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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
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.
Re: Circle C is in the xy-plane, what is the area of the circle? [#permalink]
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.
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).
Re: Circle C is in the xy-plane, what is the area of the circle? [#permalink]
08 Mar 2015, 04:52
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. _________________
Circle C is in the xy-plane, what is the area of the circle? [#permalink]
17 Nov 2015, 18:03
neither statement alone is sufficient, yet, when we analyse both statements, we can clearly construct an isosceles triangle with base from 0;2 to 0;-2 or 4 and the angle opposite the base on the center of the circle. since there is only one value for the congruent sides to be equal on the center of the circle while the value of any 2 sides to be greater than the third, technically it is possible to identify the radius. Didn't go further... C
Re: Circle C is in the xy-plane, what is the area of the circle? [#permalink]
08 Feb 2016, 16:36
Bunuel wrote:
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.
Hi:
Please could you help me understand and visualise the highlighted bit.
Re: Circle C is in the xy-plane, what is the area of the circle? [#permalink]
08 Feb 2016, 17:01
WilDThiNg wrote:
Bunuel wrote:
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.
Hi:
Please could you help me understand and visualise the highlighted bit.
Thanks
What Bunuel means is that you can not 1 UNIQUE circle by just 2 points. As circle is a planar object, you need to have 3 distinct non collinear points to define a unique circle. Refer to the attached to see that both the circle pass through (-2,0) and (0,2). Clearly the radii of the 2 circles are different ---> giving you 2 different values of the areas. Thus this statement is NOT sufficient.
Attachment:
2016-02-08_19-59-00.jpg [ 32.78 KiB | Viewed 101 times ]
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Wow! MBA life is hectic indeed. Time flies by. It is hard to keep track of the time. Last week was high intense training Yeah, Finance, Accounting, Marketing, Economics...