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PQ is a diameter of the circle above.
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22 Dec 2022, 01:11
22 Dec 2022, 01:11
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Question Stats:
84% (00:45) correct
15% (01:09) wrong based on 33 sessions
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PQ is a diameter of the circle above.
Quantity A |
Quantity B |
The length of PR |
The average (arithmetic mean) of the lengthsof PQ and PS |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: PQ is a diameter of the circle above.
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04 Jan 2023, 03:24
04 Jan 2023, 03:24
Expert Reply
OE
Notice that a diameter (such as PQ in the diagram) is the largest chord that can be drawn through a circle. The farther a chord passes from the center, the smaller the chord will be. Therefore, PQ > PR > PS. The question asks you to compare the length of PR, the middle-length chord, to the average of PQ and PS:
is PR> PQ+PS/2 ?
By moving PR and PS around, you can see that, in some cases, 2PR will be larger; in others, PQ + PS will be larger.
D is the answer
Notice that a diameter (such as PQ in the diagram) is the largest chord that can be drawn through a circle. The farther a chord passes from the center, the smaller the chord will be. Therefore, PQ > PR > PS. The question asks you to compare the length of PR, the middle-length chord, to the average of PQ and PS:
is PR> PQ+PS/2 ?
By moving PR and PS around, you can see that, in some cases, 2PR will be larger; in others, PQ + PS will be larger.
D is the answer
Re: PQ is a diameter of the circle above.
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03 Feb 2024, 21:23
03 Feb 2024, 21:23
1
Length of PR falls in between the lengths of PQ and PS
As S is moved closer to P, it gets smaller and smaller.
Similarly R can be moved closer to Q, increasing the length of PR
Depending on the distance of S and R from P and Q, the length of PR can be less than, equal to, or greater than the arithmetic mean of Lengths PQ and PS.
Thus no relationship exists between Quantity A and Quantity B
The answer is D
As S is moved closer to P, it gets smaller and smaller.
Similarly R can be moved closer to Q, increasing the length of PR
Depending on the distance of S and R from P and Q, the length of PR can be less than, equal to, or greater than the arithmetic mean of Lengths PQ and PS.
Thus no relationship exists between Quantity A and Quantity B
The answer is D
