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14 Sep 2015, 23:06
Kudos
Bookmarks
B
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:
71% (02:23) correct
29%
(02:34)
wrong
based on 331
sessions
History
Date
Time
Result
Not Attempted Yet
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the smallest sector?
A. 1/72
B. 1/36
C. 1/18
D. 1/12
E. 1/9
Kudos for a correct solution.
A. 1/72
B. 1/36
C. 1/18
D. 1/12
E. 1/9
Kudos for a correct solution.
14 Sep 2015, 23:43
Kudos
Bookmarks
Bunuel
Largest angle = 80
Let, Difference between any two angles in A.P. = d
i.e. Sum of all angles will be
80 + (80-d) + (80-2d) + (80-3d) + (80-4d) + (80-5d) + (80-6d) + (80-7d) = 640 - 28d
But sum of all central angles in a circle = 360
i.e. 640 - 28d = 360
i.e. d = 280/28 = 10
Smallest Sector = (80-7d) = 80-7*10 = 10
Smallest sector as Fraction of entire circle = 10/360 = 1/36
Answer: option B
15 Sep 2015, 02:41
Kudos
Bookmarks
Bunuel
8 spokes, then the circle is broken up into 8 sectors. The central angles of these sectors are 8 different numbers: call them a, b, c, d, e, f, g, and h, with a as the smallest number and h as the biggest number.
All of these angles add up to 360°, the total central angle in a circle.
Since there are 8 angles, the average of all the angles must be 360/8 = 45°.
Since the angle measures are evenly spaced as a series, the average of all the angles must also be the average of the smallest & the largest angles. That is, (a + h)/2 = 45.
Finally, since h = 80, we can figure out a, which equals 10.
A 10° angle is 10/360 = 1/36 of the circle. The sector with this angle occupies just 1/36 of the wheel’s area.
OA must be B.
