Question: I want to write the following sentence in a compact way:

"The difference between the old scheme and the new scheme lies in..."

Which one of the following is correct?

1. The difference between the old and **new scheme** lies in...
2. The difference between the old and **new schemes** lies in...
3. The difference between the old and **the new scheme** lies in...
4. The difference between the old and **the new schemes** lies in...

Option 1 sounds more natural to me but I cannot explain why. More important, English is not my mother tongue. In other words, I would like to know:

* Is it necessary to repeat the definite article for each element of the list?
* Does the common object (in this case, the scheme) become plural when it is listed multiple times with different pre-modifiers (in this case, old and new)?

Answer: 
I would say that you do not require the last two articles, as neither is the focus of identification.

What is being identified is 'the' difference :

> 
> The difference between old and new schemes lies in ...
> 
> 
> 

---

It could be argued that this is an example of the zero article, that is to say the absent article regarding 'old' and 'new'. See elsewhere on this site for 'null' and 'zero' articles and for references to Peter Masters.

For example : [Should 'one' be considered an article ?](https://english.stackexchange.com/questions/425829/should-one-be-considered-an-article)
I would argue for one of the following forms, my preference being for the first.

> 
> 1) ... the old scheme and the new scheme ...
> 
> 
> 2) ... the old and the new schemes ...
> 
> 
> 3) ... the two schemes, old and new, ... 
> 
> 
> 

This is because the difference is between a scheme and a scheme, not between "an old" and "a new." So this should be emphasized by the sentence structure.