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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If A and C are points in a plane, C is the center of circle ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If A and C are points in a plane, C is the center of circle ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ? (1) The circumference of circle O is xπ. (2) The area of circle O is xπ. OA A Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1273 messages Followed by: 29 members Upvotes: 59 Top Reply Quote: If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ? (1) The circumference of circle O is xπ. (2) The NUMERICAL VALUE of the area of circle O is equal to the NUMERICAL VALUE of xπ. Obs.: xπ is measured in unit of length, while areas are measured in unit of length squared. That´s why we modified statement (2) accordingly. ${\text{dist}}\left( {A,C} \right)\,\,\, = \,\,x\,\,\,\,\mathop > \limits^? \,\,\,r$ $\left( 1 \right)\,\,\,\,2\pi r = \pi x\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi \,} \,\,\,\,\,x = 2r\,\,\mathop > \limits^{r\,\, > \,0} r\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$ $\left( 2 \right)\,\,\,\pi {r^2} = x\pi \,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi \,} \,\,\,\,\,x = {r^2}\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,r = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 4 > 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,r = 0.5\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 0.25 < 0.5\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{N}}{\text{O}}} \right\rangle \hfill \\ \end{gathered} \right.$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1756 messages Followed by: 28 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ? (1) The circumference of circle O is xπ. (2) The area of circle O is xπ. OA A Source: Princeton Review Given C is the center of the circle, point A is outside of the circle if AC = x > radius of the circle (r) Let's take each statement one by one. (1) The circumference of circle O is xπ. Circumference of circle O = 2πr => 2πr = xπ x = 2r x > r. Sufficient. (2) The area of circle O is xπ. => πr^2 = xπ x = r^2 Case 1: Say r = 1/2, then r^2 = 1/4. We see that x < r. The answer is no. Case 2: Say r = 2, then r^2 = 4. We see that x > r. The answer is yes. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GRE Prep Locations: GRE Classes Miami | GRE Prep Course Munich | GRE Prep Denver | LSAT Prep Course Orlando | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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