Data Sufficiency

The points A, B, C, and D are on a 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.


This seems like a straightforward question but the answer makes absolutely no sense. Any input on the above will be highly appreciated. Thanks in advance.

From the problem stem, we can get the following details:

A-B=18
C-D=8

The aim is to find B-D.

1) The distance between C and A is the same as the distance between C and B.
As A, B and C are on the number line, we infer that C is the midpoint between A and B. So the alignment of the points could be
A-C-B or B-C-A. In both the alignments, the distance between C and A and C and B is 9 as C is the midpoint.

As we have no information about D, we can rule out option (A).

2)A is to the left of D on the number line. THis does not give us sufficient information to solve the question. Hence we can rule out option (B).

Considering 1 and 2 together, our alignment narrows down to A-C-B because of the following reasons:
1) It is mentioned that the distance between C and D is 8. This implies D is on the line A-B. And as A is to the left of D, we have the following alignments: ADCB (where the distance between B and D is 17) or ACDB (where the distance between B and D is 1)

Hence it looks like the answer is (E).
What is the OA?

Thanks for your prompt response. Yes, the OA is E. I did not account for that second possibility (i.e. ACDB) and hence arrived at "C", which is clearly wrong. Thank you once again for your prompt and helpful response.