These choices can be culled via using a combination of punctuation conventions and analysis of meaning.
In 1973 mortgage payments represented twenty-one percent of an average thirty-year-old male's income; and forty-four percent in 1984.
(A) income; and forty-four percent in 1984
In this one a semicolon connects an independent clause, what precedes the semicolon, to something that is not an independent clause. The convention or "rule" is that semicolons are used to connect independent clauses.
Even if you were not aware of that rule, there is also in this version a meaning issue that you could use to eliminate it. The way this sentence is structured it conveys absurdly that in 1973 mortgage payments represented forty-four percent in 1984, whatever that even means.
(B) income; in 1984 the figure was forty-four percent
In this version, the semicolon correctly connects two independent clauses. At the same time, what "the figure" refers to exactly is not that clear, and the sentence jumps from talking about mortgage payments to talking about "the figure." While I am not going to eliminate this one right away, it's almost definitely not the OA.
(C) income, and in 1984 forty-four percent
Hmm. This one sounds good. In 1973 this, and in 1984 that. It's parallel and makes sense.
(D) income, forty-four percent in 1984 was the figure
In this one we have an issue called a comma splice, meaning that a comma, rather than a semicolon, connects two independent clauses. Also, the sentence is awkward and we once again see the use of the term "the figure", which seems sub optimal as the first half of the sentence is talking about mortgage payments and then suddenly the second half is talking about "the figure".
(E) income that rose to forty-four percent in 1984
This version seems to convey not that the percentage of income going to mortgage payments rose but rather that income itself rose in 1984. I don't think that's what this sentence is meant to be saying.
So the one that uses punctuation in a way that is in line with convention and that most effectively conveys the intended meaning is C.
