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Problem from the MBA.com practice test 1

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by pranavc » Thu Jul 03, 2008 7:58 pm
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.
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Source: — Data Sufficiency |
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by Poornima » Thu Jul 03, 2008 8:15 pm
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?
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by pranavc » Thu Jul 03, 2008 10:08 pm
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.
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