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

It is currently 18 Jan 2019, 22:22

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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

What is the greatest possible area of a triangular region with one

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 28 Jun 2008
Posts: 39
What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post Updated on: 28 Apr 2015, 03:23
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (00:35) correct 43% (00:54) wrong based on 205 sessions

HideShow timer Statistics

What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius one and the other two vertices on the circle?

A. \(\frac{\sqrt{3}}{4}\)

B. \(\frac{1}{2}\)

C. \(\frac{\pi}{4}\)

D. 1

E. \(\sqrt{2}\)

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-greatest-possible-area-of-a-triangular-region-91398.html

Originally posted by scorpio7 on 13 Jun 2009, 14:18.
Last edited by Bunuel on 28 Apr 2015, 03:23, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Manager
avatar
Joined: 28 Jan 2004
Posts: 197
Location: India
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 13 Jun 2009, 17:27
1
The two sides of the triangle will be 1.The max. are will be when it is a right triangle.
So area will be 1/2 * 1 * 1 = 1/2
Current Student
User avatar
Joined: 03 Aug 2006
Posts: 110
Location: Next to Google
Schools: Haas School of Business
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 14 Jun 2009, 00:15
Ian Stewart, one of the mods had a great explanation for this problem which I had copied and saved for my notes. Here is a cut and paste...and again credit goes to Ian for this.

"Imagine the circle is in the co-ordinate plane, centre O at (0,0). You might as well let one of the points A be at (1,0) (you can rotate the circle to get it there if you need to). Consider OA to be the base of our triangle: b=1.

Now, if (c,d) is the third point in the triangle, then the height will be |d|. To get the largest area we need the largest height, and that clearly happens when (c,d) is (0,1) or (0.-1). So the maximum area is 1*1/2 = 1/2."
Senior Manager
Senior Manager
User avatar
Joined: 07 Jan 2008
Posts: 349
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 14 Jun 2009, 09:44
nookway wrote:
Ian Stewart, one of the mods had a great explanation for this problem which I had copied and saved for my notes. Here is a cut and paste...and again credit goes to Ian for this.

"Imagine the circle is in the co-ordinate plane, centre O at (0,0). You might as well let one of the points A be at (1,0) (you can rotate the circle to get it there if you need to). Consider OA to be the base of our triangle: b=1.

Now, if (c,d) is the third point in the triangle, then the height will be |d|. To get the largest area we need the largest height, and that clearly happens when (c,d) is (0,1) or (0.-1). So the maximum area is 1*1/2 = 1/2."



This is very good solution. My way is more sophisticated. I tried to prove that max happen when the corner of circle-based vertex is 45.
Manager
Manager
avatar
Status: Quant 50+?
Joined: 02 Feb 2011
Posts: 97
Concentration: Strategy, Finance
Schools: Tuck '16, Darden '16
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 02 Oct 2011, 16:36
wooh toughie. I thought equilateral would max area and picked A, good question.
Intern
Intern
avatar
Joined: 13 Jul 2011
Posts: 13
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 02 Oct 2011, 18:51
The area of a triangle is 1/2absinx
In this a=b=1
the maximum for sinx is 1 (Sin90=1)
The area will be 1/2*1*1=1/2
Intern
Intern
avatar
Joined: 05 Sep 2011
Posts: 7
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 03 Oct 2011, 10:11
Guys please help
Two circle
have same
radius of
unit 1. If
each goes
through the
center of
other
circle, what
is the
common area?

Posted from my mobile device
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52285
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 28 Apr 2015, 03:24
1
2
scorpio7 wrote:
What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius one and the other two vertices on the circle?

A. \(\frac{\sqrt{3}}{4}\)

B. \(\frac{1}{2}\)

C. \(\frac{\pi}{4}\)

D. 1

E. \(\sqrt{2}\)


Clearly two sides of the triangle will be equal to the radius of 1.

Now, fix one of the sides horizontally and consider it to be the base of the triangle.

\(area=\frac{1}{2}*base*height=\frac{1}{2}*1*height=\frac{height}{2}\).

So, to maximize the area we need to maximize the height. If you visualize it, you'll see that the height will be maximized when it's also equals to the radius thus coincides with the second side (just rotate the other side to see). which means to maximize the area we should have the right triangle with right angle at the center.

\(area=\frac{1}{2}*1*1=\frac{1}{2}\).

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-greatest-possible-area-of-a-triangular-region-91398.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9433
Premium Member
Re: What is the greatest possible area of a triangular region with one  [#permalink]

Show Tags

New post 04 Jan 2019, 20:04
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 greatest possible area of a triangular region with one &nbs [#permalink] 04 Jan 2019, 20:04
Display posts from previous: Sort by

What is the greatest possible area of a triangular region with one

  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®.