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

It is currently 19 Jul 2018, 10:46

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

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

2 KUDOS received
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2694
Location: New York City
If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

New post Updated on: 19 Feb 2014, 00:19
2
8
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (00:59) correct 22% (00:59) wrong based on 328 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.
Most Helpful Expert Reply
Expert Post
3 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

New post 18 Feb 2014, 22:03
3
3
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.


Answer (A)

*Edited
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

General Discussion
1 KUDOS received
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2425
Re: Intersecting circles  [#permalink]

Show Tags

New post 30 Oct 2007, 07:01
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.
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2694
Location: New York City
  [#permalink]

Show Tags

New post 26 Nov 2007, 23:35
Can you explain the answer? Not sure how the height and the side of a triangle relate in finding whether the circles intersect
Expert Post
2 KUDOS received
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3484
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User Premium Member CAT Tests
  [#permalink]

Show Tags

New post 27 Nov 2007, 00:39
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
GCt54757.gif [ 15.3 KiB | Viewed 6449 times ]

1 KUDOS received
Director
Director
avatar
Joined: 09 Aug 2006
Posts: 746
Re: Intersecting circles  [#permalink]

Show Tags

New post 27 Nov 2007, 01:26
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.
Director
Director
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 540
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

New post 18 Feb 2014, 11:42
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

Manager
Manager
avatar
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

New post 18 May 2014, 10:40
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
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 434
If three circles having radii 1, 2, and 3 respectively lie on a plane,  [#permalink]

Show Tags

New post 04 Sep 2014, 06:32
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
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.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47110
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

New post 04 Sep 2014, 07:03
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
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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 101
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

New post 04 Mar 2015, 14:47
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
Manager
Manager
User avatar
Joined: 12 Jan 2015
Posts: 210
If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

New post 02 Jun 2016, 00:23
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.. :roll:

Where I am wrong..??
Please assist.
_________________

Thanks and Regards,
Prakhar

Expert Post
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

New post 02 Jun 2016, 21:52
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.. :roll:

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
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Manager
Manager
User avatar
B
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 211
Location: India
Concentration: Finance, International Business
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

New post 07 Aug 2017, 07:06
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??
Expert Post
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
Re: If three circles having radii 1, 2, and 3 respectively lie o  [#permalink]

Show Tags

New post 07 Aug 2017, 09:35
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
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Re: If three circles having radii 1, 2, and 3 respectively lie o &nbs [#permalink] 07 Aug 2017, 09:35
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  

Events & Promotions

PREV
NEXT


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.