The organic food industry has organized a successful grassro

The organic food industry has organized a successful grassroots campaign—using Web sites, public meetings, and also mass mailings—that have convinced the Department of Agriculture to change the proposed federal regulations for organically grown food.

A. using Web sites, public meetings, and also mass mailings—that have convinced -- subject-verb agreement -- campaign have
B. using Web sites, public meetings, and mass mailings—that has convinced - Correct
C. by using Web sites, public meetings, and mass mailings—in convincing
D. by the use of Web sites, public meetings, as well as mass mailings—that convinced -- the construction "X, Y, as well as Z" simply doesn't exist.
another way to figure out that this is wrong is to realize that "as well as ..." is a MODIFIER, and thus can be stricken from the sentence without affecting the surrounding grammar.
that's problematic: if you strike "as well as mass mailings" from (d), you get remaining words that clearly don't work.

E. which used Web sites, public meetings, and mass mailings—in convincing -- incorrect verb tense. "which used" (simple past tense) shouldn't be in a tense occurring prior to "has organized" (present perfect). this construction mistakenly suggests that the campaign "used X, Y, and Z" before it was even organized in the first place.

the problem with (c) is NOT grammatical; the grammar of (c) is just fine.
the problem with (c) is that it uses two different transitions incorrectly.

* if you say "subject + clause + BY VERBing", then "by VERBing" must explain HOW the main clause occurred.
e.g.
i prepared for the test by reviewing takeaways on the MGMAT forums.
note that the boldface clause describes HOW i prepared for the test.

choice (c) means that using websites, etc. was how the industry organized the campaign -- in other words, they used the websites and public meetings to organize the campaign in the first place. that's an incorrect meaning.
(the campaign ITSELF used these things; the correct modifier in (a) and (b) shows that relationship.)

* if you say "subject + clause + IN VERBing", then subject + clause must be an ACTUAL PART of the action of VERBing.
e.g.
i solved all the problems in OG12 in preparing for the GMAT.
--> notice that solving the problems IS ACTUALLY PART OF preparing for the test.

choice (c) fails here, too, since organizing the campaign (the main clause) is not ACTUALLY PART OF convincing the government.

Answer B