The number of people flying first class on domestic flights rose sharply in 1990, doubling the increase of the previous year.

A. doubling the increase of - -ing participle word correctly links the second part sentence of the sentence to the first.
B. doubling that of the increase in - that does not refer to anything
C. double as much as the increase of . - double and "as much as" are both comparison words. "as much as is used for uncountable things"
D. twice as many as the increase in - twice and "as many as" are both comparison words - Redundancy
E. twice as many as the increase of - twice and "as many as" are both comparison words - Redundancy

souvik101990 merge the topics @shttp://gmatclub.com/forum/the-number-of-people-flying-first-class-on-domestic-flights-80878.html
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Because GMAT prefers more concise wording, "twice as many as" can be expressed as "double" replaces the word. That's why C, D , E are out.

Between A & B, B is out because doubling that of the increase in previous year" should be "that of previous year" or it shouldn't be using "that of".

In my opinion Answer is A is most suitable one.

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Yes, in option (B), "that" is used as a pronoun. It needs to have an antecedent. But it doesn't.

(B) The number of people flying first class on domestic flights rose sharply in 1990, doubling that of the increase in the previous year.

What does "that" stand for here?

"that" stands for "the increase" but it hasn't been mentioned before.

e.g.
Democrats have rated the U.N. more positively than Republicans, with Democrats' average approval rating (46%) nearly doubling that of Republicans (24%).

"that" stands for "average approval rating". The pronoun needs an antecedent.

In option (B), the pronoun "that" has no antecedent.
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The number of people flying first class on domestic flights rose sharply in 1990, doubling the increase of the previous year.

The clause “The number of people flying first class on domestic flights rose sharply in 1990” is the cause and the clause after the comma modifies this whole clause as it has to be the result/‘leading to’ of the clause before the comma.
Hence the options C,D, and E go out.

A. doubling the increase of
Doubling modifies the whole preceding clause, and ‘increase of’ that it is the increase of something else.

B. doubling that of the increase in
“That of” has no antecedent., and when it is “increase in” it basically means that the something increased itself. Previous year didn’t increase itself.

C. double as much as the increase of

D. twice as many as the increase in
Twice… i.e. the noun modifier has no noun to modify.
Many is a countable noun.
Twice also used as the frequency indicator.
and when it is “increase in” it basically means that the something increased itself. Previous year didn’t increase itself.

E. twice as many as the increase of
Many is a countable noun used here
Twice also used as the frequency indicator.

Here the word double can only be used in the most appropriate manner.