Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Each spoke is a radius of the circular wheel. If there are 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.
The correct answer is B.