gmaton15 wrote: Can anyone explain how to find the elements that are being compared. For example in the above sentences, how do we find which elements are being compared.

Since your question is concerned specifically about the comparison made in these sentences, I will only focus on the comparison bit. As such gmat_perfect has explained the solution for these question in a very detailed manner
The number of people flying first class on domestic flights rose sharply in 1990, doubling the increase of the previous year.

If I were to express this sentence in terms of numbers, then it will be as follows (just for representation purposes):
Increase in Number of people flying 1st class in 1990 = 200,000
Increase in Number of people flying 1st class in 1989 = 100,000

As you can see the comparison is really between the increase in the number in 1990 and the increase in the number in 1989. Now lets look at the construction of the sentence:

The number of people flying first class on domestic flights rose sharply in 1990, doubling the increase of the previous year.
This sentence has no comparison markers. Infact, in purely technical terms, this sentence does not state a comparison. It basically states a fact about the rise in 1990 and then it modifies this fact using a verb-ing modifier - doubling the increase of the previous year. So this sentence is correct as-is.

Now lets look at the other choices.
"¢ Doubling that of the increase in - here "that" does not refer to anything and hence this choice is incorrect.
"¢ Double as much as the increase of - Choice A is more precise than this choice due to the lack of "as much as"
"¢ Twice as many as the increase in - Incorrect since increase is an uncountable noun and hence use of "as many as" is incorrect.
"¢ Twice as many as the increase of - Incorrect since increase is an uncountable noun and hence use of "as many as" is incorrect.

Also, since we have to modify the preceding clause, we should use verb-ing form i.e. doubling.... Thus, this is another error in Choices C, D, and E.

Soaring television costs accounted for more than half the spending in the presidential campaign of 1992, a greater proportion than it was in any previous election.

This sentence clearly states a comparison - greater than. Lets first understand what is the author trying to compare. The author is saying that increasing TV costs accounted for a lot of spending in the campaign of 1992. The proportion (TV costs/total campaign costs) in 1992 was greater than the proportion in any previous election. Thus, the author is comparing two proportions - proportion in 1992, and proportions in any previous election. Now we take a look at each choice one by one.

A. greater proportion than it was in any previous election
Here the comparison is between proportion and proportion was in any previous election. This is both grammatically and logical incorrect since it compares a noun and a clause
B. a greater proportion than
Correct. A greater proportion than in any previous election. Here "proportion" is not repeated after "than" because it is understood.
For example: Tom's height is more than John's. Here we do not repeat "height" since is it understood.

For e-GMAT users, the concept of Comparison is explained in detail in the concept titled Comparison - Parallelism

Thanks,

Payal