veritasprep Official Solution
The presence of the "either X or Y" construction should grab your attention immediately in this problem, and guide you directly to that decision point. With the "either X or Y" construction (and its siblings, "both X and Y," "not only X but also Y," etc.), the X and Y portions of the construction must be parallel. And a great way to test that is to stop reading at the word "either" and start reading again with the first word after "or" and determine whether that is a complete thought. If you start with A and perform that test, you'd have:
(A) Across much of Western Europe, compulsory education ends after ninth grade, when students can choose an a vocational path.
Since the sentence would have two adjacent articles ("a" and "an") it's clearly incorrect. If you hold the others to the same test:
(B) Across much of Western Europe, compulsory education ends after ninth grade,after which students can a vocational path. (Clearly wrong - it's missing the word "choose")
(C) Across much of Western Europe, compulsory education ends after ninth grade,when students can a vocational path. (Clearly wrong - it's missing the verb "choose")
(D) Across much of Western Europe, compulsory education ends after ninth grade, when students can choose a vocational path. (Nothing wrong here!)
(E) Across much of Western Europe, compulsory education ends after ninth grade,after which students can choose vocational path. (Wrong - it's missing the article "a")
Therefore, choice D is correct. Note that you can also look at the problem simply testing the either X or Y construction to make sure that X and Y are parallel, but the technique shown above has proven to be a very quick and easy way for students to perform this test.