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08 Jul 2015, 03:53
Kudos
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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:
45%
(medium)
Question Stats:
56% (01:34) correct
44%
(01:50)
wrong
based on 172
sessions
History
Date
Time
Result
Not Attempted Yet
The operation above rotates the regular pentagon clockwise by (72n) degrees from its center. What replaces the initial b position when n = 4?
A. a
B. b
C. c
D. d
E. e
Kudos for a correct solution.
Attachment:
pentagon.gif [ 1.85 KiB | Viewed 4672 times ]
08 Jul 2015, 04:20
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Bunuel
The central Angle will be divided in to 5 equal parts when all vertices are joined with the centre of the Pentagon
Therefore Each angle = 360/5 = 72 Degree
i.e. When the Pentagon Rotates by 72 degrees then A replaced the Point B
i.e. When the Pentagon Rotates by 72*2 degrees then E replaced the Point B
i.e. When the Pentagon Rotates by 72*3 degrees then D replaced the Point B
i.e. When the Pentagon Rotates by 72*4 degrees then C replaced the Point B
Answer: Option C
General Discussion
13 Jul 2015, 02:21
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Bunuel
800score Official Solution:
Think of the polygon as you would a wheel being rotated at its center. A wheel sweeps a 360º angle everytime it returns to its initial positon. Since this is a regular pentagon, we can increment our rotations by dividing 360/5 = 72.
So everytime the center spins 72º clockwise, the polygon moves by one vertex. So, when n = 4 the pentagon rotates by 4 vertices and the initial b position is replaced by c or answer choice (C).
An alternative way to consider the problem is to realize that everytime n = 5, it returns to its original configuration. So, when n = 4, the position is occupied by the vertex that is one vertex away in the clockwise direction because it lags by one 72º turn.
