What's wrong with this question?

Ian,

the 2 statements contradict eachother as specified...
using your GMAT ideology, am picking E in the first place...

right the two statements does not talk about the same problem. In GMAT the data given in the two statements will be consistent.

With the crowd. Stems give inconsistent answers.

The answer is D because both statements are giving us the chance to apply pythogorous theorem to find out the required individually.

However, (1) & (2) result in different answers.
That might be a reason why it does not appear on GMAT.

However, what is the issue if they give rise to different values when the final answer is D? Is it conflicting with E, which states 'Statements (1) and (2) TOGETHER are NOT sufficient'?

Great job! Yes, it's true that the two statements refer to two different ladders.

mallelac, your confusion is fair, but the question is actually irrelevant, since this isn't truly a gmat question, we don't have to worry about the case. It's not as though this could show up, but you'd have to know the answer is E, because they refer to different things. It simply wouldn't ever be there at all.

The point here, again, is to be able to learn information about the question from each of the statements, even if we're not going to choose C as the answer. That could only work if the statements are talking about the same thing.

Keep an eye out for this - it's a great way to decide if a question is actually a gmat one as you're studying.

Got the same answer as the rest 10sqrt3 and 10sqrt2

I think I've seen a similar GMAT DS questions using the same ladder and building story, but goes something like this

The top of a ladder resting at an angle against a building from the base of a building. If the building is perpendicular to the ground, how far away from the building is the foot of the ladder?

1) The ladder is 20 feet long.

2) The foot of the ladder makes a 45 degree angle with the ground.

In which case the answer would be (C), need both statements to solve