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naveenhv: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Wed Dec 16, 2009 8:26 am; Thanked: 1 times

by naveenhv » Mon Apr 25, 2011 8:03 am

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Source: Beat The GMAT — Quantitative Reasoning | Mon Apr 25, 2011 8:03 am

VivianKerr: GMAT Instructor; Posts: 1035; Joined: Fri Dec 17, 2010 11:13 amFollowed by: 365 members; Location: Los Angeles, CA; Thanked: 474 times

by VivianKerr » Tue Apr 26, 2011 7:04 am

Hi Naveen,

Since PQ and OR are parallel, then we can think of PR as a transversal. When two parallel lines are cut by a transversal (a third line), then all of the acute angles are equal, and all of the obtuse angles are equal.

Following this rule, since angle PRO = 35, then angle QPR = 35.

Angle QPR is called an "inscribed angle" since it's vertex is on the circumference of the circle, and arc QR is called the "intercepted arc".

Easier GMAT questions will put the "inscribed angle"'s vertex at the center of the circle (called a "central angle"). If we know the "central angle" we can usually solve for the arc length using a proportion, since the "central angle" is always a fraction of 360 degrees.

To find the "central angle" of 35 degrees, all we have to do is double it. So the "central angle" that corresponds to the "intercepted arc" has a measure of 70.

Now we can set up a proportion using our knowledge of part/whole:

70/360 = arc QR / 2*pi*r

Again, we can do this because there are 360 degrees total around the centerpoint of a circle, and any arc of a circle can be expressed as a fraction of the circle's total circumference (found by the expression 2*pi*r).

Since the diameter is 18, the radius is 9. Plugging that in:

70/360 = arcQR / 18pi

Now we can cross-multiply to solve:

(70)(18pi) = (360)(arcQR)
1260pi = (360)(arcQR)
3.5pi = arcQR

The answer is C.

Vivian Kerr
GMAT Rockstar, Tutor
https://www.GMATrockstar.com
https://www.yelp.com/biz/gmat-rockstar-los-angeles

Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]

Thank you for all the "thanks" and "follows"!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Apr 27, 2011 5:55 am

Hi Vivian,

I think you found the length of arc QR (which is 7pi/2), but the question asks for the length of arc PQ.

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Apr 27, 2011 5:58 am

I thought a graphic might help here.

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Brent Hanneson - Creator of GMATPrepNow.com

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