The rules enacted in the European countries between 2000 and

The first thing we can do is eliminate any answers with "to 2010". The correct idiom is "between ____ and ____". So this rules out B and D.

For the remaining answer choices, we can use the meaning of the sentence. The intended meaning of the original sentence is that these rules prevented companies "from providing exporting services" — they were not able to offer services related to exporting goods. However, C and E indicate that these rules prevented companies "from exporting services". This has an entirely different meaning — that the companies were not able to export the services themselves. So because C and E change the meaning of the sentence, we can eliminate both answer choices and pick A.

There are also a few smaller issues:

1) In E, "had the effect of preventing" is much less concise than "prevented".
2) Though this isn't a hard-and-fast rule, "because" should be used for causation, while "since" should be used for a period of time. E.g. "I am napping because I am tired." vs. "I have been napping since 3:00." This makes A and D preferable to B, C, and E. However, be careful with using this rule — hard grammar rules will always be more important. We'd rather pick a grammatically correct answer that uses "since" to mean "because" than a grammatically incorrect answer that uses "because".