When we start a sentence with "unlike X, Y", we have to follow the following rules:
1. A comparison has already been started between X and Y.
2. X cannot be a clause.
3. X cannot be a prepositional phrase.
4. X and Y MUST be grammatically and logically parallel.
For this question, we have to use COMPARISON and MEANING to pick the correct answer.
Unlike mainstream American businesses, more than half of which fail, the failure rate for businesses in the Amish community hovers around 5 percent.
A. Unlike mainstream American businesses, more than half of which fail
Wrong. incorrect comparison (mainstream American business vs the rate)
B. Unlike mainstream American businesses, in which the failure rate is more than half
Wrong. incorrect comparison (mainstream American business vs the rate)
C. Unlike mainstream American businesses, where more than half of them fail
Wrong. incorrect comparison (mainstream American business vs the rate). Also "where" is wrong because where is only used to refer places.
D. While the rate of mainstream American businesses failing is more than half
Wrong. correct comparison, but WRONG MEANING. "The rate is more than half" does not make sense. Half of what? half of 1% (0.5%); or half of 100% (50%). We never say "the rate is half". It's wrong.
i. The expression “businesses failing” the way it appears in this choice is not idiomatic.
ii. The phrase “rate is more than half” is not idiomatic. The correct expression is “rate is less than 50%” or "rate is more than 10%".
E. While more than half of mainstream American businesses fail
Correct. "more than half of X fail" = the rate is more than 50%. MEANING is the first priority in this question.
The first thing to note here is that we are not bound by the limitations of “Unlike” in this choice. Here “more than half” denotes the rate of the mainstream American businesses that fail. So the comparison is logical. And construction is also parallel because we have clauses on both sides of comma for comparison. This structure is more relaxed than that with “unlike”