Official Explanation
This is an example of a long sentence that is entirely underlined. The reason the GMAT chooses to underline the entire sentence is it wants to allow for a liberal movement of phrases. So a phrase that appears at the end of (A) can appear at the beginning, say, of (E).
With such questions, modification/logical predication is usually the focus of what’s being tested. This makes 3:2 splits, so unfortunately the best way to go through such questions is by going through each answer choice one at a time.
(A) implies that carbohydrates themselves are found in many fad diets. Weird.
Side note: if the original meaning of the sentence is totally absurd, as is the case here, it is not in violation of the rules to change the meaning. This typically happens only in medication questions.
(B) The “they” could either refer to “carbohydrates” or “diets”.
(C) The “which” could logically refer to several nouns in the clause that precedes it. It is also unclear just what the “resulting” is referring to.
(D) The use of the summative modifier “a strategy” avoids any illogical comparisons. “A regimen” is a nice touch. Though not exactly a summative modifier, it refers to “depriving the body of carbohydrates”.
(E) The “which” implies that carbohydrates are common to fad diets. If one argues that “which is” is singular, one would still have to account for the noun in the clause preceding the comma “which” refers to.