Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Jul 2014, 23:04

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the circle above, PQ is parallel to diameter OR, and OR

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 24 Jun 2009
Posts: 61
Followers: 1

Kudos [?]: 8 [0], given: 2

In the circle above, PQ is parallel to diameter OR, and OR [#permalink] New post 27 Nov 2009, 11:12
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

70% (01:32) correct 30% (02:36) wrong based on 10 sessions
I got this right but I eyeballed it. Does anyone know the proper way to solve this problem?

Image

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-circle-above-pq-is-parallel-to-diameter-or-93977.html
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Manager
Manager
User avatar
Joined: 29 Oct 2009
Posts: 211
Followers: 67

Kudos [?]: 564 [0], given: 18

GMAT Tests User
Re: Tough GMATPrep geo question - length of minor arc PQ [#permalink] New post 27 Nov 2009, 11:43
Assume centre of the circle to be point C.

Since angle ORP = 35^{\circ} , angle OCP will be = 70^{\circ}

Note: This follows from the circle property that an inscribed angle (angle ORP in our case) is exactly half the corresponding central angle (angle OCP in our case).

Now, we can calculate the length of arc OP :

Length of arc OP = (angle OCP)*(radius of circle) = \frac{7\pi}{18}*9 = \frac{7\pi}{2}
Note: An angle of 70^{\circ} corresponds to \frac{7\pi}{18} radians.

Also, since chord PQ is parallel to the diameter, arc OP must be equal to arc QR.

Therefore, total length of arc OP + QR = \frac{7\pi}{2}+\frac{7\pi}{2} = 7\pi

Now, length of arc PQ will be = half the circumference of the circle - combined length of arcs OP and QR

Half the circumference of the circle = \pi*r = 9\pi

Thus length of arc PQ = 9\pi - 7\pi = 2\pi

Answer : A
_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : distance-speed-time-word-problems-made-easy-87481.html

VP
VP
avatar
Joined: 05 Mar 2008
Posts: 1477
Followers: 11

Kudos [?]: 193 [0], given: 31

GMAT Tests User
Re: Tough GMATPrep geo question - length of minor arc PQ [#permalink] New post 27 Nov 2009, 11:50
shanewyatt wrote:
I got this right but I eyeballed it. Does anyone know the proper way to solve this problem?

Image


OCP will equal 70 so qcr = 70 and you know the part under the diameter = 180

140+180 = 320

PQ = 360-320/360

40/360 = 1/9
circumference = 18 pi
1/9*18pi = 2pi
Re: Tough GMATPrep geo question - length of minor arc PQ   [#permalink] 27 Nov 2009, 11:50
Display posts from previous: Sort by

In the circle above, PQ is parallel to diameter OR, and OR

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.