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

 It is currently 20 Sep 2018, 19:21

### 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

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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49271
If the circle above has center O and circumference 18π, then the perim  [#permalink]

### Show Tags

21 Nov 2017, 23:16
00:00

Difficulty:

15% (low)

Question Stats:

90% (00:46) correct 10% (00:36) wrong based on 39 sessions

### HideShow timer Statistics

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 [ 7.12 KiB | Viewed 734 times ]

_________________
Intern
Joined: 29 Aug 2016
Posts: 33
Re: If the circle above has center O and circumference 18π, then the perim  [#permalink]

### Show Tags

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.

B

Sent from my iPhone using GMAT Club Forum
Senior SC Moderator
Joined: 22 May 2016
Posts: 1977
If the circle above has center O and circumference 18π, then the perim  [#permalink]

### Show Tags

23 Nov 2017, 15:02
Bunuel wrote:

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 =

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
$$\frac{1}{6}*18π = 3π$$

From circumference:
2πr = 18π
r = 9

Perimeter = (3π + 2*9) = 3π + 18

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: If the circle above has center O and circumference 18π, then the perim  [#permalink]

### Show Tags

27 Nov 2017, 12:25
Bunuel wrote:

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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If the circle above has center O and circumference 18π, then the perim &nbs [#permalink] 27 Nov 2017, 12:25
Display posts from previous: Sort by

# Events & Promotions

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