I like to break this one down like this:

Looking at your example sentence, 'on the basis of avoidance' is terrible misuse idiom construction with the word basis. It is also too passive, which is another way of saying not concise. Therefore, A is out.

The key to this one is a grammatically correct connection of the expression about avoiding duplication of facilities. B, C, and D can be eliminated because all of those expressions are awkward misuses.

This one is a bit difficult because each and every answer choice is a different idiom. E is correct. For one thing, it's the only expression that uses the word 'because' clearly connecting meaning. 'if only' is extraneous, and obviously only there to confuse as to the clear right answer.

Option A.
'on the basis of' is an awkward construction and it is not regarded as a choice to pick at all.This option is wrong.

Option B.
This is also similar to A above the idioms construction is totally out of reality and it is improper.

Option C.
'solely' this is also a bad one connection and not a proper linker is used here.Thus, this option is incorrect.

OPtion D.
'while' this signifies when two things are happening simultaneously, but that is not typical of this sentence.This option is definitely incorrect.

Option E.
This is the correct option.This option has the best linker particular for this sentence. And can be chosen all over the rest