What is the radius of the circle with Center O

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This is from OG 10th Edition. Sorry, I dont have the OA

What is the radius of the circle below with Center O?

1) The ratio of OP to PQ is 1 to 2
2) P is the midpoint of chord AB

Any suggestions? Thanks.

Regards,
Sri
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Circle with Center O

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by [email protected] » Wed Jul 04, 2012 10:52 am
For DS questions involving Geometry, there's a nice rule that says, "To find one length, we need at least one other length."
Since no lengths are provided in either statement, the answer must be E

If you're interested, we have a free video about Geometry DS questions here: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

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by eagleeye » Wed Jul 04, 2012 10:54 am
Hi Sri:

This requires a bit of alternate thinking. We need to find the length of the radius.

Statement 1 talks about a ratio. No length given. Not sufficient
Statement 2 also talks about a ratio. Again, no length given. Not sufficient.
Together, they both talk about ratios. None talks about length. Hence, together they are insufficient as well.

E is the answer.

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by gmattesttaker2 » Wed Jul 04, 2012 4:44 pm
Hello Brent and Eagleeye,

Many thanks for your explanations here.

Best Regards,
Sri

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by prasi009 » Sun Dec 01, 2013 4:25 am
if u refer to the figure and assume the first statement as

x:2x

and next as

y:y (as p is the mid point of ab)

Draw radii to A nd B mark both as r

now we can say

r=root(x^2 + y^2)

anyway we cannot determine the actual lengths or radii


besides my argument is flawed in assuming the intersection is at right angles

so in any any any case no matter what u do u simply cannot find the length as pointed out
by someone here its all ratios there is no ways we can tell the actual length

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gmattesttaker2 wrote:
Wed Jul 04, 2012 10:36 am
This is from OG 10th Edition. Sorry, I dont have the OA

What is the radius of the circle below with Center O?

1) The ratio of OP to PQ is 1 to 2
2) P is the midpoint of chord AB

Solution:

Question Stem Analysis:


We need to determine the radius of circle O, i.e., the length of OQ.

Statement One Alone:

We see that OQ is 3 * OP. However, since we can’t determine the length of OP, we can’t determine the length of OQ. Statement one alone is not sufficient.

Statement Two Alone:

This just tells us that AP = PB and AB is perpendicular to OQ. It doesn’t allow us to determine the length of OQ. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we still can’t determine the length of OQ. We actually can’t even determine the length of any segment in the diagram, such as OP, PQ, AP, or BP. Both statements together are still not sufficient.

Answer: E

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