It is currently 13 Dec 2017, 11:02

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The center of a circle is (5, -2). (5, 7) is outside the circle,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Intern
Intern
avatar
Joined: 08 May 2014
Posts: 8

Kudos [?]: 42 [2], given: 1

The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 24 Nov 2014, 21:53
2
This post received
KUDOS
13
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:34) correct 33% (01:40) wrong based on 337 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
[Reveal] Spoiler: OA

Kudos [?]: 42 [2], given: 1

Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 602

Kudos [?]: 31 [0], given: 41

Schools: Cambridge'16
Re: The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 24 Nov 2014, 22:21
Idea is that possible radius is between two points: (1,-2) and (5,7)

5-1=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.

7-2 =5 values of R, but 7 is out and maximal possible is 4

A

Kudos [?]: 31 [0], given: 41

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 278

Kudos [?]: 487 [2], given: 13

Premium Member
Re: The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 25 Nov 2014, 01:52
2
This post received
KUDOS
3
This post was
BOOKMARKED
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) = \(\sqrt{(5-1)^2 + (-2+2)^2}\) \(= 4\)


distance between the center of the circle (5,-2) and (5,7) = \(\sqrt{(5-5)^2 + (7+2)^2}\) \(= 9\)

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.

Kudos [?]: 487 [2], given: 13

Manager
Manager
avatar
Joined: 27 Nov 2014
Posts: 66

Kudos [?]: 25 [0], given: 21

Re: The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 27 Nov 2014, 23:47
1
This post was
BOOKMARKED
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

Kudos [?]: 25 [0], given: 21

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 278

Kudos [?]: 487 [1], given: 13

Premium Member
Re: The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 28 Nov 2014, 07:53
1
This post received
KUDOS
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
sol.jpg [ 7.82 KiB | Viewed 2964 times ]

Kudos [?]: 487 [1], given: 13

Intern
Intern
User avatar
Joined: 11 Apr 2015
Posts: 36

Kudos [?]: 13 [0], given: 98

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

New post 30 Jun 2016, 09:19
1
This post was
BOOKMARKED
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

Kudos [?]: 13 [0], given: 98

Senior Manager
Senior Manager
User avatar
G
Joined: 22 Nov 2016
Posts: 251

Kudos [?]: 64 [0], given: 42

Location: United States
Concentration: Leadership, Strategy
GPA: 3.4
Reviews Badge CAT Tests
Re: The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 06 Jul 2017, 12:31
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.


Last edited by sasyaharry on 06 Jul 2017, 16:06, edited 1 time in total.

Kudos [?]: 64 [0], given: 42

BSchool Forum Moderator
User avatar
D
Joined: 26 Feb 2016
Posts: 1702

Kudos [?]: 750 [0], given: 20

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Re: The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 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 \(\sqrt{(x1-x2)^2 + (y1-y2)^2}\)


Since a point inside the circle is (1,-2).
The distance from the center of the circle is \(\sqrt{(5-1)^2 + (-2+2)^2}\)(which is equal to 4)
The point outside the circle is (5,7)
The distance from the center of the circle is \(\sqrt{(5-5)^2 + (7+2)^2}\)(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)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 750 [0], given: 20

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 11 Sep 2015
Posts: 1906

Kudos [?]: 2743 [0], given: 364

Location: Canada
Re: The center of a circle is (5, -2). (5, 7) is outside the circle, [#permalink]

Show Tags

New post 25 Oct 2017, 09:19
Expert's post
Top Contributor
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)
Image


(1, -2) is INSIDE the circle
We can quickly determine that the distance from (1, -2) to the circle's center (5, -2) is 4 units...
Image

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
Image


(5, 7) is OUTSIDE the circle
The distance from (5, 7) to the circle's center (5, -2) is 9 units...
Image
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 9

So, we now have lower and upper limits of the radius.
The radius of the circle is GREATER THAN 4 and LESS THAN 9
In other words, 4 < r < 9

Since the radius, r, is an INTEGER, there are only four possible values of r.
r can equal 5, 6, 7, or 8

Answer:
[Reveal] Spoiler:
A


Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2743 [0], given: 364

Re: The center of a circle is (5, -2). (5, 7) is outside the circle,   [#permalink] 25 Oct 2017, 09:19
Display posts from previous: Sort by

The center of a circle is (5, -2). (5, 7) is outside the circle,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.