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Data Sufficiency (Geometry) question

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Data Sufficiency (Geometry) question

by Avinash_Tyagi » Sun Jul 24, 2011 9:39 pm
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I was wondering, why is statement 1 not sufficient on its own? (I figured ABCD must be a square since a circle is inscribed within it, and therefore both triangles must be 45-45-90 degree triangles), but the book says that statement 1 is not sufficient on its own, so what did I miss that makes statement one insufficient?
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by Anurag@Gurome » Sun Jul 24, 2011 10:18 pm
Avinash_Tyagi wrote:Image

I was wondering, why is statement 1 not sufficient on its own? (I figured ABCD must be a square since a circle is inscribed within it, and therefore both triangles must be 45-45-90 degree triangles), but the book says that statement 1 is not sufficient on its own, so what did I miss that makes statement one insufficient?
In the question, it is mentioned that ABCD is a rectangle, then we cannot assume that ABCD is a square. It is not given that a circle is inscribed in a square. The figure is not drawn to scale, may be that's the reason you got confused. Please check it again.
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by Avinash_Tyagi » Sun Jul 24, 2011 10:33 pm
Ok, So we can't assume that its a square, ok, that helps explain why statement one is not sufficient on its own.

But then how does combining the statements then make it sufficient? The book says the answer is C both statements combined but statement 2 only indicates the two are parallel, it doesn't seem like its enough.

Also thanks for the help.
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by Ozlemg » Sun Jul 24, 2011 11:41 pm
Avinash_Tyagi wrote:Ok, So we can't assume that its a square, ok, that helps explain why statement one is not sufficient on its own.

But then how does combining the statements then make it sufficient? The book says the answer is C both statements combined but statement 2 only indicates the two are parallel, it doesn't seem like its enough.

Also thanks for the help.
Hi

I did not find an excat number. I think your mistake is assuming too much. We shouldnt assume that the inscribed shape is a circle (most likely it is an elips without any info) or its angles are 90 degree etc.

IMO, this problem can be solved using property of similarity of triangles, and (2) gives a crucial info, if we correctly transcribe, the inscribed shape is a circle and Q is the diameter.
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by Frankenstein » Sun Jul 24, 2011 11:58 pm
Avinash_Tyagi wrote:Image

I was wondering, why is statement 1 not sufficient on its own? (I figured ABCD must be a square since a circle is inscribed within it, and therefore both triangles must be 45-45-90 degree triangles), but the book says that statement 1 is not sufficient on its own, so what did I miss that makes statement one insufficient?
Hi,
I am not convinced with the entire discussion. So, I will just give my views. The figure clearly shows that the circle is inscribed in the rectangle. So, it has to be a square. A circle cannot be inscribed in a rectangle unless it is a square.

QB = sqrt(8)
From this we can calculate PR,QB and all. All we know is PS and RS are perpendicular to each other. But, PS cannot be calculated unless we know RS is parallel to BC which will help us know that the triangle PSR is 45-90-45 triangle which helps us to find PS.

It is possible that you guys were deceived by the figure and assumed PS || CD and RS || QC, statement(2) should help you know that you cannot take it for granted while solving from statement(1) alone. Btw, Can you post the source? I expect a better framed question if it were from an official source.
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by Avinash_Tyagi » Mon Jul 25, 2011 8:52 am
The source is the REA GMAT book 5th edition

Ok, so the issue is that you cannot take for granted that the two triangles are similar until you know that RS is parallel to BC, and therefore you can't take for granted that the triangle i nthe circle is a 45-45-90 until you have statement two.
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