Intended primarily to stimulate family summer travel,
the new airfare, which allows both an adult and a
child to fly for the price of one ticket, and also
shortens the advance-purchase requirement for family
travel to a minimum of seven days rather than
fourteen.

(A) and also shortens the advance-purchase require-
ment for family travel to a minimum of seven
days rather than
(B) and also lessens the advance-purchase
requirement for family travel to a seven-day
minimum from
(C) also shortens the advance-purchase requirement
for family travel to a minimum of seven days
rather than that of
(D) also lessens the advance-purchase requirement
for family travel to a seven-day minimum from
(E) also shortens the advance-purchase requirement
for family travel to a minimum of seven days
rather than

Would go for C.We do not require another and,hence eliminate 3 choices.Usage of seven day minimum is ambiguous.Hence C.

WILL GO FOR "E"

A, B makes the sentence fragment – eliminate it.
Among C, D and E:
D: lessen (requires two comparable entities) – Eliminate it
E: Good one but it compares days with number – eliminate it
Answer: C

i'd go with (e). PLEASE POST OFFICIAL ANSWERS ALONG WITH QUESTIONS.

* "and" at the beginning is inappropriate. here's why:
the new airfare, which allows both an adult and a child to fly for the price of one ticket, and also shortens
the yellow part is a modifier, which can be eliminated in the determination of subject-verb agreement. clearly, we need to write "the new airfare shortens...", and not "the new airfare and also shortens...".

* "lessen" is a weird word to use in this sort of context. usually, "lessen" is used with abstract qualities such as tension, disagreement, excitement, and so forth; i've never seen "lessen" used for discrete quantitative things (such as numbers of days, in this problem).

* "seven-day minimum" is awkward by gmat standards; i recall a question in the purple OG verbal supplement in which "two-year low level" was labeled as awkward, so we can assume that "seven-day minimum" would be subject to the same rules. what's more, if you use the adjective "seven-day", then "fourteen" isn't parallel to anything, as it would have to be followed by a hyphen.
"minimum of seven days" is better.

* "that of" doesn't make any sense, because nothing belongs to fourteen.

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the writing here is sloppier than that usually employed on the gmat; i find it weird to say that an airfare "shortens a requirement". to me, an airfare is just a price, so it can't shorten anything; you'd have to say that the deal, or the airline itself, "shortens" the requirement. it's uncharacteristic of the gmat to contain problems with such sloppy wording.
oh well.
at least the problem is present in all of the answer choices, so that you don't have to worry about it.