Lots of disagreement on this one within the first few hours! I like that. It means we picked a fun one.
As is often the case on official SC questions, this one is mostly about logic and meaning, and the mechanics take a backseat. Fun times. And tricky, in my opinion.
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(A) neutrinos are harmless elementary particles that are produced in nuclear reactions and that
The first thing that catches my eye is the parallelism, and that looks OK: "...neutrinos are harmless elementary particles
that are produced in nuclear reactions and
that interact very weakly with matter." Fair enough.
And the meaning seems OK to me, too: it is indeed fortunate that neutrinos are harmless and that they interact weakly with matter. If they weren't harmless, we would have been toast thirty years ago, and we never would have experienced the joys of GMAT Club, the Colorado Rockies, snapchat, Game of Thrones, Steph Curry, or Taylor Swift. Keep (A).
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(B) neutrinos, which are harmless, are elementary particles produced in nuclear reactions and which
I'm uncomfortable with that last bit that begins with "and which..." In theory, it's parallel with "which are harmless", but it's a little bit weird to have "which" without a comma here, since "which" is generally used as a non-essential modifier. I'm not 100% sure that this is wrong, but it doesn't seem quite right, either.
But more importantly: the meaning is warped. Stripping out the non-essential modifier, we have "fortunately, neutrinos... are elementary particles produced in nuclear reactions." No, it really isn't fortunate that neutrinos are produced in nuclear reactions. The fortunate part is that they're harmless. (B) is out.
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(C) neutrinos are harmless elementary particles produced in nuclear reactions and which
There's that silly "and which" thing again. But in this case, there's nothing that could possibly be parallel to "which." So there's no grey area here at all: (C) is definitely wrong.
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(D) these harmless elementary particles are produced in nuclear reactions, and neutrinos
This has the same meaning problem as (B), since it seems to be saying that it's fortunate that neutrinos are produced in nuclear reactions. That really isn't the point of the sentence. (D) is out.
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(E) these elementary particles, harmless products of nuclear reactions, are neutrinos that
I see two issues here. First, the fact that the neutrinos are harmless is buried in a modifying phrase, and that's not great. Again, the heart of this part of the sentence is that it's fortunate that neutrinos are harmless, so (E) does a lousy job of conveying the meaning of the sentence.
Second, I also don't really understand that last modifier beginning with "that" -- sure, neutrinos interact weakly with matter, but the phrase "these elementary particles... are neutrinos that interact weakly with matter" suggests that there might be other types of neutrinos out there. And I don't think that's true. (E) doesn't quite get the meaning right, and that leaves us with (A).