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I would eliminate B and E, because they change the meaning of the sentence by putting "contaminated with virus" just after Nation's blood supply instead of "eliminating blood". Now, out of A,C and D, C is awkward and wordy, D uses "to eliminate" which I am not very sure of so i would go with A. What's the OA?

IMO C.

A - in eliminating blood, contaminated with the virus, from the nation’s blood supply - This doesn't make any sense along with the non underlined part - modifier error.
B - usage of that makes it as if nation's blood supply is contaminated with virus. - modifier error
D/E - helpful to eliminate is unidiomatic.

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https://www.beatthegmat.com/aids-t107788.html#456502

It should be "helpful in," not "helpful to," which eliminates D and E.

B misplaces the modifier so it sounds like the nation's blood supply is contaminated with the virus.

In A, if we remove the modifying phrase (which we can do: if it's set off by commas, it's nonessential to the meaning of the sentence), so it makes it sound like we're eliminating blood from the nation's supply.

"blood supply blood" is a bit awkward in C, but the meaning is correct.

NOTE: I would choose A as the best answer if the commas around "contaminated with the virus" were not there. That means the modifying phrase is essential to the meaning, so we know which blood is being eliminated.