GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 16:55 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If three circles having radii 1, 2, and 3 respectively lie o

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

Hide Tags

SVP  Joined: 21 Jan 2007
Posts: 2240
Location: New York City
If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

2
10 00:00

Difficulty:   15% (low)

Question Stats: 78% (01:31) correct 22% (01:31) wrong based on 220 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

Originally posted by bmwhype2 on 30 Oct 2007, 06:45.
Last edited by Bunuel on 19 Feb 2014, 00:19, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

3
5
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
General Discussion
SVP  Joined: 29 Aug 2007
Posts: 1910
Re: Intersecting circles  [#permalink]

Show Tags

1
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.
SVP  Joined: 21 Jan 2007
Posts: 2240
Location: New York City

Show Tags

Can you explain the answer? Not sure how the height and the side of a triangle relate in finding whether the circles intersect
CEO  B
Joined: 17 Nov 2007
Posts: 3038
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40 Show Tags

2
2
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 7903 times ]

Director  Joined: 09 Aug 2006
Posts: 590
Re: Intersecting circles  [#permalink]

Show Tags

1
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.
Senior Manager  Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 446
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

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
Manager  Joined: 18 May 2014
Posts: 54
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

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: 411
If three circles having radii 1, 2, and 3 respectively lie on a plane,  [#permalink]

Show Tags

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
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 V
Joined: 02 Sep 2009
Posts: 58464
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

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
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.
_________________
Senior Manager  P
Joined: 27 Aug 2014
Posts: 345
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

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.

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
Manager  Joined: 12 Jan 2015
Posts: 193
If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

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.

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..??
_________________
Thanks and Regards,
Prakhar
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

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.

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..??

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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager  B
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 187
Location: India
Concentration: Finance, International Business
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

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 V
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

1
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Non-Human User Joined: 09 Sep 2013
Posts: 13421
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

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.
_________________ Re: If three circles having radii 1, 2, and 3 respectively lie o   [#permalink] 08 Mar 2019, 14:45
Display posts from previous: Sort by

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

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

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