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

 It is currently 25 Sep 2018, 06:12

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 in the figure above, AB is the diameter of a circle of radius 6

Author Message
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 852
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
If in the figure above, AB is the diameter of a circle of radius 6  [#permalink]

Show Tags

Updated on: 09 May 2015, 04:26
2
6
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:31) correct 33% (02:41) wrong based on 140 sessions

HideShow timer Statistics

Attachment:

T6375.png [ 7.62 KiB | Viewed 2307 times ]
If in the figure above, AB is the diameter of a circle of radius 6, what is the perimeter of the shaded region?

A. π+6+6√3
B. π+12+6√3
C. 2π+9+6√3
D. 2π+12+6√3
E. 2π+12+12√3

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Originally posted by reto on 09 May 2015, 04:22.
Last edited by Bunuel on 09 May 2015, 04:26, edited 1 time in total.
Edited the question.
Manager
Joined: 09 Jan 2013
Posts: 76
Concentration: Entrepreneurship, Sustainability
GMAT 1: 650 Q45 V34
GMAT 2: 740 Q51 V39
GRE 1: Q790 V650
GPA: 3.76
WE: Other (Pharmaceuticals and Biotech)
Re: If in the figure above, AB is the diameter of a circle of radius 6  [#permalink]

Show Tags

09 May 2015, 07:34
1
ABC is a 30-60-90 triangle since the AB is the diameter.

Since AB = 12, AC = 6√3

Now if ARC BC makes an angle of 30°, it would make 60° at the center.
Length of arc $$BC = 60/360*2π*6 = 2π$$

Thus, perimeter of the highlighted region = AB+AC+arcBC = 12+6√3+2π

Attachments

File comment: image

Untitled.png [ 9.97 KiB | Viewed 2254 times ]

Director
Joined: 12 Nov 2016
Posts: 758
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If in the figure above, AB is the diameter of a circle of radius 6  [#permalink]

Show Tags

08 Mar 2017, 13:33
What I don't understand about this problem- why wouldn't it work if we tried to use 30 degrees to calculate the arc length? Using that I arrived at answer B- how do you know its a 30 60 90 triangle?
Senior SC Moderator
Joined: 22 May 2016
Posts: 1981
If in the figure above, AB is the diameter of a circle of radius 6  [#permalink]

Show Tags

03 Apr 2017, 18:10
Nunuboy1994 wrote:
What I don't understand about this problem- why wouldn't it work if we tried to use 30 degrees to calculate the arc length? Using that I arrived at answer B- how do you know its a 30 60 90 triangle?

We know it's a 30-60-90 triangle because any inscribed triangle that has the diameter of the circle as one of its sides is a right triangle. If it's a right triangle, one of the angles is 90. We are given that the other angle is 30. Therefore it must be 30 + 90 + X = 180. X = 60.

(Converse is also true. IF a right triangle is inscribed in a circle, its hypotenuse will be the diameter.)

(Take a look at GMAT Club Math Book, Triangles - Right Triangle Inscribed in a Circle, $$https://gmatclub.com/forum/math-triangles-87197.html$$)

Posted from my mobile device
_________________

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

If in the figure above, AB is the diameter of a circle of radius 6 &nbs [#permalink] 03 Apr 2017, 18:10
Display posts from previous: Sort by

If in the figure above, AB is the diameter of a circle of radius 6

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®.