Bunuel
The holistic philosophy behind so many methods of treatment that have been practiced almost exclusively in Asian countries for centuries are gradually seeping into the mindset of Western physicians.
A. The holistic philosophy behind so many methods of treatment that have been practiced almost exclusively in Asian countries for centuries are
B. The holistic philosophy behind so many methods of treatment that are practiced almost exclusively in Asian countries for centuries are
C. Behind so many methods of treatment practiced almost exclusively in Asian countries for centuries are a holistic philosophy that is
D. The holistic philosophy behind so many methods of treatment practiced almost exclusively in Asian countries for centuries is
E. Behind so many methods of treatment that are practiced almost exclusively in Asian countries for centuries is a holistic philosophy that is
VERITAS PREP OFFICIAL SOLUTION:
As you assess your decision points on this problem, you should not a very clear distinction on the last word of each answer choice between "is" and "are" - this means that you are very likely dealing with a subject-verb agreement decision.
Looking at that verb, which noun in the sentence could logically "gradually seep into the mindset of Western physicians"? The subject has to be "philosophy," a singular noun, begging the singular verb "is." This means that you can eliminate choices (A) and (B).
Among the other choices, you'll see that your remaining decisions points also involve verbs. Choice (C) commits a different subject-verb agreement error, using "behind so many methods...are a holistic philosophy." The subject there is "philosophy" (remember: if a sentence or clause begins with a modifier, the subject of the verb that follows the modifier is not part of the modifier. This is a good example of Subject-Verb Inversion, in which a sentence leads with a modifier, then a verb, then the subject.) so the plural verb "are" is incorrect.
Choice (E) makes a tense mistake. The expression "methods that are practiced...for centuries" does not work, as "are" is a current verb but "for centuries" requires a verb that dates back to the past, such as "have been practiced."
Choice (D) gets the subject-verb agreement right and omits "are practiced" to avoid that mistake, and is therefore the correct answer.