If X, Y, and Z are points on the number line, what is the distance bet

On this one, linear thinking can get you into trouble. Most people will create the following type of number line (in which a hyphen, "-," represents a distance of 1):

(1) X-------Y

Analysis: Clearly, Statement (1) is NOT sufficient, since point Z does not appear anywhere in the given information.

(2) Y------------Z

Analysis: Of course, Statement (2) is NOT sufficient, since point X is now missing.

Together, this is what many hasty test-takers would assume:

X-------Y------------Z

Analysis: Note the order of X, Y, and Z. In this scenario, the distance from X to Z would indeed be 7 + 12, or 19 units.

However, we are not told that the points must occur in alphabetical order. We could just as easily reinterpret Statement (2) to start with point Z on the left:

Z------------Y

Putting this together with Statement (1), the picture would then look different:

Z-----X-------Y

Analysis: The distance between X and Y is still 7 units, and the distance between Y and Z is still 12 units, so we are conforming to the two statements perfectly, yet the answer went from 19 to YZ - XY, or 12 - 7 units, which would give us a distance of 5 units between X and Z instead.

If two valid scenarios lead to conflicting results, then the answer goes straight to (E). These statements are insufficient to answer the question, whether taken together or individually.

- Andrew