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

Question

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

Zarrolou · Answer

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

Bunuel · Answer

Below diagram might help: 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.

Shashank1149 · Answer

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

Bunuel · Answer

(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.

Shashank1149 · Answer

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

Bunuel · Answer

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.

Md231 · Answer

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.

Md231 · Answer

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.

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

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