Remember that the GMAT is the authority on GMAT English, and that this is especially true with idioms. If you're not confident that a particular idiom issue has ever shown up on a real GMAT, don't sweat it. I haven't seen any other idiom questions involving "control," so I'll give an account of Standard Written English, which is sometimes more liberal than GMAT English.
About the idiom: "control of" is fine when followed by an object, the thing being controlled. It is awkward at best otherwise.
CORRECT: He seemed in control of the car until he hit the black ice.
CORRECT: It can be very difficult to take control of a privately held company.
AWKWARD: A privately held company can be very difficult to take control of.
If you add a prepositional phrase to the end of the clause, the awkward example passes over into just plain wrong.
CORRECT: It can be very difficult to take control of a privately held company by tender offer.
INCORRECT: A privately held company can be very difficult to take control of by tender offer.
In fact, apart from this idiom, you ought to be skeptical of any answer that follows "of" with another preposition.
About the odd use of the conditional in E: ENAFEX refers to chapter 7 of the Manhattan GMAT Sentence Correction
Strategy Guide, specifically to pages 112 and 113. I won't try to capture all those pages have to say here, but I will note that you can often sort out verb tense issues by appealing to logic or meaning as much to grammar. The FR keeping control of the economy isn't conditional on anything, so don't use the conditional "would."
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