heshamelaziry wrote:The area of a certain circle is 8 times the area of a sector of the circle. What is the perimeter of the sector ?
A- The circumference of the circle is 12Pi.
B- The area of the sector is 9Pi/2
We know that everything about sectors of circles is proportional. We have the general circle sector ratio:
(degree measure of sector)/360 = (arc length of sector)/circumference = (area of sector)/(area of circle)
From the original, we know that (area of sector)/(area of circle) = 1/8; therefore, we can figure out the degrees of the arc (360/8) and the relationship between the arc length and the circumference (1:8).
What we're missing right now is a measurement - our circle could be tiny or could be huge.
The GMAT loves to test circles in data sufficiency, because if you know 1 concrete measurement you automatically know all the others; if you know 1 of radius, diameter, circumference or area, you know the entire circle.
So, we need pretty much any concrete measurement, keeping in mind that the perimeter of the sector is r + r + arc length of the sector.
(1) circumference = 12pi. Perfect, we can calculate radius and the arc length of the sector: sufficient.
(2) area of the sector = 9pi/2. Perfect, we can calculate the area of the entire circle, then the radius, then the circumference, then the arc length of the sector: sufficient.
Each statement is sufficient alone: choose D.
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Based on your question, it looks like you want to see the calculations as well. We'd never need (or want) to do so on a DS question, but here you go:
(1) 2(pi)r = 12pi
r = 6
12pi = 8(arc length)
1.5pi = arc length
perimeter of sector = 2r + arc length = 12 + 1.5pi
(2) area of the sector = 9pi/2
area of circle = 8(9pi/2) = 36pi
36pi = pi(r^2)
36 = r^2
6 = r
circumference of circle = 2pi(r) = 12pi
12pi = 8(arc length)
1.5pi = arc length
perimeter of sector = 2r + arc length = 12 + 1.5pi
