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

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GMAT Prep

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 C lie between point A and point B?

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

OA A

[ceilidh.erickson]

With NUMBER LINE problems in DS, remember that information about distance alone does not give us information about direction.

When unpacking the question, try to imagine different scenarios with the given information. Try to come up with one scenario in which C is between A and B, and one in which it it *not* between A and B:


(The mirror images of these positions would also work).

If we want to know whether C is between A and B (regardless of which is on the right or the left), we need to know the distance between A and B.

1) The distance between point A and point B is 25.
This answers our target question. If these points are 25 apart from each other, there is no way for C to be on the outside of them and still be 5 away from A and 20 away from B. C must be in between the two. Sufficient.

2) Point A lies to the left of point B.
Insufficient. Refer back to the original diagram: it's possible for A to be to the left of B with C in between, but it's also possible for A to be to the left of B, but C to be to the left of A. Insufficient.

The answer is A.