|q – p| is the distance between p and q on the number line. |p –q| is the same as |q –p| to begin with.
So, in this case we are told |a -b| + |b -c| = |c – a|. Think about this. What does this mean? There are three points on the number line. We are talking about 3 distances on the number line here. We know that sum of some two of the distances is equal to the third. What does this tell us?
This tells us that the point b has to be in between a and c. With this we are done. We can have a or c to be 99 and b to be 98.
Maximum value b can take is 98. Classic question.
Correct Answer: A. 98