• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If the circle above has center O and circumference 18Ï€, the

This topic has expert replies
Moderator
Posts: 1225
Joined: 29 Oct 2017
Followed by:2 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Official Guide

Image

If the circle above has center O and circumference 18Ï€, then the perimeter of sector RSTO is
$$A.\ 3\pi+9$$
$$B.\ 3\pi+18$$
$$C.\ 6\pi+9$$
$$D.\ 6\pi+18$$
$$E.\ 6\pi+24$$
OA B.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 13600
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1256 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 10, 2018 5:42 am
AAPL wrote:Official Guide

Image

If the circle above has center O and circumference 18Ï€, then the perimeter of sector RSTO is
$$A.\ 3\pi+9$$
$$B.\ 3\pi+18$$
$$C.\ 6\pi+9$$
$$D.\ 6\pi+18$$
$$E.\ 6\pi+24$$
OA B.
The circle has circumference 18Ï€
circumference = (2)(radius)(Ï€)
So, (2)(radius)(Ï€) = 18Ï€
Solve to get: radius = 9

So, OR = 9 and OT = 9

Now, we'll deal with arc RST
Here the sector angle = 60°
60°/360° = 1/6
So, the arc RST represents 1/6 of the ENTIRE circle
Since the ENTIRE circle has circumference 18Ï€, the length of arc RST = (1/6)(18Ï€) = 3Ï€

So, the perimeter of sector RSTO = 9 + 9 + 3Ï€
= 18 + 3Ï€

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide
Image
Sign up for free Question of the Day emails
And check out all of these free resources

User avatar
GMAT Instructor
Posts: 1449
Joined: 09 Oct 2010
Thanked: 59 times
Followed by:32 members

by fskilnik@GMATH » Mon Sep 10, 2018 10:07 am
AAPL wrote:Official Guide

Image

If the circle above has center O and circumference 18Ï€, then the perimeter of sector RSTO is
$$A.\ 3\pi+9 \,\,\,\,\,\,\,\, B.\ 3\pi+18 \,\,\,\,\,\,\,\, C.\ 6\pi+9 \,\,\,\,\,\,\,\, D.\ 6\pi+18 \,\,\,\,\,\,\,\, E.\ 6\pi+24$$
\[\left. \begin{gathered}
?\,\,\, = \,\,\,2R + \frac{{60}}{{360}}\left( {2\pi R} \right)\,\,\,\, \Rightarrow \,\,\,\,\,\boxed{\,\,? = 2R\,\,\left( {1 + \frac{\pi }{6}} \right)\,\,\,}\,\,\, \hfill \\
2\pi R = 18\pi \,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi } \,\,\,\,2R = 18 \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, = \,\,\underleftrightarrow {18\left( {1 + \frac{\pi }{6}} \right)}\,\, = \,\,18 + 3\pi \]

Please note that even in a trivial problem like this one, we never forget the main motto of our method:

Present FOCUS and DATA in an structured way and CONNECT them as soon as possible!

Regards,
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 4203
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:21 members

by Scott@TargetTestPrep » Wed Apr 10, 2019 4:58 pm
AAPL wrote:Official Guide

Image

If the circle above has center O and circumference 18Ï€, then the perimeter of sector RSTO is
$$A.\ 3\pi+9$$
$$B.\ 3\pi+18$$
$$C.\ 6\pi+9$$
$$D.\ 6\pi+18$$
$$E.\ 6\pi+24$$
OA B.
We see that the perimeter of sector RSTO consists of 2 radii of the circle and arc RST.

Since the circumference of the circle O is 18Ï€, its radius must be 9. Since the angle measure of sector RSTO is 60 degrees, the length of arc RST must be 1/6 of the circumference of the circle (notice that 60 degrees is 1/6 of 360 degrees). Therefore, arc RST has a length of 1/6 x 18Ï€ = 3Ï€. So the perimeter of sector RSTO is

3Ï€ + 9 + 9 = 3Ï€ + 18

Answer: B

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage