My view on it can be put this way.
Plural 'Inventories' splits the answer choice into ACE and BD. (BD is wrong)

Not accompanied is a better use than unaccompanied.

Gives me E directly.

I dont remember the rules and stuff but from whatever I remember,
Rising inventories and Corresponding increases (in sales) are parallel.

Rising inventories and corresponding increasing sales are not parallel.

Here, X, Y and Z all are compound nouns and are parallel.
X = Rising inventories - this is definitely a compound noun, similar to frying pan, writing table
Y = increases in sales - noun phrase
Z = production cutbacks = compound noun

(A) when unaccompanied correspondingly by increases in sales, can lead
(B) when not accompanied by corresponding increases in sales, possibly leads
(C) when they were unaccompanied by corresponding sales increases, can lead
(D) if not accompanied by correspondingly increased sales, possibly leads
(E) if not accompanied by corresponding increases in sales, can lead

B & D out because "Rising inventories" = plural subject
A = correspondingly = meaning is not clear, C and D are clear in this respect. ... corresponding increases ...
C = were = past tense, wrong, also, sales increases does not sound good, increase in sales is good.

IMO answer is E

Wow - great explanation, tetura84...that's exactly right. "Inventories", "Increases", and "Cutbacks" are all nouns and therefore parallel - the other items for each are just different modifiers.

To Mohish's initial point, man, I'd avoid digging into "participle vs. gerund phrase" until it's absolutely necessary...and I'm willing to go on record having solved every SC problem in every OG version available, as saying that it's never absolutely necessary. Here, just going off of verbs (S-V agreement and verb tense from C) can eliminate 3 options without having to get that detailed. The dirty little secret of GMAT Sentence Correction is that it's usually a lot more "big picture" and can be solved with logic than it is minute-detail-oriented.