GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 27 Jun 2019, 03:34

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.

Close

Request Expert Reply

Confirm Cancel

If the circle above has center O and circumference 18m, then the perim

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Board of Directors
User avatar
D
Joined: 01 Sep 2010
Posts: 3385
If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post Updated on: 21 May 2017, 11:49
Top Contributor
6
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:14) correct 19% (01:42) wrong based on 193 sessions

HideShow timer Statistics


Image

If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Attachment:
6p5jvHu.jpg
6p5jvHu.jpg [ 10.49 KiB | Viewed 5309 times ]

_________________

Originally posted by carcass on 21 May 2017, 11:39.
Last edited by Bunuel on 21 May 2017, 11:49, edited 3 times in total.
Edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55804
Re: If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 21 May 2017, 11:48
1
2
carcass wrote:
Image

If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Attachment:
6p5jvHu.jpg


The perimeter of of sector RSTO is (radius OR) + (radius OT) + (minor arc RT).

The circumference is \(18\pi\): \(2\pi{r}=18\pi\) --> \(r=9\);

Since angle ROT is 60 degrees then minor arc RT is \(\frac{60}{360}*circumference=3\pi\);

So, the perimeter of sector RSTO is (radius OR) + (radius OT) + (minor arc RT) = \(9+9+3\pi=3\pi+18\).

Answer: B.
_________________
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 740
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 21 May 2017, 19:06
carcass wrote:
Image

If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Attachment:
6p5jvHu.jpg


Circumference = 2\(\pi\)r = 18\(\pi\)
r = \(\frac{18}{2}\) = 9

Perimeter of sector RSTO = Arc Length + r + r
Arc Length = 2\(\pi\)r\(\frac{C}{360}\) (C is central angle of the sector)
C = \(60^{\circ}\)
Arc Length = 2\(\pi\)r\(\frac{60}{360}\) = 2*9*\(\pi\)\(\frac{60}{360}\) = 3\(\pi\)

Therefore Perimeter of sector RSTO = 3\(\pi\) + 9 + 9 = 3\(\pi\) + 18
Answer B...

_________________
Kindly press "+1 Kudos" to appreciate :)
Intern
Intern
avatar
B
Joined: 28 May 2015
Posts: 36
Location: India
GMAT 1: 710 Q51 V34
GPA: 4
Reviews Badge
Re: If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 22 May 2017, 13:20
Let's solve it part by part

Arc makes 60 deg i.e. 1/6 of 360 deg that is 1/6 of circumference = π.18/6 = 3.π

Now we know the formula of circumference = π . D where D is diameter
C = π• 18
Observe OR + OT = diameter = 18

Answer B

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
Intern
Intern
avatar
B
Joined: 29 Aug 2016
Posts: 35
GMAT ToolKit User
Re: If the circle above has center O and circumference 18π, then the perim  [#permalink]

Show Tags

New post 22 Nov 2017, 05:44
Answer is B. 3*pi + 18.

We can find the radius from the circumference which is equal to 2*pi*r.

And the length of the arc is (Angle/360) X Circumference.

Hence the answer.

B


Sent from my iPhone using GMAT Club Forum
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2955
If the circle above has center O and circumference 18π, then the perim  [#permalink]

Show Tags

New post 23 Nov 2017, 15:02
Bunuel wrote:
Image
If the circle above has center O and circumference 18π, then the perimeter of the sector RST is

(A) 3π + 9
(B) 3π + 18
(C) 6π + 9
(D) 6π + 18
(E) 6π + 24

Attachment:
2017-11-21_1032_002.png

Perimeter of sector RST =
RST arc length + 2*(radius)

Sector RST is what fraction of the circle?

\(\frac{SectorAngle}{Circle}=\frac{60°}{360°}=\frac{1}{6}\)

Sector RST = \(\frac{1}{6}\) of the circle.

RST arc length?
\(\frac{1}{6}\) of circumference
\(\frac{1}{6}*18π = 3π\)

Radius length?
From circumference:
2πr = 18π
r = 9

Perimeter = (3π + 2*9) = 3π + 18

Answer B
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.


Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: If the circle above has center O and circumference 18π, then the perim  [#permalink]

Show Tags

New post 27 Nov 2017, 12:25
Bunuel wrote:
Image
If the circle above has center O and circumference 18π, then the perimeter of the sector RST is

(A) 3π + 9
(B) 3π + 18
(C) 6π + 9
(D) 6π + 18
(E) 6π + 24

Attachment:
2017-11-21_1032_002.png


We see that arc RST corresponds with a central angle of 60 degrees; thus, arc RST is 60/360 = 1/6 of the circumference of the circle. Thus, arc RST = ⅙ x 18π = 3π.

Since the circumference = 18π, the radius of the circle = 18π/(2π) = 9. We see that RO and TO are radii, so each is equal to 9.

Thus, the perimeter of sector RST is 3π + 9 + 9 = 3π + 18.

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
avatar
B
Joined: 10 Sep 2014
Posts: 78
Location: Bangladesh
GPA: 3.5
WE: Project Management (Manufacturing)
If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 04 May 2018, 07:52
1
Bunuel what is the concept underneath this line "Since angle ROT is 60 degrees then minor arc RT is \(\frac{60}{360}*circumference=3\pi\);" Please clarify how you're getting 3pi from 60 degree single angle ROT. Thanks.
Manager
Manager
avatar
B
Joined: 03 Oct 2016
Posts: 124
Re: If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 04 May 2018, 08:06
sadikabid27 wrote:
Bunuel what is the concept underneath this line "Since angle ROT is 60 degrees then minor arc RT is \(\frac{60}{360}*circumference=3\pi\);" Please clarify how you're getting 3pi from 60 degree single angle ROT. Thanks.


Length of arc of the circle is calculated by \(\frac{The Angle Arc Makes With Center}{360}\) * Circumference.

In this case its, \(\frac{60}{360}\)*\(18pi\)= \(3pi\).

Hope its clear.
_________________
:-) Non-Allergic To Kudos :-)
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3787
Location: Canada
Re: If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 10 Sep 2018, 06:44
Top Contributor
carcass wrote:
Image

If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Attachment:
6p5jvHu.jpg



The circle has circumference 18π
circumference = (2)(radius)(π)
So, (2)(radius)(π) = 18π
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 18π, the length of arc RST = (1/6)(18π) =

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

Answer: B
_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6681
Location: United States (CA)
Re: If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 14 Sep 2018, 09:30
carcass wrote:
Image

If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Attachment:
6p5jvHu.jpg


Since the circumference of circle O is 18π, the radius is 9. Therefore, OR = OT = 9. Furthermore, since angle ROT is 60 degrees, which is 1/6 of 360 degrees, arc RST is 1/6 of the circumference. Therefore, arc RST = 3π. So the perimeter of sector RSTO is 9 + 9 + 3π = 18 + 3π.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Director
User avatar
P
Joined: 04 Sep 2015
Posts: 565
Location: India
WE: Information Technology (Computer Software)
Premium Member Reviews Badge
Re: If the circle above has center O and circumference 18m, then the perim  [#permalink]

Show Tags

New post 14 Sep 2018, 11:42
[quote="carcass"]Image

If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


first find the arc,

60/360=x/18π,
x=3π.

then find radius,

2πr=18π,so r=9.
9+9+3π=18+3π. Answer B.
GMAT Club Bot
Re: If the circle above has center O and circumference 18m, then the perim   [#permalink] 14 Sep 2018, 11:42
Display posts from previous: Sort by

If the circle above has center O and circumference 18m, then the perim

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne