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29 Nov 2017, 22:59
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (01:33) correct
44%
(01:21)
wrong
based on 87
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, square PQRS, initially in position I, has been rotated about point S to position II. If P2, Q2 and R2 are the second positions of P, Q and R respectively, and if a
side of the square is 1, what is the length of the path followed by P in rotating to P2 ?
(A) π/4
(B) 1
(C) π/2
(D) 2
(E) π
Attachment:
2017-11-30_0950_002.png [ 5.44 KiB | Viewed 2848 times ]
29 Nov 2017, 23:03
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C.
The path followed by P is a quarter circle. Hence the length is 2*pi*r/4. Here r=1. Hence pi/2
Sent from my iPhone using GMAT Club Forum
The path followed by P is a quarter circle. Hence the length is 2*pi*r/4. Here r=1. Hence pi/2
Sent from my iPhone using GMAT Club Forum
30 Nov 2017, 11:44
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Bunuel
This is a question where we need to have the ability to visualize properly.
From the diagram, we can notice that the position of S has not changed.
Thus, if we consider S as the centre and the length SP as the radius of a circle, we can easily say that the length SP was rotated by 90 degrees and hence the trajectory followed by the point P is of an arc of a quarter circle ( a sector of circle with central angle as 90 degrees)
Thus the length of the path = \(\frac{90}{360} * 2πr = \frac{1}{4} * 2 * π * 1 = \frac{π}{2}\)
Therefore the correct answer is Option C.
