AD = 18
BC = 8

What is BD?

Statement 1: AC = BC, we can have two possibilities:

-------------A-----------------C----------------B---D------ so BD = 1


-------------A,B---------------C--------------------D------ A and B are on the same point, so BD = 18

Insufficient


Statement 2: A is to the left of D.

There is no info on the position of B relative to A or D. Insufficient.

Both statements together:
Both possibilities shown in statement 1 also satisfies statement 2. So insufficient.

Choose E.

-BM-

Well done BM

The point A, B, C, and D are on the number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D?

(1) The distance between C and A is the same as the distance between C and B.

(2) A is to the left of D on the number line.

As per bluementor
-------------A,B---------------C--------------------D------ A and B are on the same point, so BD = 18 but if this is the case then it negates the statement in question where it is specified as AB= 18.

so Solution is like following.

As per statement 1 :
c is midpoint of A & B. but D can be on right of B and on left of B so insufficient

As per statement 2: A is left to D, so D can be on left of B in that case the distance b/n BD = 1 and hence the A will be left to D
Also D can be in between A& C in that case A will be left to D because AC = 9 and CD = 8 but in that case distance between BD = 17. Insufficient

Hence C