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

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Manager
Joined: 22 May 2007
Posts: 218
A , B , and C are points on the plane. Is AB \lt 10 ? 1. AC [#permalink]

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07 Jul 2008, 08:57
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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
Joined: 01 Jan 2008
Posts: 622

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07 Jul 2008, 09:01
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
Senior Manager
Joined: 19 Mar 2008
Posts: 351

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07 Jul 2008, 09:07
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
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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07 Jul 2008, 09:10
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
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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07 Jul 2008, 09:12
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
Manager
Joined: 08 Jun 2008
Posts: 71

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07 Jul 2008, 09:17
I agree with E. I just did on one of the challenges.
Don't think of it as a triangle problem.
Intern
Joined: 01 Jul 2008
Posts: 41

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07 Jul 2008, 09:45
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, 09:45
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