eitijan wrote:If A, B, and C are distinct points on the number line. Is the length of the line segment AB less than 10?
(1) The sum of the lengths of line segments AC and BC is 10
(2) The sum of the lengths of line segments AB and AC is more than 10
IMO B
Experts, please comment.
Given: A, B, C are distinct points on the number line
Required: Is AB < 10
Statement 1: The sum of the lengths of line segments AC and BC is 10
We can place the points on the line in the following ways
Case 1:
----A-----B----C-----
In this case, since AC + BC = 10, hence AB < 10
Case 2:
----A-----C----B----
In this case, AC + BC = 10
Hence AB = 10
Two different answers,
Insufficient
Statement 2: The sum of the lengths of line segments AB and AC is more than 10
Again let us take the two cases
Case 1:
----A----B----C----
We are given that AB + AC > 10
Nothing can be said about AB
Case 2:
----A----C----B----
We are given that AB + AC > 10
Again, nothing can be said about AB.
Insufficient
Correct Option:
E
