On number line problems, you can never assume that points on a number line are evenly spaced unless you are EXPLICITLY told.
Is CD > BC ?
The question itself implies that we can't treat these points as evenly spaced. We're asking if 2 of the points are farther apart than 2 of the other points.
(1) AD = 20
The distance between the 2 farthest points does not allow us to compare the distances between the points in between. One possibility:
0--2--------------17-----20
Or it could be:
0-1-2--------------------20
Insufficient.
(2) AB = CD
Once again, knowing that the distances between these sets of points are equal doesn't tell us anything about the distance from B to C. One possibility is that they're all equidistant:
0--2--4--6
Or, perhaps B and C are much farther apart than A and B or C and D:
0--2---------------10--12
Insufficient.
When we put the statements together, be still don't have enough information to determine the relative distance between B and C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
