A line contains the points A, B, C, and D. Point B is between points A and C

A line contains the points A, B, C, and D. Point B is between points A and C. Point D is between points C and B. Which of the following inequalities must be true about the lengths of these segments?

1. BC < AB
2. BD < AB
3. BD < CD
4. CD < AB
5. CD < BC

Answer

The correct answer is E.

There are many different arrangements of points that satisfy the conditions. But, in all of these, the order of points starting from point A is A, B, D, C.

Because D is between C and B, distance CD is always shorter than distance BC. So, CD < BC.