Last visit was: 23 Jul 2024, 19:29 It is currently 23 Jul 2024, 19:29
Toolkit
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

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.

# In the xy-plane, point (r, s) lies on a circle with center at the orig

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 08 Jul 2004
Posts: 322
Own Kudos [?]: 2207 [162]
Given Kudos: 0
Math Expert
Joined: 02 Sep 2009
Posts: 94589
Own Kudos [?]: 643388 [84]
Given Kudos: 86728
Manager
Joined: 28 Apr 2012
Posts: 239
Own Kudos [?]: 961 [13]
Given Kudos: 142
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE:Information Technology (Computer Software)
General Discussion
Intern
Joined: 09 Oct 2012
Posts: 1
Own Kudos [?]: 3 [3]
Given Kudos: 6
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
3
Kudos
Thanks for the brilliant explanation. One thing I don't get the question is that, the point (r,s) could be anywhere in the circle, not only on its circumference. Why does it refer only to a point on the circumference? Thanks!
Manager
Joined: 21 Mar 2011
Status:GMATting
Posts: 96
Own Kudos [?]: 288 [2]
Given Kudos: 104
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
2
Bookmarks
If a circle, lying on a xy-plane, has its center at the origin, the equation is x^2+y^2=R^2, where x & y are points on the circle and R is the radius of the circle.

Since x & y from the equation x^2+y^2=R^2 is similar to r & s in the question, we can rewrite as r^2+s^2=R^2.

Statement (1) gives us the value of radius, R; Therefore, r^2+s^2=4; Sufficient.
Statement (2) gives us the value of a point on the circle
=> sub x & y values of the point in r^2+s^2=R^22: 2+2 = 4;
r^2 = 4; Sufficient.

Manager
Joined: 07 Apr 2015
Posts: 127
Own Kudos [?]: 192 [0]
Given Kudos: 185
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
Hi,

i don't understand from Bunuels solution how we come up with the value of S in statement 1 in order to answer what r^2 + s^2 is?

r^2 equals 4, that is all clear, but s should be y-value, how do we get that?
Math Expert
Joined: 02 Sep 2009
Posts: 94589
Own Kudos [?]: 643388 [1]
Given Kudos: 86728
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
1
Bookmarks
noTh1ng wrote:
Hi,

i don't understand from Bunuels solution how we come up with the value of S in statement 1 in order to answer what r^2 + s^2 is?

r^2 equals 4, that is all clear, but s should be y-value, how do we get that?

$$r^2+s^2=radius^2$$. (1) says that radius = 2, thus $$r^2+s^2=2^2$$.
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6027
Own Kudos [?]: 13821 [9]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
6
Kudos
3
Bookmarks
noTh1ng wrote:
Hi,

i don't understand from Bunuels solution how we come up with the value of S in statement 1 in order to answer what r^2 + s^2 is?

r^2 equals 4, that is all clear, but s should be y-value, how do we get that?

Hi noTh1ng,

In the xy-plane, 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 (2√, −2√) lies on the circle

You seem to have misunderstood a little here.

The equation of Circle is given by $$x^2 + y^2 = Radius^2$$

Given : (r,s) lie on the circle
i.e. (r,s) will satisfy the equation of Circle
i.e. $$r^2 + s^2 = Radius^2$$

Question : Find the value of $$r^2 + s^2$$? but since $$r^2 + s^2 = Radius^2$$ therefore, the question becomes

Question : Find the value of $$Radius^2$$?

Statement 1: The circle has radius 2
i.e. $$r^2 + s^2 = Radius^2 = 2^2 = 4$$
SUFFICIENT

Statement 2: The point (√2, −√2) lies on the circle
i.e. (√2, −√2) will satisfy the equation of circle
i.e. (√2)^2 + (−√2)^2 = Radius^2
hence, $$r^2 + s^2 = Radius^2 = 2^2 = 4$$ Hence,
SUFFICIENT

I hope it helps!

Please Note: You have been confused r (X-co-ordinate) and r (Radius) as it seems from your question
Manager
Joined: 29 Dec 2014
Posts: 53
Own Kudos [?]: 7 [1]
Given Kudos: 996
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
1
Kudos
Hi,

A very fundamental or, maybe, a silly question, in GMAT, when a question like this reads 'on a circle', it's supposed to mean, on the circumference of the circle, and not the whole of the area of the circle.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 94589
Own Kudos [?]: 643388 [1]
Given Kudos: 86728
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
1
Kudos
WilDThiNg wrote:
Hi,

A very fundamental or, maybe, a silly question, in GMAT, when a question like this reads 'on a circle', it's supposed to mean, on the circumference of the circle, and not the whole of the area of the circle.

Thanks

Yes, on the circle means on the circumference.
In the circle means within.
Intern
Joined: 08 Jul 2017
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 4
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
So, for statement 2, any coordinates that are on the circle can be used to substitute for (r,s)?
Math Expert
Joined: 02 Sep 2009
Posts: 94589
Own Kudos [?]: 643388 [1]
Given Kudos: 86728
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
1
Kudos
parkerd wrote:
So, for statement 2, any coordinates that are on the circle can be used to substitute for (r,s)?

Yes, if a circle is centred at the origin, then the x and y-coordinates of any point on the circle (so on the circumference) will satisfy $$x^2+y^2=radius^2$$
Intern
Joined: 08 Jul 2017
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 4
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
If the (r,s) was inside the circle would you still be able to solve with the same equation like in statement 1? Or be able to substitute for (r,s) with the given values on the circle like in statement 2?
Math Expert
Joined: 02 Sep 2009
Posts: 94589
Own Kudos [?]: 643388 [0]
Given Kudos: 86728
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
parkerd wrote:
If the (r,s) was inside the circle would you still be able to solve with the same equation like in statement 1? Or be able to substitute for (r,s) with the given values on the circle like in statement 2?

If (r, s) were IN the circle, then the answer would be E because each statement gives us basically the same info - the length of the radius. How can we find the sum of the squares of a random point inside the circle just knowing the radius?
Director
Joined: 24 Oct 2016
Posts: 581
Own Kudos [?]: 1369 [0]
Given Kudos: 143
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
GMAT 3: 690 Q48 V37
GMAT 4: 710 Q49 V38 (Online)
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
saurya_s wrote:
In the xy-plane, 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

If a point (a, b) is on a circle with center at origin and radius = r, then a^2 + b^2 = r^2

Simply Q: r = ?

1) Sufficient
2) 2 + 2 = 4 = r^2 => Sufficient

Intern
Joined: 03 Aug 2019
Posts: 22
Own Kudos [?]: 4 [0]
Given Kudos: 686
Location: India
GPA: 4
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
Statement 1 - r and s are two different points on a circle so both have values of 2^2 and 2^ so r^2+s^2 = 8
Is this the correct inference?
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [0]
Given Kudos: 432
Location: United States
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
gayatri259 wrote:
Statement 1 - r and s are two different points on a circle so both have values of 2^2 and 2^ so r^2+s^2 = 8
Is this the correct inference?

That's not correct.

The question stem tells us the point lies on the circle with center at the origin (0,0). If the radius is 2, this means the coordinates could be (2,0), (0,2), etc.)

$$r^2 + s^2$$ will always equal 4.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19189
Own Kudos [?]: 22704 [1]
Given Kudos: 286
Location: United States (CA)
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
1
Kudos
saurya_s wrote:
In the xy-plane, 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

DS02741

Solution:

Question Stem Analysis:

We need to determine the value of r^2 + s^2, given that (r, s) is a point on the circle with center at the origin. Notice that the equation of such a circle is x^2 + y^2 = R^2 where R is the radius of the circle. Since (r, s) is a point on the circle, we have r^2 + s^2 = R^2. That is, in order to determine the value of r^2 + s^2, we either need to know the coordinates of a point on the circle or just the value of R.

Statement One Alone:

Since the radius of the circle is 2, R = 2. Therefore, r^2 + s^2 = 2^2 = 4. Statement one alone is sufficient.

Statement Two Alone:

Since (√2, -√2) is a point on the circle, x = √2 and y = -√2 will satisfy x^2 + y^2 = R^2. Substituting, we find R^2 = x^2 + y^2 = (√2)^2 + (-√2)^2 = 2+ 2 = 4. Proceeding as above, we obtain r^2 + s^2 = 4. Statement two alone is sufficient.

Non-Human User
Joined: 09 Sep 2013
Posts: 34053
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
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.
Re: In the xy-plane, point (r, s) lies on a circle with center at the orig [#permalink]
Moderator:
Math Expert
94589 posts