What is the radius of the circle with Center O

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

What is the radius of the circle with Center O

by gmattesttaker2 » Wed Jul 04, 2012 10:36 am

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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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Source: Beat The GMAT — Data Sufficiency | Wed Jul 04, 2012 10:36 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Jul 04, 2012 10:52 am

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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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pm; Thanked: 339 times; Followed by:49 members; GMAT Score:770

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

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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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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

by gmattesttaker2 » Wed Jul 04, 2012 4:44 pm

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Hello Brent and Eagleeye,

Many thanks for your explanations here.

Best Regards,
Sri

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prasi009: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Dec 01, 2013 1:01 am

by prasi009 » Sun Dec 01, 2013 4:25 am

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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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: What is the radius of the circle with Center O

by Scott@TargetTestPrep » Mon Jul 05, 2021 6:13 am

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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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