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

It is currently 19 Oct 2018, 17:55

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

A circle in the coordinate plane passes through points (-3, -2) and (1

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Oct 2015, 09:23
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:57) correct 33% (01:56) wrong based on 327 sessions

HideShow timer Statistics

A circle in the coordinate plane passes through points (-3, -2) and (1, 4). What is the smallest possible area of that circle?

A. 13π
B. 26π
C. 262√π
D. 52π
E. 64π

_________________

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

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 518
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Oct 2015, 10:29
4
Bunuel wrote:
A circle in the coordinate plane passes through points (-3, -2) and (1, 4). What is the smallest possible area of that circle?

A. 13π
B. 26π
C. 262√π
D. 52π
E. 64π


the given coordinates we can build a triangle. Let's say the chord is the diameter, so let's calculate the hypotenuse
4^2+6^2=52, area=Pi*r^2=13Pi Answer (A)
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Oct 2015, 15:12
1
1
Bunuel wrote:
A circle in the coordinate plane passes through points (-3, -2) and (1, 4). What is the smallest possible area of that circle?

A. 13π
B. 26π
C. 262√π
D. 52π
E. 64π


Circle with minimum area will be when the 2 coordinates become the ends of the diameter. In all other cases, the coordinates will end up being the chord of the circle, thus giving you circles with larger areas (as dia = greatest chord in a circle).

Based on the given coordinates, the distance between the coordinates = \(\sqrt{(-3-1)^2+(-2-4)^2}\) = \(\sqrt{52}\)

Thus, area =\(\frac{\pi*d^2}{4} = 13 \pi\) . A is the correct answer.
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Oct 2015, 19:08
1
A circle in the coordinate plane passes through points (-3, -2) and (1, 4). What is the smallest possible area of that circle?

The smallest possible area for the circle will be one that has the distance between the 2 aforementioned points as the diameter.

The distance between the two points is sqrt(52).
radius = sqrt(52)/2
Area= pi*(sqrt(52)/2)^2

Answer:
A. 13π
Manager
Manager
avatar
Joined: 02 Jul 2015
Posts: 106
Schools: ISB '18
GMAT 1: 680 Q49 V33
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Oct 2015, 19:34
1
Answer is 13pi.

The minimum area would be if these points are the endpoints of a diameter. using the distance formula or constructing a triangle and calculating the value of hypotenuse, we get the value of distance of the diameter and accordingly calculate the value of area.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 18 Oct 2015, 12:01
Bunuel wrote:
A circle in the coordinate plane passes through points (-3, -2) and (1, 4). What is the smallest possible area of that circle?

A. 13π
B. 26π
C. 262√π
D. 52π
E. 64π


VERITAS PREP OFFICIAL SOLUTION:

This problem requires you to leverage the definition that the longest chord in any circle is the diameter. Since the line connecting the two given points on the circle, (-3, -2) and (1, 4), is a chord, the smallest possible circle would occur if that chord were the diameter (the longest possible line).

Given that, taking the distance between (-3, -2) and (1, 4) will provide you with the diameter of that smallest possible circle. Since the horizontal difference (between x-coordinates) is 4 and the vertical difference (between y-coordinates) is 6, you can calculate the distance using Pythagorean Theorem:

4^2+6^2=c^2, so c^2=52 and \(c=\sqrt{52}=2\sqrt{13}\).

Remember that this distance is the diameter, so to find the area you'll want to cut it in half to find the radius. Therefore the radius is \(\sqrt{13}\) and \(\pi r^2=\pi (\sqrt{13})^2=13\pi\).
_________________

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

Manager
Manager
avatar
B
Joined: 20 Apr 2014
Posts: 94
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Apr 2016, 10:56
I selected A. but sorry Bunuel, I can not understand your point here. is there any drawing. I can not imagine. Sorry again.
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Apr 2016, 12:02
2
hatemnag wrote:
I selected A. but sorry Bunuel, I can not understand your point here. is there any drawing. I can not imagine. Sorry again.


Let me try. When you draw series of circles through the points (-3,-2) and *(1,4), you will see that the line connecting these 2 points can be either a chord or the diameter (refer to the attached figure)
Attachment:
4-11-16 2-57-19 PM.jpg
4-11-16 2-57-19 PM.jpg [ 59.09 KiB | Viewed 2268 times ]


If the line is a chord, then the radius of this circle will be > the distance between the 2 points (=\(2\sqrt {13}\))

But, if the line is the diameter of the circle, then the distance = diameter of the circle. As area of a circle is dependent on the diameter of the circle, the smallest area of the circle will be when the line joining the 2 points above is the diameter of the circle.

Thus, the circle with minimum area will have a diameter = \(2\sqrt {13}\) and thus Area = \(\frac{\pi *(2\sqrt {13})^2}{4}\) = \(13*\pi\)
Manager
Manager
avatar
B
Joined: 20 Apr 2014
Posts: 94
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 11 Apr 2016, 20:08
Great analysis. thank you pretty much Engr2012.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8459
Premium Member
Re: A circle in the coordinate plane passes through points (-3, -2) and (1  [#permalink]

Show Tags

New post 21 Sep 2018, 04:10
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: A circle in the coordinate plane passes through points (-3, -2) and (1 &nbs [#permalink] 21 Sep 2018, 04:10
Display posts from previous: Sort by

A circle in the coordinate plane passes through points (-3, -2) and (1

  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®.