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There are three circles, with radii 2, 4 and 5, respectively

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There are three circles, with radii 2, 4 and 5, respectively [#permalink] New post 15 Jun 2013, 12:26
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There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?

(1) The centres of the three circles lie on a straight line

(2) The greatest distance between the centres of any two of these circles is 7
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink] New post 15 Jun 2013, 12:43
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There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?

(1) The centres of the three circles lie on a straight line
Not sufficient. Consider the case in which, even on the same line they are 1 away from each other ( hence they intersect) or the case in which they are 100 away from each other (hence they do not intersect)

(2) The greatest distance between the centres of any two of these circles is 7
Since even the distance between the 4 and 5 radius circle is 7, they will intersect. Those two circles intersect because the distance between their centers is less than 4+5=9.
Sufficient
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink] New post 15 Jun 2013, 12:55
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guerrero25 wrote:
There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?

(1) The centres of the three circles lie on a straight line

(2) The greatest distance between the centres of any two of these circles is 7


Below diagram might help:
Attachment:
Circles.png
Circles.png [ 12.21 KiB | Viewed 900 times ]
Even in this case two circles intersect.

Similar questions to practice:
if-x-and-y-are-points-in-a-plane-and-x-lies-inside-the-135194.html (OG13)
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Hope it helps.
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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.


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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink] New post 05 Nov 2013, 08:58
Bunuel wrote:
guerrero25 wrote:
There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?

(1) The centres of the three circles lie on a straight line

(2) The greatest distance between the centres of any two of these circles is 7


Below diagram might help:
Attachment:
Circles.png
Even in this case two circles intersect.

Similar questions to practice:
if-x-and-y-are-points-in-a-plane-and-x-lies-inside-the-135194.html (OG13)
a-certain-circular-area-has-its-center-at-point-p-and-has-101485.html (GMAT Prep)
circle-c-is-in-the-xy-plane-what-is-the-area-of-the-circle-99766.html
in-the-figure-shown-the-circle-has-center-o-and-radius-107309.html
on-the-number-line-shown-is-zero-halfway-between-r-and-s-89015.html
is-the-radius-of-the-circle-greater-than-105060.html
if-point-x-is-inside-a-circle-with-center-o-and-radius-2-is-102751.html
if-a-and-c-are-points-in-a-plane-c-is-the-center-of-circle-133325.html

Hope it helps.



Dear Bunuel,

What if centers of circles are
5 radius : (0,0)
4 radius : (0.5,0)
2 radius : (1,0)

Here, Centers are on straight line but circles are not intersecting. Hence it should be E right?

Thank you
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink] New post 05 Nov 2013, 09:05
Expert's post
Shashank1149 wrote:
Bunuel wrote:
guerrero25 wrote:
There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?

(1) The centres of the three circles lie on a straight line

(2) The greatest distance between the centres of any two of these circles is 7


Below diagram might help:
Attachment:
Circles.png
Even in this case two circles intersect.

Similar questions to practice:
if-x-and-y-are-points-in-a-plane-and-x-lies-inside-the-135194.html (OG13)
a-certain-circular-area-has-its-center-at-point-p-and-has-101485.html (GMAT Prep)
circle-c-is-in-the-xy-plane-what-is-the-area-of-the-circle-99766.html
in-the-figure-shown-the-circle-has-center-o-and-radius-107309.html
on-the-number-line-shown-is-zero-halfway-between-r-and-s-89015.html
is-the-radius-of-the-circle-greater-than-105060.html
if-point-x-is-inside-a-circle-with-center-o-and-radius-2-is-102751.html
if-a-and-c-are-points-in-a-plane-c-is-the-center-of-circle-133325.html

Hope it helps.



Dear Bunuel,

What if centers of circles are
5 radius : (0,0)
4 radius : (0.5,0)
2 radius : (1,0)

Here, Centers are on straight line but circles are not intersecting. Hence it should be E right?

Thank you


(2) says that the greatest distance between the centres of any two of these circles is 7. In your examples this condition is not met.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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avatar
Joined: 29 May 2013
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink] New post 05 Nov 2013, 10:01
Bunuel wrote:
Shashank1149 wrote:
There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?

(1) The centres of the three circles lie on a straight line

(2) The greatest distance between the centres of any two of these circles is 7

Below diagram might help:
Attachment:
Circles.png
Even in this case two circles intersect.

Similar questions to practice:
if-x-and-y-are-points-in-a-plane-and-x-lies-inside-the-135194.html (OG13)
a-certain-circular-area-has-its-center-at-point-p-and-has-101485.html (GMAT Prep)
circle-c-is-in-the-xy-plane-what-is-the-area-of-the-circle-99766.html
in-the-figure-shown-the-circle-has-center-o-and-radius-107309.html
on-the-number-line-shown-is-zero-halfway-between-r-and-s-89015.html
is-the-radius-of-the-circle-greater-than-105060.html
if-point-x-is-inside-a-circle-with-center-o-and-radius-2-is-102751.html
if-a-and-c-are-points-in-a-plane-c-is-the-center-of-circle-133325.html

Hope it helps


Dear Bunuel,

What if centers of circles are
5 radius : (0,0)
4 radius : (0.5,0)
2 radius : (1,0)

Here, Centers are on straight line but circles are not intersecting. Hence it should be E right?

Thank you


(2) says that the greatest distance between the centres of any two of these circles is 7. In your examples this condition is not met.
[/quote]

Dear Bunuel,

Sorry but I really didn't understand. It said GREATEST, that means distance can be zero to seven. I suppose in my example it's met. If it just said that the distance between any two circles is 7 then I guess your point is correct. Can you pls explain why GREATEST is not playing significant role here?

Thank you
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink] New post 05 Nov 2013, 10:07
1
This post received
KUDOS
Expert's post
Shashank1149 wrote:
Dear Bunuel,

Sorry but I really didn't understand. It said GREATEST, that means distance can be zero to seven. I suppose in my example it's met. If it just said that the distance between any two circles is 7 then I guess your point is correct. Can you pls explain why GREATEST is not playing significant role here?

Thank you


You misinterpreted the statement. It means that the distance IS 7 between the centers of 2 particular circles of the 3 but the distance between any other two of these circles is not more than that.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
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Re: There are three circles, with radii 2, 4 and 5, respectively   [#permalink] 05 Nov 2013, 10:07
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