle with cente

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What is the area of the shaded region? (1) Radius of circle with cente  [#permalink]

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New post 04 Sep 2018, 23:30
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A
B
C
D
E

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  45% (medium)

Question Stats:

48% (00:47) correct 52% (01:21) wrong based on 20 sessions

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What is the area of the shaded region?

(1) Radius of circle with center O is one-third the radius of the circle with center P.
(2) The area of the unshaded region is 36π


Attachment:
image013.jpg
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Re: What is the area of the shaded region? (1) Radius of circle with cente  [#permalink]

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New post 05 Sep 2018, 01:18
Bunuel wrote:
Image
What is the area of the shaded region?

(1) Radius of circle with center O is one-third the radius of the circle with center P.
(2) The area of the unshaded region is 36π


Attachment:
image013.jpg
St1) figure is not restricted. Various sizes circle are possible with varying common overlaps. Another way to think is count information is asked but ratio information is given.
Not suff.

St2) various radius can give 36pi as area of unshaded region. So overlap will keep on changinh.

Combining: the radius is restricted and unshed area is restricted. So only one unique value of common overlap exist

Answer seems C

Thank you = Kudos
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Re: What is the area of the shaded region? (1) Radius of circle with cente  [#permalink]

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New post 05 Sep 2018, 02:02
i think the ans should be e

chetan2u can you please help in solving this?
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Re: What is the area of the shaded region? (1) Radius of circle with cente  [#permalink]

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New post 05 Sep 2018, 02:17
sumit411 wrote:
Bunuel wrote:
Image
What is the area of the shaded region?

(1) Radius of circle with center O is one-third the radius of the circle with center P.
(2) The area of the unshaded region is 36π


Attachment:
image013.jpg
St1) figure is not restricted. Various sizes circle are possible with varying common overlaps. Another way to think is count information is asked but ratio information is given.
Not suff.

St2) various radius can give 36pi as area of unshaded region. So overlap will keep on changinh.

Combining: the radius is restricted and unshed area is restricted. So only one unique value of common overlap exist

Answer seems C

Thank you = Kudos


area of A + Area of B - 2(shaded region) = 36 pi

with the available info, we can not calculate the area of the shaded region
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Re: What is the area of the shaded region? (1) Radius of circle with cente  [#permalink]

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New post 05 Sep 2018, 02:21
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1
rahulkashyap wrote:
i think the ans should be e

chetan2u can you please help in solving this?


Yes you are correct..

Individually each statement is incorrect so let's look at combined
There can be various ways ..
1) both are concentric as shown in sketch , so 36π=πr^2 as the area is smaller circle will be completely shaded.. r=6
R of larger circle =6*3=18
Area of unshaded portion is π(18^2-6^2)

2) say the radius of each are very large 100 and 3*100
Then a small overlapped portion can give you 36π

So different answers possible

E
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Re: What is the area of the shaded region? (1) Radius of circle with cente &nbs [#permalink] 05 Sep 2018, 02:21
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