Question: 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.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are not sufficient.
“What is the Radius of the Circle above with Center O?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Problem statement Analysis:
We need to determine the radius of circle O, i.e., the length of OQ.
We will check each statement one by one.
Statement One Alone:
We see that OQ is 3 * OP. However, we can’t determine the length of OP. Since, we can’t determine the length of OP, we cannot determine the length of OQ.
Hence, statement one alone is not sufficient.
Statement Two Alone:
Tells us that AP = PB and AB is perpendicular to OQ. It doesn’t allow us to determine the length of OQ.
Hence, 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.
Hence, E is the correct answer.
Approach Solution 2:
From Statement 1, we get:
OP:PQ=1:2
OQ is the radius.It is not possible to calculate a single value for radius based on ratio.
Hence, the statement is Insufficient
From Statement 2, we get:
P is the midpointt of chord AB
Again this implies triangles OAP & OQP are congruent but gives no unique value can be calculated based on this.
This is also Insufficient.
Combining the two,we do not get any absolute value for radius.
Hence, E is the correct answer.
Approach Solution 3:
Find Out:
We need to determine the radius of circle O, i.e., the length of OQ.
Statement One:
OQ is 3 * OP.
We can’t determine the length of OP,
we also can’t determine the length of OQ.
Hence, statement one alone is not sufficient.
Statement Two:
This 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:
We still can’t determine the length of OQ. We cannot determine the length of any segment in the diagram, such as OP, PQ, AP, or BP. Both statements together are still not sufficient.
Hence, E is the correct answer.
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