Data Sufficiency

This particular problem gives us four different numbers on a number line (A, B, C, and D) and tells us the distance between two sets of points (A to B and C to D). We should also note that these points are not necessarily in alphabetical order. Whenever we have GMAT Quant questions dealing with shapes, graphs, number lines, etc., it's a really good call to draw out examples - this is the visual equivalent of plugging in numbers.) Applying this trick here, and remembering that the distance between A and B is longer than between C and D, we see that our line could look like this:

this:

this:

and so on.

We need to find the distance between B and D. This means that we need to gather information

• about the order of the points

• about how our first set of points (A and B) relate to our second set of points (C and D)

Statement 1
If A and B are two different points and are both the same distance from C, this means that the distance between A and C must also be 18 and that C must be directly between the two points like so:

We also know that D is only 8 away from C, so it is closer to C than either A or B. However, we still don't know where D is compared to these points. It could be between points A and C, making it 26 away from B:

or between points C and B, making it 10 away from B:

Since we don't know whether the distance between B and D is 26 or 10, Statement 1 is insufficient.

Statement 2
Statement 2 tells us that A is to the left of D. Well, A is to the left of D in both of the number lines above, and the distance between B and D is not the same in either. So this doesn't tell us much. If the statement told us that A was directly to the left of D, this might be a little more helpful ... but it didn't and it isn't. Statement 2 is insufficient.

BOTH
Well, we already established that A is to the left of D (fulfilling Statement 2) in both of the number lines we created to fulfilling Statement 1, so even with the information from both statements, we don't know whether the distance between B and D is 26 or 10. Since we still can't solve for a single solution, the correct answer is E: Statements 1 and 2 TOGETHER are NOT sufficient to answer the question.

We actually featured this problem recently on the PrepScholar GMAT blog as one of the 5 Hardest Data Sufficiency Questions. I recommend checking out the article for more strategies and trends we can take away from this and other 700+ level problems!