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



1 gives very little information

2 is a good trap but not sufficient because while it is clear that their areas may overlap, they may or may not overlap. Example- two may be concentric circles.

Combining also, the reasoning above in 2 keeps both yes and no possibility open.

E.

Good question but doesn't taste like GMAT.
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]
Ohhh, my bad. They are bound to touch for sure, using 2.

I am treating touching and intersecting as different but touching is a foreally of intersecting.

B it is.

Md231 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



1 gives very little information

2 is a good trap but not sufficient because while it is clear that their areas may overlap, they may or may not overlap. Example- two may be concentric circles.

Combining also, the reasoning above in 2 keeps both yes and no possibility open.

E.

Good question but doesn't taste like GMAT.
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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]
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