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For the farmer who takes care to keep them cool, providing them with high-energy feed, and milking them regularly, Holstein cows are producing an average of 2,275 gallons of milk each per year.
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(A) providing them with high-energy feed, and milking them regularly, Holstein cows are producing
I fell for this one at first. Here, weirdly, providing them with and milking them incorrectly seem to be modifying the prep phrase for the former who takes care of them to be cool or could modify Holstein cows are producing, neither of those options make much sense. If you didn’t fall for it xD, eliminate!
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(B) providing them with high-energy feed, and milked regularly, the Holstein cow produces
No parallelism, also SV error because them doesn’t agree with Holstein cow. Easy to Eliminate.
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(C) provided with high-energy feed, and milking them regularly, Holstein cows are producing
Not much better than B, no parallelism. Out.
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(D) provided with high-energy feed, and milked regularly, the Holstein cow produces
The SV error in B is back although the parallelism seems ok here. Keep them cool, provided with x and milked y (past participles)
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(E) provided with high-energy feed, and milked regularly, Holstein cows will produce
The Parallelism is good here & them agrees with Holstein cows. The use of future tense is also fine because you can show the effect of the cows having been kept cool, milked etc: in the future! E is the answer!