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A, B, and C are points on the plane. Is AB<10 ? (1) AC+BC=10 (2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient. What is wrong in this reasoning?

Since the question is not explicitly saying that these three points are not on the same line, from stmt1 you get AB <= 10 and that is the reason stmt1 is not sufficient.

A, B, and C are points on the plane. Is AB<10 ? (1) AC+BC=10 (2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient. What is wrong in this reasoning?

1. You assumed that a, b and c makes a triangle but how do we know that a, b and c are on on the same plane. If so, then ab = ac + bc = 10.

In that case also AB cant be 10. It has to be less than 10 (the third side is smaller than the sum of other two sides)

GMAT TIGER wrote:

ritula wrote:

A, B, and C are points on the plane. Is AB<10 ? (1) AC+BC=10 (2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient. What is wrong in this reasoning?

1. You assumed that a, b and c makes a triangle but how do we know that a, b and c are on on the same plane. If so, then ab = ac + bc = 10.

In that case also AB cant be 10. It has to be less than 10 (the third side is smaller than the sum of other two sides)

GMAT TIGER wrote:

ritula wrote:

A, B, and C are points on the plane. Is AB<10 ? (1) AC+BC=10 (2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient. What is wrong in this reasoning?

1. You assumed that a, b and c makes a triangle but how do we know that a, b and c are on on the same plane. If so, then ab = ac + bc = 10.

2. ab > 0.

So E.

Thats the point here. We do not know whether a, b and c make a triangle or a line.

A, B, and C are points on the plane. Is AB<10 ? (1) AC+BC=10 (2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient. What is wrong in this reasoning?

Just try these two sets: ************************ Case I: A(0,0), B(6,0), C(3,4) AC=BC=5 AB+BC=6+5=11>10 AB=6<10 ************************ A(0,0), B(10,0), C(5,0) AC=BC=5 AB+BC=10+5=15>10 AB=10=10 ************************ Thus, AB can be equal to 10 OR less than 10.