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A) under the leadership of Suleiman II took control of Rhodes and many of the largest Mediterranean islands, their unsuccessful siege of Vienna in 1529 marked the beginning of the long decline of their empire, which stopped the advance of Islam into central and western Europe and ensured
I'm not crazy about the "which" here: it seems to be modifying "empire", and that's not quite right. I guess that the "which" modifier could plausibly "reach behind" the prepositional phrase and modify "the long decline of their empire." If you think this is reasonable, you could hang onto (A) initially, but as we'll see in a moment, there are better options below. (And for more on exceptions to the "touch rule" for noun modifiers, check out our
Topic of the Week on "that".)
Also, the verb tenses are the same throughout the sentence ("took control", "marked", "stopped", "ensured", and that's not ideal, because the actions logically took place at different points in the past. Again, you could be conservative about this, but we have better options below. Eliminate (A).
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B) led by Suleiman II took control of Rhodes and many of the largest Mediterranean islands, they sieged unsuccessfully in Vienna in 1529, and this marked the beginning of the long decline of their empire, stopping the advance of Islam into central and western Europe and ensuring
"They sieged... in Vienna" isn't great here -- I think it's reasonable to say something like "the army's siege of Vienna" or maybe "the army sieged Vienna", but as written, it's not really clear what, exactly, is being "sieged." A bakery in Vienna? A coffeehouse? A neighborhood? Who knows?
"This" is also incorrect. In normal speech, we sometimes treat "this" like a pronoun, but I've never seen a correct GMAT sentence that uses "this" as a pronoun. It can be an article that introduces a noun ("this book", "this week"), but not a pronoun.
Plus, the verb tense issue we discussed in (A) is still a problem with (B). So we can eliminate (B).
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C) under the leadership of Suleiman II had taken control of Rhodes and many of the largest Mediterranean islands, their unsuccessful siege of Vienna in 1529 marked the beginning of the long decline of their empire, stopping the advance of Islam into central and western Europe and ensuring
I like the verbs here: "had taken control" logically happens before "their unsuccessful siege... marked". And then "stopping" and "ensuring" are modifiers -- and that makes sense, since those two phrases give us more information about the preceding clause. Keep (C).
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D) who were led by Suleiman II had taken control of Rhodes and many of the largest Mediterranean islands, the Ottoman Turks had been unsuccessful in sieging Vienna in 1529, marking the beginning of the long decline of their empire, stopping the advance of Islam into central and western Europe, and ensuring
Now we're getting a little bit overzealous with the past perfect tense: if we look at the sentence strictly and literally, "had taken control" and "had been unsuccessful" must describe two actions that happen before some other action in the past. What's that other action? "Were led by Suleiman II"?? That makes no sense at all.
Plus, the parallelism is pretty odd here. I'm not sure that it makes sense for "marking", "stopping", and "ensuring" to all take the form of parallel modifiers. Eliminate (D).
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E) led by Suleiman II had taken control of Rhodes and many of the largest Mediterranean islands, the Ottoman Turks unsuccessfully sieged Vienna in 1529, marked the beginning of the long decline of their empire, stopped the advance of Islam into central and western Europe, and ensured
The parallelism definitely doesn't make any sense in (E). The last few actions ("marked", "stopped" and "ensured") describe the consequences of the unsuccessful siege. There are plenty of different ways we could make this work, but those four verbs really shouldn't be parallel to each other.
(C) makes much more sense than (E), and it is our winner.