I usually follow a simple time line when I have to decide between simple past or past perfect.
Provided the events are connected to one another (i.e one influences the other in some way) and they are NOT parallel, then you use the time-line and say that the event that happened in the far past takes a perfect tense and the event in the near past takes a simple tense.
In this case, we can clearly see that the events are linked, but the word "before" indicates that you don't need to use a perfect tense. But in the following case:
Before its independence in 1947, Britain ruled India as a colony and they would relinquish power only after a long struggle by the native people.
A. Before its independence in 1947, Britain ruled India as a colony and they would relinquish power
B. Before independence in 1947, Britain had ruled India as a colony and relinquished power
C. Before its independence in 1947, India was ruled by Britain as a colony and they relinquished power
D. Before independence in 1947, India had been ruled as a colony by Britain, which relinquished power
E. Before independence in 1947, India had been a colony of the British, who relinquished power
Just by looking at the sentence, you can see that the modifier is misplaced. "Before its independence in 1947" refers to India and not Britain. So you can eliminate options A and B immediately.
Let's look at the remaining issues and answer choices now:
C: The modifier issue is corrected, but "they relinquished power" uses the wrong pronoun. No matter which antecedent you're referring to by using "they" it's wrong since all the entities mentioned take singular pronouns.
D: "India had been ruled as a colony by Britain, which relinquished power" adopts a passive voice and hence is not preferred on the GMAT. Also, Britain as a country did not relinquish power - the British people relinquished power, so the use of "which" in this scenario is also wrong.
E: This sentence correctly makes use of the modifier, and converts the pronoun to refer to the antecedent British, and hence corrects that issue as well.
A lot of people find this one confusing since you use a perfect tense here despite being given the word "before" - so in this situation, the other answers all had OTHER wrong elements. Though the usage of simple perfect is preferred in this situation, option E is grammatically consistent and the best among the given choices. Similarly, in the question you posted, if "was" was not an option, then "had been" would have been the right answer.