It is currently 20 Feb 2018, 07:53

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If three circles having radii 1, 2, and 3 respectively lie o

Author Message
TAGS:

### Hide Tags

CEO
Joined: 21 Jan 2007
Posts: 2734
Location: New York City
If three circles having radii 1, 2, and 3 respectively lie o [#permalink]

### Show Tags

30 Oct 2007, 05:45
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:01) correct 22% (01:01) wrong based on 315 sessions

### HideShow timer Statistics

If three circles having radii 1, 2, and 3 respectively lie on a plane, do any two of these circles intersect?

(1) Centers of the circles form an equilateral triangle with height $$2\sqrt{3}$$

(2) Centers of the circles do not lie on the same line.

M14-02
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Feb 2014, 23:19, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
SVP
Joined: 29 Aug 2007
Posts: 2467

### Show Tags

30 Oct 2007, 06:01
1
KUDOS
bmwhype2 wrote:
Three circles have radii 1, 2, and 3 respectively lie on the plane. Do any two circles intersect?

1. Centers of the circles form an equilateral triangle with height 2*sqrt(3)
2. Centers of the circles do not lie on the same line

Can someone draw out the answer? Regards

A.

height = 2sqrt3
hypoteneous = side of the eq. triangle = 4.

so clearly not.
CEO
Joined: 21 Jan 2007
Posts: 2734
Location: New York City

### Show Tags

26 Nov 2007, 22:35
Can you explain the answer? Not sure how the height and the side of a triangle relate in finding whether the circles intersect
CEO
Joined: 17 Nov 2007
Posts: 3583
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

### Show Tags

26 Nov 2007, 23:39
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
A

Interesting question: does "osculation" means "intersection"? I guess yes. There is one point that belong to both circles. am I right?
Attachments

GCt54757.gif [ 15.3 KiB | Viewed 6054 times ]

Director
Joined: 09 Aug 2006
Posts: 754

### Show Tags

27 Nov 2007, 00:26
1
KUDOS
bmwhype2 wrote:
Three circles have radii 1, 2, and 3 respectively lie on the plane. Do any two circles intersect?

1. Centers of the circles form an equilateral triangle with height 2*sqrt(3)
2. Centers of the circles do not lie on the same line

Can someone draw out the answer? Regards

A

stat 1:
since h = 2 sqrt(3), each side = 4
If the circles don't intersect, then one of the sides will be 3+2 = 5 which is not possible. Therefore, we can determine that at least 2 of the circles intersect. Suff.

Stat 2:
This doesn't tell us anything. They could or could not intersect. Insuff.
Non-Human User
Joined: 09 Sep 2013
Posts: 13828
Re: Three circles have radii 1, 2, and 3 respectively lie on the [#permalink]

### Show Tags

18 Feb 2014, 10:40
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.
_________________
Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 590
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: Three circles have radii 1, 2, and 3 respectively lie on the [#permalink]

### Show Tags

18 Feb 2014, 10:42
Bunuel,

Is their better way to approach this question?
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India
If three circles having radii 1, 2, and 3 respectively lie o [#permalink]

### Show Tags

18 Feb 2014, 21:03
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
bmwhype2 wrote:
Three circles have radii 1, 2, and 3 respectively lie on the plane. Do any two circles intersect?

1. Centers of the circles form an equilateral triangle with height 2*sqrt(3)
2. Centers of the circles do not lie on the same line

Can someone draw out the answer? Regards

Using statement 1, make an equilateral triangle with height $$2\sqrt{3}$$ which is a little more than 3.4 since $$\sqrt{3}$$ is a little more than 1.7. The side of this triangle will be 4 (since $$Height = (\sqrt{3}/2) * Side = 2*\sqrt{3}$$)

On any one vertex, we will have the circle with the radius 2. On another, you will have to draw a circle with radius 3 but since the length of the side is only 4, this circle will intersect the circle with radius 2. Hence, statement 1 alone is sufficient.

Statement 2 doesn't tell us where the circles lie. They could lie very close to each other and intersect or very far from each other and not intersect. This statement alone is not sufficient.

*Edited
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 18 May 2014 Posts: 61 Location: United States Concentration: General Management, Other GMAT Date: 07-31-2014 GPA: 3.99 WE: Analyst (Consulting) Re: If three circles having radii 1, 2, and 3 respectively lie o [#permalink] ### Show Tags 18 May 2014, 09:40 From 1) Let "a" be the side of the Equilateral triangle. Given height = 2*3= 6 . ( height of equilater triangle with side a is sqrt(3) * a/2) ==> a= 4* sqrt(3). therefore the distance between the centers of all the three circles ,taken two at a time is = 4 * sqrt(3) . which clearly shows that the circles don't itersect. ( 4*sqrt(3) is greater than the all possible sum of the radii of the circles taken two at a time 2+3 , 1+2 , 1+3 = 5,3,4. ) Sufficient From 2) The distance between two circles is less than 6 , which implies it may be greater than 5 or less than 5. We are not sure the circles will intersect or not . Insufficient Hence A Senior Manager Joined: 21 Oct 2013 Posts: 444 If three circles having radii 1, 2, and 3 respectively lie on a plane, [#permalink] ### Show Tags 04 Sep 2014, 05:32 If three circles having radii 1, 2, and 3 respectively lie on a plane, do any two of these circles intersect? (1) Centers of the circles form an equilateral triangle with height 2√3. (2) Centers of the circles do not lie on the same line. Hi, can anyone show how geometry looks like for St(1), please. OE [Reveal] Spoiler: Statement (1) by itself is sufficient. From S1 we know how the circles are positioned relative to each other (we know the distances between the centers). Therefore, we can answer the question whether the circles cross or not. Statement (2) by itself is insufficient. The information that is missing is the distance between the centers. Math Expert Joined: 02 Sep 2009 Posts: 43828 Re: If three circles having radii 1, 2, and 3 respectively lie o [#permalink] ### Show Tags 04 Sep 2014, 06:03 goodyear2013 wrote: If three circles having radii 1, 2, and 3 respectively lie on a plane, do any two of these circles intersect? (1) Centers of the circles form an equilateral triangle with height 2√3. (2) Centers of the circles do not lie on the same line. Hi, can anyone show how geometry looks like for St(1), please. OE [Reveal] Spoiler: Statement (1) by itself is sufficient. From S1 we know how the circles are positioned relative to each other (we know the distances between the centers). Therefore, we can answer the question whether the circles cross or not. Statement (2) by itself is insufficient. The information that is missing is the distance between the centers. Merging topics. Please refer to the discussion above. _________________ Manager Joined: 27 Aug 2014 Posts: 98 Concentration: Finance, Strategy GPA: 3.9 WE: Analyst (Energy and Utilities) Re: If three circles having radii 1, 2, and 3 respectively lie o [#permalink] ### Show Tags 04 Mar 2015, 13:47 VeritasPrepKarishma wrote: bmwhype2 wrote: Three circles have radii 1, 2, and 3 respectively lie on the plane. Do any two circles intersect? 1. Centers of the circles form an equilateral triangle with height 2*sqrt(3) 2. Centers of the circles do not lie on the same line Can someone draw out the answer? Regards Using statement 1, make an equilateral triangle with side $$2\sqrt{3}$$ which is a little more than 3.4 since $$\sqrt{3}$$ is a little more than 1.7. On any one vertex, we will have the circle with the radius 1. On another, you will have to draw a circle with radius 3 but since the length of the side is only 3.4, this circle will intersect the circle with radius 1. Hence, statement 1 alone is sufficient. Statement 2 doesn't tell us where the circles lie. They could lie very close to each other and intersect or very far from each other and not intersect. This statement alone is not sufficient. Answer (A) Hi Karishma, The length of the side of the triangle would be 4, and not 2sqrt(3). This is the height as specified in the question. However the answer does not vary. Santora Non-Human User Joined: 09 Sep 2013 Posts: 13828 Re: If three circles having radii 1, 2, and 3 respectively lie o [#permalink] ### Show Tags 19 May 2016, 03:51 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. _________________ Manager Joined: 12 Jan 2015 Posts: 222 If three circles having radii 1, 2, and 3 respectively lie o [#permalink] ### Show Tags 01 Jun 2016, 23:23 VeritasPrepKarishma wrote: bmwhype2 wrote: Three circles have radii 1, 2, and 3 respectively lie on the plane. Do any two circles intersect? 1. Centers of the circles form an equilateral triangle with height 2*sqrt(3) 2. Centers of the circles do not lie on the same line Can someone draw out the answer? Regards Using statement 1, make an equilateral triangle with side $$2\sqrt{3}$$ which is a little more than 3.4 since $$\sqrt{3}$$ is a little more than 1.7. On any one vertex, we will have the circle with the radius 1. On another, you will have to draw a circle with radius 3 but since the length of the side is only 3.4, this circle will intersect the circle with radius 1. Hence, statement 1 alone is sufficient. Statement 2 doesn't tell us where the circles lie. They could lie very close to each other and intersect or very far from each other and not intersect. This statement alone is not sufficient. Answer (A) Hi VeritasPrepKarishma, As per you "length of the side is only 3.4" but according to me the lenght of side should be 4. formulae- Altitude of equilateral triangle= (\sqrt{3}/2) * (side) 2\sqrt{3} = (\sqrt{3}/2) * (side) So, side= 4.. Where I am wrong..?? Please assist. _________________ Thanks and Regards, Prakhar Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7942 Location: Pune, India Re: If three circles having radii 1, 2, and 3 respectively lie o [#permalink] ### Show Tags 02 Jun 2016, 20:52 PrakharGMAT wrote: VeritasPrepKarishma wrote: bmwhype2 wrote: Three circles have radii 1, 2, and 3 respectively lie on the plane. Do any two circles intersect? 1. Centers of the circles form an equilateral triangle with height 2*sqrt(3) 2. Centers of the circles do not lie on the same line Can someone draw out the answer? Regards Using statement 1, make an equilateral triangle with side $$2\sqrt{3}$$ which is a little more than 3.4 since $$\sqrt{3}$$ is a little more than 1.7. On any one vertex, we will have the circle with the radius 1. On another, you will have to draw a circle with radius 3 but since the length of the side is only 3.4, this circle will intersect the circle with radius 1. Hence, statement 1 alone is sufficient. Statement 2 doesn't tell us where the circles lie. They could lie very close to each other and intersect or very far from each other and not intersect. This statement alone is not sufficient. Answer (A) Hi VeritasPrepKarishma, As per you "length of the side is only 3.4" but according to me the lenght of side should be 4. formulae- Altitude of equilateral triangle= (\sqrt{3}/2) * (side) 2\sqrt{3} = (\sqrt{3}/2) * (side) So, side= 4.. Where I am wrong..?? Please assist. Yes, you are right. The height is given so the side will be 4. You will not be able to draw the circles with radii 2 and 3 without intersecting. The answer stays the same. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 203
Location: India
Re: If three circles having radii 1, 2, and 3 respectively lie o [#permalink]

### Show Tags

07 Aug 2017, 06:06
I have been posting my queries but i am not receiving any reply to the same. Can someone please help me with my doubts. From the statement 1 by finding out the length of the side for equilateral triangle how can we say that they are not intersecting??
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India
Re: If three circles having radii 1, 2, and 3 respectively lie o [#permalink]

### Show Tags

07 Aug 2017, 08:35
1
KUDOS
Expert's post
longhaul123 wrote:
I have been posting my queries but i am not receiving any reply to the same. Can someone please help me with my doubts. From the statement 1 by finding out the length of the side for equilateral triangle how can we say that they are not intersecting??

You get that the side of the equilateral triangle is 4. The centres of the 3 circles lie on the three vertices of the triangle.
On any one vertex, we will have the circle with the radius 2. On another, you will have to draw a circle with radius 3 but since the length of the side is only 4, this circle will intersect the circle with radius 2. Hence two of these circles will intersect.
Hence, statement 1 alone is sufficient.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Re: If three circles having radii 1, 2, and 3 respectively lie o   [#permalink] 07 Aug 2017, 08:35
Display posts from previous: Sort by