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The Official Guide For GMAT® Quantitative Review, 2ND EditionAttachment:
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What is the radius of the circle above 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