On the number line, the distance between point A and point C is 5 and the distance between point B and point C is 20. Does point C lie between A and B?

1) The distance between point A and point B is 25
2) Point A liest to the left of Point B.

From the Qs:
A-----C = 5
B-----C = 20
A--(5)--C---(20)--B ?

Is AB = 25 or A to the left of Point B ----> Based on this rephrasing, I chose D. However the correct answer is A, can you explain your MGMT approach to getting the right answer?

The difficulty with the rephrase on this particular question is the easily overlooked possibility that C lies to the left of A. With "visual" problems it is usually advantageous to create a diagram so you can see (literally) what you are working with. Then, if necessary, you can worry about a rephrase. Below are the potential scenarios for our problem.

A---C---B; AC = 5, BC = 20, AB = 25

C---A---B; CA = 5, CB = 20, AB = 15

B---A---C; BC = 20, AC = 5, AB = 15

B---C---A; BC = 20, AC = 5, BA = 25

From here, you can attempt a rephrase. Is AB = 25? , the first part of your rephrase, is okay. However, it is obvious that we cannot make a generalization about the relative positions of A and B. Rather than falling into this potential pitfall, I would simply use my diagram to attack the statements.

Statement (1): The distance between point A and point B is 25.
Sufficient: According to the diagram, C must be between A and B. Eliminate BC on AD/BCE grid.

Statement (2): Point A lies to the left of Point B.
Insufficient: According to our diagram, C could either be between A and B (scenario 1) or C could be to the left of A and B (scenario 2).

The correct answer is A.

Is there a more robust/mathematical explanation than the one above? Or, is it better to use a diagram-based approach to solve these kinds of problems?

the short answer is "no".
(the long answer is "absolutely not". heh.)

this question is a little bit ironic, because this sort of analysis (case-wise breakdown of possibilities, as annoying and tedious as it is rigorous) is absolutely central to just about all areas of higher mathematics -- i.e., this approach is about as “robust/mathematical” as anything could possibly be.

however, i'm sure that the question you actually meant to ask was “can i use algebra to do this”, to which the answer is no.