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A , B , and C are points on the plane. Is AB \lt 10 ? 1. AC [#permalink]
 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
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Director
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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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Senior Manager
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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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Current Student
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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 |
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Current Student
Joined: 28 Dec 2004
Posts: 3439
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 11
Kudos [?]:
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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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Manager
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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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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.
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