I received a PM asking me to reply. (Also, FYI, I won't be able to respond to any PMs / answer any more questions until around the second week in January.)

I'm not a big fan of this problem. It doesn't seem very GMAT-like to me.

I assume that the missing "s" at the end of "others" in answer choice E is merely a typo. If the problem really does say "other" instead of "others," then what I say below is invalid because E is wrong.

The sentence contains a list of three. Both A and E demonstrate parallelism (but with slightly different structures). B, C, and D don't.

A:
Some officials hope to end the border skirmish <by -ing A>, others <by -ing B>, and still others <by -ing C>.

E:
Some officials <hope A>, others <propose B>, and still others <demand C>.

Problem with A: "by proposing imposing stiff economic sanctions..." Is imposing an adjective here, modifying sanctions, similiar to "he has an imposing presence"? As in: sanctions that are imposing? Or is the proposal to impose sanctions? I'm not sure. That's a clarity issue.

Problem with A: item C on the list. "officials hope to end the skirmish by demanding that NATO <do something>." Will the demand actually end the skirmish? No - only if NATO agrees to do something.

Problem with E: the placement of the word "stiff" - in the original sentence, the sanctions themselves were described as "stiff." Now, the imposition is described as "stiff" - why the change? There's nothing wrong with calling the sanctions stiff.

E does, however, clear up the other two problems with A. Now it's clear that we have a proposal to impose sanctions, not a proposal for sanctions that have an imposing characteristic. And now we have "officials demand that NATO <do something>" which skirts the earlier problem (that the officials hoped to end the skirmish by making a demand).

So, as I mentioned, I don't like this one overall, but if I had to choose, I guess I'd go with E. But I would also stop studying this one right now.

Yep - yet another reason why I don't really like this one overall.

I also forgot to add: on the real test, you'll never see a correct answer that uses "proposing imposing" - it'll say something like "proposing to impose" or "proposing the imposition of" or something other than that awkward double -ing set-up.