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A , B , and C are points on the plane. Is AB \lt 10 ? 1. AC

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Manager
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A , B , and C are points on the plane. Is AB \lt 10 ? 1. AC [#permalink] New post 07 Jul 2008, 07:57
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A , B , and C are points on the plane. Is AB \lt 10 ?

1. AC + BC = 10
2. AB + AC \gt 10
Director
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Re: DS- Good one [#permalink] New post 07 Jul 2008, 08:01
aaron22197 wrote:
A , B , and C are points on the plane. Is AB \lt 10 ?

1. AC + BC = 10
2. AB + AC \gt 10


E: if A, C, B are on the same line and C is between A and B: AC = 4, BC = 6 (for example) -> AB = 10
if A, B and C are not on the same line than AB < AC + BC = 10
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Re: DS- Good one [#permalink] New post 07 Jul 2008, 08:07
aaron22197 wrote:
A , B , and C are points on the plane. Is AB \lt 10 ?

1. AC + BC = 10
2. AB + AC \gt 10


Three points must be able to form a triangle.

(1) As a rule, the sum of length of the two shorter sides of a triangle must be greater than that of the longest side.
Assume AB is the longest side, AB < AC + BC = 10
Assume AB is the 2nd longest side, AB < AC + BC = 10
Assume AB is the shortest side, AB < AC + BC = 10
===> sufficient

(2) Given AB + AC >10. AB can be any number > 0.
===> insufficient
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Re: DS- Good one [#permalink] New post 07 Jul 2008, 08:10
what if they are just points on the x-axis?? how do you know its a triangle?

judokan wrote:
aaron22197 wrote:
A , B , and C are points on the plane. Is AB \lt 10 ?

1. AC + BC = 10
2. AB + AC \gt 10


Three points must be able to form a triangle.

(1) As a rule, the sum of length of the two shorter sides of a triangle must be greater than that of the longest side.
Assume AB is the longest side, AB < AC + BC = 10
Assume AB is the 2nd longest side, AB < AC + BC = 10
Assume AB is the shortest side, AB < AC + BC = 10
===> sufficient

(2) Given AB + AC >10. AB can be any number > 0.
===> insufficient
Current Student
Joined: 28 Dec 2004
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Re: DS- Good one [#permalink] New post 07 Jul 2008, 08:12
I agree with E as well..same reasoning..i dont know if these points are triangle or just a numberline..



maratikus wrote:
aaron22197 wrote:
A , B , and C are points on the plane. Is AB \lt 10 ?

1. AC + BC = 10
2. AB + AC \gt 10


E: if A, C, B are on the same line and C is between A and B: AC = 4, BC = 6 (for example) -> AB = 10
if A, B and C are not on the same line than AB < AC + BC = 10
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Re: DS- Good one [#permalink] New post 07 Jul 2008, 08:17
I agree with E. I just did on one of the challenges.
Don't think of it as a triangle problem.
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Re: DS- Good one [#permalink] New post 07 Jul 2008, 08:45
Lets consider A B C are on the same line as A-C-B,

then AB=AC+BC=10, hence AB not less than 10.

For any other scenario apart from the above one, AB<10 holds true. Thus data is not sufficient in point 1 to determine AB<10.

Hence E.
Re: DS- Good one   [#permalink] 07 Jul 2008, 08:45
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A , B , and C are points on the plane. Is AB \lt 10 ? 1. AC

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