gmatassassin88 First, let's cut out all the modifiers (in this case, that's most of the sentence!) and look at the basic grammatical cores of B and E:
B) The disappearance seems to be doomed.
E) The disappearance seems inevitable.
We can already see that E must win. The disappearance of something can't be doomed; only the thing itself can be doomed. It would be like if I said "The loss of my job is in danger." I can say that the loss of my job is approaching, or I can say that my job is in danger, but mixing the two together creates a meaningless jumble. The loss is not in danger!
I can't tell you all the ways that "to be" is used, since this is one of the central verbs of our entire language, but here "to be" in particular is not the issue. The idiom we're using is "seems to X." I can say "the machine seems
to be broken" or "the company seems
to have an unlimited budget" or "the dog seems
to require five meals a day." The point is that in this construction, we follow "seems" (or one of many other verbs, such as appears, tends, or claims) with an infinitive verb that describes what action "seems" to happen.
So we can actually cut all of A-D on the basis of sentence core alone. A and C have the same problem as B (disappearance is doomed), but these and D also use the plural "seem," which can't work with "disappearance." For this reason, we don't really need to look at the modifiers at all--this is one of my time-saving secrets! However, as discussed earlier in the thread, "requiring" does seem to modify the main action ("The disappearance . . . seems"), and this would mean that the disappearance itself required these things. For that reason, the correct answer changes the intervening modifier to a noun modifier with the repetition of the clarifying word "lifestyles." This makes it clear that the modifier is intended to apply to "lifestyles" and not "disappearance."