February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 25 Apr 2012
Posts: 681
Location: India
GPA: 3.21
WE: Business Development (Other)

Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
13 Jul 2014, 11:09
Question Stats:
76% (01:00) correct 24% (01:11) wrong based on 441 sessions
HideShow timer Statistics
Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical. (2) At least two different diameters of the circle contain point Q.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Sep 2009
Posts: 53020

Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
14 Jul 2014, 01:57
Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical. Only the center is equidistant from more than two points on the circumference. Hence Q must be the center. Sufficient. (2) At least two different diameters of the circle contain point Q. Two diameters intersect at the center, hence Q must be the center. 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



Manager
Joined: 13 Mar 2013
Posts: 163
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
09 Sep 2015, 23:29
Hi Bunuel , I got the option one . But for option 2 i am confused . (2) At least two different diameters of the circle contain point Q . At least two different diameter means the diameter of different length . Then how come point Q becomes the center of the circle . Please explain . if possible by diagram . Thanks
_________________
Regards ,



Math Expert
Joined: 02 Sep 2009
Posts: 53020

Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
10 Sep 2015, 00:18
abhisheknandy08 wrote: Hi Bunuel ,
I got the option one .
But for option 2 i am confused . (2) At least two different diameters of the circle contain point Q . At least two different diameter means the diameter of different length . Then how come point Q becomes the center of the circle . Please explain . if possible by diagram . Thanks The diameter of a circle is the length of the line through the center and touching two points on its edge. The lengths of all possible diameters are the same and different diameters cross each other at the center. So, if two different diameters have one point in common, then it must be the center. Attachment:
Untitled.png [ 2.38 KiB  Viewed 6532 times ]
_________________
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



Current Student
Joined: 20 Jul 2014
Posts: 20
Location: India
GPA: 3.16

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
24 Sep 2016, 00:24
Just wanted to understand  if statement 1 said there exist 2 points instead of 3, this statement would be insufficient right? I am just thinking logically, there can be 2 lines drawn from any point which would be equal ?



Manager
Joined: 28 Jun 2016
Posts: 207
Location: Canada
Concentration: Operations, Entrepreneurship

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
26 Sep 2016, 12:37
Neeraj91 wrote: Just wanted to understand  if statement 1 said there exist 2 points instead of 3, this statement would be insufficient right? I am just thinking logically, there can be 2 lines drawn from any point which would be equal ? Yes you are right. It has to be equidistant from at least three points. Sent from my iPhone using GMAT Club Forum mobile app



Manager
Joined: 26 Mar 2016
Posts: 71
Location: Greece
GPA: 2.9

Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
13 Jan 2017, 09:52
My approach to the problem. (1) If there are 3 points which lie on the circle's circumference then it must be true that Q is the center of the circle. Lets test a case in which Q is NOT the center of the circle. If Q is NOT the center of the circle, located ANYWHERE inside the circle, we CAN draw another circle inside this one in which Q is the center as you can see below. In this case the new circle can only be tangent at ONE point of the bigger circle's circumference or even not be tangent at all , making it IMPOSSIBLE for other points to be equidistant from the center of the new circle to the big circle's circumference. (2) Every pair of diameters of the circle intersect at only one point inside the circle. The center of the circle.
Attachments
.png [ 2.79 KiB  Viewed 3706 times ]
_________________
+1 Kudos if you like the post



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
23 Feb 2017, 04:46
Prompt analysis Point Q lies inside the circle. Super set The answer could be either YES or NO Translation We need other information such that we can answer the question based on the property of the circle Statement analysis St 1: 3 non collinear points will be equidistant from only one point. If a circle passes through 3 non collinear points,, then the 4 fourth point which will be equidistant from those 3 points will be the centre of the circle.Hence option b,c and e eliminated. St 2: two diameters intersect at the centre.if the intersection point is q, therefore q is the centre. Hence option D
_________________
GMAT Mentors



Manager
Joined: 23 Dec 2013
Posts: 145
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44
GPA: 3.76

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
21 May 2017, 19:53
WoundedTiger wrote: Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical. (2) At least two different diameters of the circle contain point Q. Statement 1: An infinite number of points can be equidistant from two points on a circle, but only the center of a circle can be equidistance from more than 2 points. So Q must be the center. Statement 2: Diameters must pass through the center and they only intersect at the center, so Q must be the center of the circle if two diameters converge there.



Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 196
Location: India
Concentration: Finance, International Business

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
29 Jul 2017, 20:48
I have doubt in the statement 2, It says that the point Q is at least on the 2 diameters , so point Q can be on the diameter also. So its not that Q is the center of the circle. Kindly correct me . I know my concept is somewhere incorrect



Math Expert
Joined: 02 Sep 2009
Posts: 53020

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
30 Jul 2017, 00:50



Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
GPA: 2.66

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
05 Sep 2017, 15:11
WoundedTiger wrote: Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical. (2) At least two different diameters of the circle contain point Q. Statement 1 This scenario only holds true if each of the lines are equidistant, which can only occur if they branch out from the center of the circle Statement 2 Bunuel if two lines are not parallel then they intersect right? And in this scenario the lines must clearly intersect at the center? D



Math Expert
Joined: 02 Sep 2009
Posts: 53020

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
05 Sep 2017, 19:45
Nunuboy1994 wrote: WoundedTiger wrote: Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical. (2) At least two different diameters of the circle contain point Q. Statement 1 This scenario only holds true if each of the lines are equidistant, which can only occur if they branch out from the center of the circle Statement 2 Bunuel if two lines are not parallel then they intersect right? And in this scenario the lines must clearly intersect at the center? D ________________ Yes, that's correct.
_________________
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



NonHuman User
Joined: 09 Sep 2013
Posts: 9869

Re: Point Q lies in the interior of a particular circle.
[#permalink]
Show Tags
28 Sep 2018, 04:05
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Point Q lies in the interior of a particular circle.
[#permalink]
28 Sep 2018, 04:05






