Author 
Message 
Retired Moderator
Joined: 28 May 2014
Posts: 528

In the coordinate system, the center of a circle lies at (2, 3)
[#permalink]
Show Tags
19 Mar 2018, 20:36
Question Stats:
38% (01:38) correct 63% (01:36) wrong based on 72 sessions
HideShow timer Statistics
In the coordinate system, the center of a circle lies at (2, 3). If point A with coordinates (1, 7) does not lie outside the circle, which of the following points must lie inside the circle? I. (0, 7) II. (5, 1) III. (2, 7) A) I only B) II only C) III only D) I and II only E) None of the above
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
440 to 730: If I Can, You Can Too



Senior Manager
Joined: 31 Jul 2017
Posts: 464
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: In the coordinate system, the center of a circle lies at (2, 3)
[#permalink]
Show Tags
19 Mar 2018, 22:02
saswata4s wrote: In the coordinate system, the center of a circle lies at (2, 3). If point A with coordinates (1, 7) does not lie outside the circle, which of the following points must lie inside the circle?
I. (0, 7) II. (5, 1) III. (2, 7)
A) I only B) II only C) III only D) I and II only E) None of the above The maximum distance which Point A can lie from centre = 5 (Its the distance from centre of circle to Point A). (5,1) & (2,7) lies at the circle as their distance from Centre of Circle is 5. Distance from (0,7) to (2,3) is less than 5. Hence, (0,7) lies inside the circle.
Option A.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Manager
Joined: 04 Feb 2016
Posts: 72
Location: India
Concentration: Technology, Marketing
GPA: 4
WE: Sales (Computer Software)

Re: In the coordinate system, the center of a circle lies at (2, 3)
[#permalink]
Show Tags
20 Mar 2018, 00:52
r <=5 since the point must be on or inside the circle. Option I gives R < 5. If R = 5 we do not know for certain if the point is inside the circle, hence option II is out. Option III is anyways greater than 5. A.
_________________
GMAT1 650 Q48 V32.



Intern
Joined: 17 Jan 2018
Posts: 44

Re: In the coordinate system, the center of a circle lies at (2, 3)
[#permalink]
Show Tags
20 Mar 2018, 03:08
Origin, O  (2,3) A (1,7)  Does not lie outside the circle, implies it is either on the circle or inside the circle. Distance between (2,3) and (1,7) = 5 So, radius of the circle <= 5 Q) Must lie inside the circle, implies NEITHER outside the circle NOR on the circle. D < 5 ===> D!>=5 Point 1  Distance between (2,3) and (0,7) ===> Less than 5 Point 2  Distance between (2,3) and (5,1) ===> Equals to 5 Point 3  Distance between (2,3) and (2,7) ===> More than 5 Answer is Only I. Option A. saswata4s wrote: In the coordinate system, the center of a circle lies at (2, 3). If point A with coordinates (1, 7) does not lie outside the circle, which of the following points must lie inside the circle?
I. (0, 7) II. (5, 1) III. (2, 7)
A) I only B) II only C) III only D) I and II only E) None of the above



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2015

Re: In the coordinate system, the center of a circle lies at (2, 3)
[#permalink]
Show Tags
25 Mar 2018, 11:51
Solution If the point \(A (1,7\)) does not lie outside the circle, then it can lie either on the circle or inside the circle as shown in the diagram. Let us denote the distance between the point \(A (1,7)\) and centre of the circle \((2,3)\) by \(D\). D= \(\sqrt{(2(1))^2+(37)^2}\) D= 5 Now, when the distance of point A is 5, then we are uncertain whether it lies on the circle or inside the circle. However, if the distance of any point from centre is less than 5 then we can infer, that the point is certainly inside the circle. Let us find the distance of all the points given in options. 1 (0,7) Distance= \(\sqrt{(20)^2+(37)^2}\) Distance= \(\sqrt{20}\), which is less than \(5\). Hence (0,7) lies inside the circle.2 (5, 1) Distance= \(\sqrt{(25)^2+(3(1))^2}\) Distance= \(5\) 3 (2, 7) Distance= \(\sqrt{(2(2))^2+(37)^2}\) Distance= \(\sqrt{32}\), which is greater than \(5\). Answer: A
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com




Re: In the coordinate system, the center of a circle lies at (2, 3) &nbs
[#permalink]
25 Mar 2018, 11:51






