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Is the ratio of the area of circle A to the area of square B

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Is the ratio of the area of circle A to the area of square B [#permalink] New post 19 Jun 2011, 22:22
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Is the ratio of the area of circle A to the area of square B greater than ?

(1) Square B has a side of length 2.

(2) Square B is inscribed in circle A.
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Re: Good Geometry Test [#permalink] New post 20 Jun 2011, 03:07
guygmat wrote:
Is the ratio of the area of circle A to the area of square B greater than ?

(1) Square B has a side of length 2.

(2) Square B is inscribed in circle A.


Question seems incomplete. Can you please check? Thanks.
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Re: Good Geometry Test [#permalink] New post 20 Jun 2011, 07:47
if question was...that ratio >1

its B as irrespective of sizes invloved...area of anything inscribed will be always less
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Re: Good Geometry Test [#permalink] New post 20 Jun 2011, 10:20
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guygmat wrote:
Is the ratio of the area of circle A to the area of square B greater than ?

(1) Square B has a side of length 2.

(2) Square B is inscribed in circle A.


While the question is incomplete, it actually doesn't matter; the answer has to be B. If a square is *inscribed* in a circle, then you can find the exact ratio of the area of the circle to the area of the square. We don't need any lengths - the ratio is always the same (if it's not clear why this is true, it's a useful exercise: draw a square inscribed in a circle, label the radius as 'r', and find the ratio of the area of the circle to the area of the square: you'll notice that all of your r's cancel out).

So it doesn't matter what the question actually says here; the answer has to be B.
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Re: Good Geometry Test [#permalink] New post 21 Jun 2011, 07:31
Alright! so the ratio is always 2pi then..great!
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Re: Good Geometry Test [#permalink] New post 21 Jun 2011, 13:03
gmatpapa wrote:
Alright! so the ratio is always 2pi then..great!


You've left out a slash or colon between the 2 and the Pi, but yes, the ratio of the square's area to the circle's area will be 2 to Pi here, no matter what the radius is equal to.
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Re: Good Geometry Test [#permalink] New post 23 Jun 2011, 02:28
a tells nothing about the circle. Not sufficient.

b radius ^ 2 = 2* (side-sq/2) ^ 2 = (side-sq)^2 /2

thus area's => pi *radius^2 and 2* radius^2.

this gives the ratio. sufficient.

B it is.
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Re: Good Geometry Test   [#permalink] 23 Jun 2011, 02:28
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