There are three circles, with radii 2, 4 and 5, respectively : GMAT Data Sufficiency (DS)
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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]

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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]

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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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Kudos [?]: 90119 [2] , given: 10418

Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]

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15 Jun 2013, 12:55
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Expert's post
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 [ 12.21 KiB | Viewed 2030 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)
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
on-the-number-line-shown-is-zero-halfway-between-r-and-s-89015.html
if-a-and-c-are-points-in-a-plane-c-is-the-center-of-circle-133325.html

Hope it helps.
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Kudos [?]: 6 [0], given: 76

Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]

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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
on-the-number-line-shown-is-zero-halfway-between-r-and-s-89015.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

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

Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 35951
Followers: 6866

Kudos [?]: 90119 [0], given: 10418

Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]

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05 Nov 2013, 09:05
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
on-the-number-line-shown-is-zero-halfway-between-r-and-s-89015.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

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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Intern
Joined: 29 May 2013
Posts: 11
Concentration: Operations, Strategy
Schools: ISB '15
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Kudos [?]: 6 [0], given: 76

Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]

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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
on-the-number-line-shown-is-zero-halfway-between-r-and-s-89015.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

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
Math Expert
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Posts: 35951
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Kudos [?]: 90119 [1] , given: 10418

Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]

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05 Nov 2013, 10:07
1
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.
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]

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27 Jun 2016, 09:54
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Re: There are three circles, with radii 2, 4 and 5, respectively   [#permalink] 27 Jun 2016, 09:54
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