On the number line, the distance between point A and point C

[MBA Applicant 2007/8]

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?

[dbernst]

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.

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?

[g.k.sharma]

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.

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?

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?

[RonPurewal]

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.