GMAT PREP -Someone please help me with this math question.

[SB]

Question:

Imagine a equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

(a) 5
(b) 8
(c) 11
(d) 15
(e) 19

Answer C

When I solve this question, I am getting 22 as diameter, and 11 as the radius. Can someone please help me if you get the 11 as the answer for the diameter?

This is how I am getting 22.

Since inscribed angle for the triangle is 60, the arc angle will be 120. therefore 24=(120/360)*2pi(r)
36=pi(r)
(r) = 11.
Thus, diameter = 22

Let me know what I am doing wrong.. This question is from the GMAT PREP CD and thus I do not think the CD is wrong.....

thanks

SB

[StaceyKoprince]

Please read (and follow!) the guidelines in the stickies. GMATPrep problems have their own folders. Also, your subject line should be the first 5-8 words of the problem itself. I'll move this over to the right folder for you this time but please remember for next time! Thanks. :)

[GMAT700]

I think the solution may be:

Arc Length ABC, if you draw it correctly inscribed in a circle, represents 2/3 of the circle's circumference, not 1/3. So there are two minor arcs measuring 120 degrees, 120/360 + 120/360 = 1/3 +1/3 = 2/3 of 2piR.

Now solving for the approx. value for the Diameter:

24 = 2/3 2piR
divide both sides by 2/3:
36=2piR
divide both sides by pi
36/3.14 = 2R = diameter

Diameter is approx. 11

Hope this helps =p

[RonPurewal]

http://www.manhattangmat.com/forums/co- ... t2660.html