Sentence Correction

the answer is (c).

first of all, the subject of "illustrate" is "episodes". ("in the relations between nations" - as well as the various transmogrifications of that phrase in the other answer choices - is a prepositional phrase, and as such can be ignored in the search for SV agreement, since the verb lies outside the prepositional phrase.)
this means that you need the plural verb "illustrate", so we're already down to (c) and (d).

(d) is wrong for two reasons:
* "relation of one nation with another" is just ugly and unidiomatic
* "and illustrate" creates two problems.
- first, it falsely suggests that the presentation of episodes and the illustration of faults in treaties are 2 completely separate phenomena - a notion that's mistaken not only by pure common sense, but also because it contravenes the meaning inherent in the original sentence.
- second, if you create this compound verb with "and", then the subject of both parts becomes "lecture". in that case, there's SV diagreement, because "lecture" is singular.

as for the so-called official answer (b), that's at least two different colors of wrong. first, "relation of one nation with another" is not proper idiomatic english. second, there's the SV disagreement, as mentioned above.

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to recap:
there is absolutely, positively no way that the official answer to this question is (b).
(c) is the best answer by a country mile.

two things:
1) while this is still a good practice problem - it tests SV agreement, idiom, and clarity - it definitely sets off my "non-official radar". it's rare not only for real gmat problems to contain long, unbroken, difficult-to-follow sentences with NO internal punctuation, but also for them to contain relatively wordy / informal constructions (e.g. "what is wrong with" vs. the much more formal and concise "(the) problems with").


2) if this problem is taken from a source that indicates (b) as the correct answer, run, don't walk, away from that source. run for your life.
if you can set fire to it while simultaneously running for your life, all the better.