One split is the “with” phrase vs. the “when” clause at the beginning. The prepositional phrase “with X” has to modify the thing that has X. Here, the phrase is “with a world population of 3.5 billion”, and this raises the fascinating question: what is the thing, or what could be the thing, that is in possession of “a world population of 3.5 billion”? It doesn’t make sense to refer to the year 1970 this way, and there’s nothing following the comma that is a likely target, so this preposition phrase structure is problematic. (A) & (B) are wrong. By contrast, the “when” clause has to modify a time, so it certainly can modify the year 1970. That fits beautifully into the sentence, so we have to choose one of the last three.
Now, let’s look at the split after the comma--we have “they have doubled ...”, “doubling”, or “it has doubled.” The “they” is a mystery pronoun, a pronoun with no properly defined antecedent. The GMAT hates mystery pronouns. The choices with the mystery pronoun, (A) & (E), are wrong. The participle “doubling” is also wrong: this could only be right if it were modifying some noun that were performing the action of doubling, and such a noun doesn’t exist in this sentence. Therefore, the choices with the participle “doubling”, (B) & (C), are wrong. This leaves only (D), which has a very elegant structure that is 100% grammatically correct: “it [Earth’s population] has doubled.”
(D) is the correct answer.
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