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

It is currently 17 Feb 2019, 08:52

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     February 17, 2019

     February 17, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Valentine's day SALE is on! 25% off.

     February 18, 2019

     February 18, 2019

     10:00 PM PST

     11:00 PM PST

    We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

What is the area of the shaded portion in circle O, as pictured above,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
Joined: 06 Jun 2014
Posts: 88
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
GPA: 3.47
GMAT ToolKit User
What is the area of the shaded portion in circle O, as pictured above,  [#permalink]

Show Tags

New post 06 Feb 2016, 16:17
1
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

84% (01:26) correct 16% (03:07) wrong based on 64 sessions

HideShow timer Statistics

What is the area of the shaded portion in circle O, as pictured above, with m< O=60° and radius r = 10?

A) \(\frac{50}{3}\) \(\pi\) − \(50\sqrt{3}\)

B) \(\frac{50}{3}\) \(\pi\) − 50

C) \(\pi \sqrt{3}\)

D) \(\frac{50}{3}\) \(\pi\) − \(25\sqrt{3}\)

E) \(\frac{50}{3}\) \(\pi\)

Attachments

Geometry_Q14Image.jpg
Geometry_Q14Image.jpg [ 6.99 KiB | Viewed 3863 times ]

Intern
Intern
avatar
Joined: 03 Feb 2016
Posts: 10
Re: What is the area of the shaded portion in circle O, as pictured above,  [#permalink]

Show Tags

New post 06 Feb 2016, 17:31
It is not a hard problem, if you know the Area of a circle segment and the value of sin for a 60 degree angle.

A=\(\frac{r^2}{2}\)*(\(\frac{\pi*\alpha}{180}\)-sin\(\alpha\))

Sin \(\alpha\) 60 = \(\frac{\sqrt{3}}{2}\)

Another way is to find the Area of the triangle and the Area of the sector of circle to find the Area of the Segment of the Circle.

Area Sector - Area Triangle = Area Segment.

Hope it helps.

Ans. D)
Intern
Intern
avatar
Joined: 14 Jul 2015
Posts: 22
GMAT 1: 680 Q44 V40
GMAT 2: 710 Q49 V37
What is the area of the shaded portion in circle O, as pictured above,  [#permalink]

Show Tags

New post 07 Feb 2016, 01:32
1
As mentioned by FelixM, you simply need to take the area of the sector/circle slice and subtract the area of the interior triangle.

Area of the circle slice:

1. \(\frac{60°}{360°} * π 10 ^2\)
2. (1) reduces into \(\frac{{π 50}}{3}\)

Area of the triangle:
1. We see that the interior angle of our triangle is 60°. We are dealing with an equilateral triangle.
2. We bisect our triangle down the middle to find our height. When we bisect the triangle, that creates two sub-triangles, mirrored, each conforming to the 30-60-90 special triangle. Plugging in the magic numbers for this triangle gives us a triangle height of \(5\sqrt{3}\).
3. \(5 \sqrt{3} * 10 * \frac{1}{2} = 25 \sqrt{3}\)

To find the area of the shaded portion:
1. As mentioned above, subtract the area of the triangle from the area of the sector: \(\frac{{π 50}}{3} - 25\sqrt{3}\), which is option D.
Manager
Manager
avatar
Joined: 06 Jun 2014
Posts: 88
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
GPA: 3.47
GMAT ToolKit User
Re: What is the area of the shaded portion in circle O, as pictured above,  [#permalink]

Show Tags

New post 09 Feb 2016, 17:47
1
There are only two formulas we need to know for this question:
1) Area of Sector: \(\frac{n}{360}\) * \(\pi\) \(r^2\)
2) Area of an Equilateral Triangle: \(\frac{Side^2 \sqrt{3}}{4}\)

Area of Sector - Area of an Equilateral

\(\frac{60 \pi 10^2}{360} - \frac{10^2 \sqrt{3}}{4}\)

\(\frac{50 \pi}{3} - 25\sqrt{3}\)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9836
Premium Member
Re: What is the area of the shaded portion in circle O, as pictured above,  [#permalink]

Show Tags

New post 26 Jan 2019, 16:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: What is the area of the shaded portion in circle O, as pictured above,   [#permalink] 26 Jan 2019, 16:59
Display posts from previous: Sort by

What is the area of the shaded portion in circle O, as pictured above,

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


Copyright

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

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®.