Author 
Message 
Manager
Joined: 30 May 2010
Posts: 186

In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
24 Aug 2010, 22:45
Question Stats:
69% (00:35) correct 31% (01:07) wrong based on 137 sessions
HideShow timer Statistics
In the xyplane, point (r,s) lies on a circle with center at the origin. What is the value of \(r^2+s^2\)? (1) The circle has radius 2. (2) The point \((sqrt{2}, sqrt{2})\) lies on the circle. OPEN DISCUSSION OF THIS QUESTION IS HERE: inthexyplanepointrsliesonacirclewithcentera165616.html== Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
Official Answer and Stats are available only to registered users. Register/ Login.



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2697
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
24 Aug 2010, 22:55
1
This post received KUDOS
Equation of the circle is \(x^2+ y^2 = a^2\) where a = radius since r,s lies on the circle the equation becomes r^2+s^2 = a^2 statement 1: radius = \(a= 2 => r^2+s^2 = 2^2 = 4\) , thus sufficient. statement 2: we have given one point on the circle and we have the center at the origin. Thus we can find out the distance between these 2 points which will be 2. This distance is basically the radius. Since we have the radius, the statement is sufficient. Hence D
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Manager
Joined: 30 May 2010
Posts: 186

Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
24 Aug 2010, 23:45
I had forgotten the equation for the circle. Thanks!



Senior Manager
Joined: 25 Feb 2010
Posts: 420

Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
28 Aug 2010, 10:07
can some one please explain how B is correct ?
_________________
GGG (Gym / GMAT / Girl)  Be Serious
Its your duty to post OA afterwards; some one must be waiting for that...



Manager
Joined: 30 May 2010
Posts: 186

Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
28 Aug 2010, 11:06
Draw a right triangle from the origin to that point. Now solve for the hypotenuse, and you get 2. This is the radius of the circle.



Manager
Joined: 06 Apr 2010
Posts: 138

Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
09 Dec 2010, 10:31
2
This post was BOOKMARKED
In the xyplane, point (r, s) lies on a circle with center at the origin. What is the value of r^2 + s^2?
(1) The circle has radius 2. (2) The point (\(\sqrt{2}\), \(\sqrt{2}\)) lies on the circle.



Math Expert
Joined: 02 Sep 2009
Posts: 44416

Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
09 Dec 2010, 10:45
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
udaymathapati wrote: In the xyplane, point (r, s) lies on a circle with center at the origin. What is the value of \(r^2 + s^2\)? (1) The circle has radius 2. (2) The point (\sqrt{\(2\)}, \sqrt{\(2\)}) lies on the circle. THEORY: In an xy Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that: \((xa)^2+(yb)^2=r^2\) This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a rightangled triangle whose other sides are of length xa and yb. If the circle is centered at the origin (0, 0), then the equation simplifies to: \(x^2+y^2=r^2\) BACK TO THE ORIGINAL QUESTION: In the xyplane, point (r, s) lies on a circle with center at the origin. What is the value of \(r^2 + s^2\)?Now, as \(x^2+y^2=r^2\) then the question asks about the value of radius^2. (1) The circle has radius 2 > radius^2=4. Sufficient. (2) The point \((\sqrt{2}, \ \sqrt{2})\) lies on the circle > substitute x and y coordinates of a point in \(x^2+y^2=r^2\) > \(2+2=4=r^2\). Sufficient. Answer: D.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 44416

Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
Show Tags
14 Aug 2017, 05:43




Re: In the xyplane, point (r, s) lies on a circle with center
[#permalink]
14 Aug 2017, 05:43






