Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Aug 2014, 05:18

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Circle C is in the xy-plane, what is the area of the circle?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 02 Aug 2006
Posts: 119
Location: Mumbai
Followers: 1

Kudos [?]: 14 [0], given: 3

Circle C is in the xy-plane, what is the area of the circle? [#permalink] New post 25 Aug 2010, 03:46
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

45% (02:51) correct 55% (01:09) wrong based on 172 sessions
Circle C is in the xy-plane, what is the area of the circle?

(1) Points (-2, 0) and (0,2) lie on the circle.
(2) The radius of the circle is equal to or less than 2^(1/2).
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22143
Followers: 3407

Kudos [?]: 24912 [3] , given: 2697

Re: DS-Circle [#permalink] New post 25 Aug 2010, 04:29
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
jitendra wrote:
Circle C is in the xy-plane, what is the area of the circle?

(1) Points (-2, 0) and (0,2) lie on the circle.
(2) The radius of the circle is equal to or less than 2^(1/2).


area=\pi{r^2}, so we should find the value of radius.

It would be better if you visualize this problem.

(1) Points (-2, 0) and (0,2) lie on the circle --> two points DO NOT define a circle (three points does), hence we can have numerous circles containing these two points, thus we can not find single numerical value of radius. Not sufficient.

Side note: if you put points (-2, 0) and (0,2) on XY-plane you can see that center of the circle must be on the line y=-x (the center of the circle must be equidistant from two pints given).

(2) The radius of the circle is equal to or less than \sqrt{2} --> r\leq{\sqrt{2}}. Clearly insufficient.

(1)+(2) The distance between the 2 points given is d=\sqrt{2^2+2^2}=2\sqrt{2}, so it's min length of diameter of the circle passing these points (diameter of a circle passing 2 points can not be less than the distance between these 2 points), thus half of 2\sqrt{2} is min length of the radius of the circle --> r\geq{\sqrt{2}} but as from (2) r\leq{\sqrt{2}} then r=\sqrt{2} --> area=\pi{r^2}=2\pi. Sufficient.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 14 Jun 2010
Posts: 334
Followers: 2

Kudos [?]: 14 [0], given: 7

Re: DS-Circle [#permalink] New post 25 Aug 2010, 09:03
Good question...As Bunuel said its easier to visualise this and solve than just solving on paper!
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1365
Followers: 11

Kudos [?]: 136 [0], given: 10

GMAT Tests User
Re: DS-Circle [#permalink] New post 05 May 2011, 21:44
a+b

distance = 2* 2^(1/2) and r <= 2^(1/2)

if r = 1, then diameter = 2 which is less than 2 * 2^(1/2).Not possible.
means r = 2^(1/2).

thus area = pi * [2^(1/2)]^2.

Hence C
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22143
Followers: 3407

Kudos [?]: 24912 [0], given: 2697

Re: Circle C is in the xy-plane, what is the area of the circle? [#permalink] New post 27 Jun 2013, 21:30
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Intern
Intern
avatar
Joined: 05 May 2013
Posts: 27
GMAT 1: 730 Q50 V39
GRE 1: 1480 Q800 V680
Followers: 0

Kudos [?]: 20 [1] , given: 5

Re: Circle C is in the xy-plane, what is the area of the circle? [#permalink] New post 28 Jun 2013, 21:46
1
This post received
KUDOS
Adding to Bunnel's explanation, another way to arrive at why r >=\sqrt{2} is because the sum of any two sides of a triangle is greater than or equal to the third side. The triangle under consideration would be the one formed by the points (-2,0) , (0,2) and the center of the circle. Two sides of this triangle are equal to the radii of the circle. Thus, r+r >= distance between points (-2,0) , (0,2) = 2 \sqrt{2}.
Thanks.
Intern
Intern
avatar
Joined: 21 Mar 2013
Posts: 44
GMAT Date: 03-20-2014
Followers: 0

Kudos [?]: 14 [0], given: 56

GMAT ToolKit User
Re: DS-Circle [#permalink] New post 06 Feb 2014, 19:51
Bunuel wrote:
jitendra wrote:

Side note: if you put points (-2, 0) and (0,2) on XY-plane you can see that center of the circle must be on the line y=-x (the center of the circle must be equidistant from two pints given).


Can you please elaborate on this point.
Re: DS-Circle   [#permalink] 06 Feb 2014, 19:51
    Similar topics Author Replies Last post
Similar
Topics:
What is the area of circle O? alex90 3 23 Apr 2013, 00:35
What is the area of the circle nick_sun 4 09 Jul 2007, 03:50
Circle C and link k lie in the xy-plane. If Circle C is willget800 7 30 Apr 2006, 18:31
Circle C and line k lie in the xy-plane. If circle C is joemama142000 9 18 Dec 2005, 12:26
If the area of square S and the area of the circle C are maaverick 3 19 Mar 2005, 13:00
Display posts from previous: Sort by

Circle C is in the xy-plane, what is the area of the circle?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.