January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 08 May 2014
Posts: 8

The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
24 Nov 2014, 21:53
Question Stats:
67% (01:31) correct 33% (01:38) wrong based on 500 sessions
HideShow timer Statistics
The center of a circle is (5, 2). (5, 7) is outside the circle, and (1, 2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8
Official Answer and Stats are available only to registered users. Register/ Login.




Senior Manager
Joined: 13 Jun 2013
Posts: 275

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
25 Nov 2014, 01:52
anik89 wrote: The center of a circle is (5, 2). (5, 7) is outside the circle, and (1, 2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 distance between the center of the circle (5,2) and (1,2) = \(\sqrt{(51)^2 + (2+2)^2}\) \(= 4\) distance between the center of the circle (5,2) and (5,7) = \(\sqrt{(55)^2 + (7+2)^2}\) \(= 9\) now, since point (1,2) lies inside the circle, therefore radius of the circle will be greater than 4. and also since point (5,7) lies outside the circle, therefore radius of the circle will be less than 9 i.e. 4<r<9 now since r is an integer, therefore possible values of r are 5,6,7 and 8. hence answer should be A.




Director
Joined: 23 Jan 2013
Posts: 559

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
24 Nov 2014, 22:21
Idea is that possible radius is between two points: (1,2) and (5,7)
51=4, meaning that point inside the circle is 4 numbers out of center (5,2), we should count it in Y axe in (5,7) direction, so 2+4=2 and radius is between 2 and 7.
72 =5 values of R, but 7 is out and maximal possible is 4
A



Intern
Joined: 27 Nov 2014
Posts: 46

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
27 Nov 2014, 23:47
The center of a circle is (5, 2). (5, 7) is outside the circle, and (1, 2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r?
does inside the circle means not on the circle ?
if no then (5,7) if lies on the circle then we should consider that point also.
than also total is 5
Please clarify and correct where m i wrong ?
Regards SG



Senior Manager
Joined: 13 Jun 2013
Posts: 275

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
28 Nov 2014, 07:53
smartyguy wrote: The center of a circle is (5, 2). (5, 7) is outside the circle, and (1, 2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r?
does inside the circle means not on the circle ?
if no then (5,7) if lies on the circle then we should consider that point also.
than also total is 5
Please clarify and correct where m i wrong ?
Regards SG hi, the situation mentioned in the question can be visualized in the following manner. i hope it helps.
Attachments
sol.jpg [ 7.82 KiB  Viewed 5538 times ]



Intern
Joined: 11 Apr 2015
Posts: 32
Location: Germany
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Project Management (Energy and Utilities)

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
30 Jun 2016, 09:19
r must be greater than 4 and smaller than 9, hence r=5,6,7 or 8. Answer A
_________________
"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times." Bruce Lee
"I hated every minute of training, but I said, "Don’t quit. Suffer now and live the rest of your life as a champion."" Muhammad Ali



Manager
Joined: 22 Nov 2016
Posts: 208
Location: United States
Concentration: Leadership, Strategy
GPA: 3.4

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
Updated on: 06 Jul 2017, 16:06
The radius can be 5,6,7 or 8. All these cases satisfy the two given conditions.
_________________
Kudosity killed the cat but your kudos can save it.
Originally posted by sasyaharry on 06 Jul 2017, 12:31.
Last edited by sasyaharry on 06 Jul 2017, 16:06, edited 1 time in total.



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
06 Jul 2017, 12:51
Given data : R, the radius of the circle has to be an integer Center of the circle (5,2) Point inside the circle (1,2) Point outside the circle (5,7) Formula used : Distance between 2 points (x1,y1) and (x2,y2) is \(\sqrt{(x1x2)^2 + (y1y2)^2}\)
Since a point inside the circle is (1,2). The distance from the center of the circle is \(\sqrt{(51)^2 + (2+2)^2}\)(which is equal to 4) The point outside the circle is (5,7) The distance from the center of the circle is \(\sqrt{(55)^2 + (7+2)^2}\)(which is equal to 9) Since we have found out the range of the radius which is 4 < R < 9 We have four values for R (5,6,7,8) (Option A)
_________________
You've got what it takes, but it will take everything you've got



CEO
Joined: 11 Sep 2015
Posts: 3332
Location: Canada

The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
Updated on: 16 Apr 2018, 11:23
anik89 wrote: The center of a circle is (5, 2). (5, 7) is outside the circle, and (1, 2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 The center of a circle is (5, 2)As we can see from the image below, there are infinitely many circles that have their center at (5, 2) (1, 2) is INSIDE the circleWe can quickly determine that the distance from (1, 2) to the circle's center (5, 2) is 4 units... So a circle with a radius of 4 would PASS THROUGH the point (1, 2). Since (1, 2) is INSIDE the circle, we know that the radius of the circle must be GREATER THAN 4(5, 7) is OUTSIDE the circleThe distance from (5, 7) to the circle's center (5, 2) is 9 units... So a circle with a radius of 9 would PASS THROUGH the point (5, 7). Since (5, 7) is OUTSIDE the circle, we know that the radius of the circle must be LESS THAN 9So, we now have lower and upper limits of the radius. The radius of the circle is GREATER THAN 4 and LESS THAN 9In other words, 4 < r < 9Since the radius, r, is an INTEGER, there are only four possible values of r. r can equal 5, 6, 7, or 8 Answer: Cheers, Brent
_________________
Test confidently with gmatprepnow.com
Originally posted by GMATPrepNow on 25 Oct 2017, 09:19.
Last edited by GMATPrepNow on 16 Apr 2018, 11:23, edited 1 time in total.



VP
Joined: 09 Mar 2016
Posts: 1287

The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
31 Mar 2018, 06:21
pushpitkc wrote: Given data : R, the radius of the circle has to be an integer Center of the circle (5,2) Point inside the circle (1,2) Point outside the circle (5,7)
Formula used : Distance between 2 points (x1,y1) and (x2,y2) is \(\sqrt{(x1x2)^2 + (y1y2)^2}\)
Since a point inside the circle is (1,2). The distance from the center of the circle is \(\sqrt{(51)^2 + (2+2)^2}\)(which is equal to 4) The point outside the circle is (5,7) The distance from the center of the circle is \(\sqrt{(55)^2 + (7+2)^2}\)(which is equal to 9)
Since we have found out the range of the radius which is 4 < R < 9 We have four values for R(5,6,7,8) (Option A) Hi pushpitkc, i have one technical question \(\sqrt{(51)^2 + (2+2)^2}\)(which is equal to 4) can you expand it how you got 4 ... after taking square root i get this (51) + (2+2) which is 8 thank you



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3627

The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
31 Mar 2018, 06:55
dave13 wrote: Hi pushpitkc, i have one technical question \(\sqrt{(51)^2 + (2+2)^2}\)(which is equal to 4) can you expand it how you got 4 ... after taking square root i get this (51) + (2+2) which is 8 thank you Hey dave13 , \(\sqrt{(a)^2 + (b)^2}\) is not equal to \(a + b\) You should always solve the equation first (meaning add \(a^2\) and \(b^2\)) and then take the square root. Does that make sense?
_________________
My GMAT Story: From V21 to V40 My MBA Journey: My 10 years long MBA Dream My Secret Hacks: Best way to use GMATClub  Importance of an Error Log! Verbal Resources: All SC Resources at one place  All CR Resources at one place Blog: Subscribe to Question of the Day Blog GMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here. New! Best Reply Functionality on GMAT Club! Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free Check our new About Us Page here.



VP
Joined: 09 Mar 2016
Posts: 1287

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
31 Mar 2018, 07:15
abhimahna wrote: dave13 wrote: Hi pushpitkc, i have one technical question \(\sqrt{(51)^2 + (2+2)^2}\)(which is equal to 4) can you expand it how you got 4 ... after taking square root i get this (51) + (2+2) which is 8 thank you Hey dave13 , \(\sqrt{(a)^2 + (b)^2}\) is not equal to \(a + b\) You should always solve the equation first (meaning add \(a^2\) and \(b^2\)) and then take the square root. Does that make sense? many thanks abhimahna yes it make totally perfect sence \(\sqrt{(51)^2 + (2+2)^2}\)(which is equal to 4) so i get \(\sqrt{(4)^2 + (0)^2}\) \(4 + 0\) = 4 fantastic



Manager
Joined: 10 Apr 2018
Posts: 180

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
11 Jan 2019, 19:09
Bunuel, Can we tag this question to Coordinate Geometry. Thanks Probus



Math Expert
Joined: 02 Sep 2009
Posts: 52284

Re: The center of a circle is (5, 2). (5, 7) is outside the circle,
[#permalink]
Show Tags
12 Jan 2019, 02:30




Re: The center of a circle is (5, 2). (5, 7) is outside the circle, &nbs
[#permalink]
12 Jan 2019, 02:30






