The original text contains a misplaced modifier. When we have a modifying phrase at the beginning of a sentence, such as "Invented in China over three centuries ago," we know that the noun that appears right after that phrase must be the thing that the modifying phrase describes. In this case, this means the thing that was invented in China over three centuries ago. 

All of the answer choices except "Invented in China over three centuries ago, the compass has served as a navigational tool for explorers and trade merchants alike" make is sound as though explorers and trade merchants were invented in China over three centuries ago, which is not correct.

When a sentence begins with an introductory modifying clause, such as "A popular tourist destination," the noun right after that clause must be the entity that the clause describes—in this case, Central Park. Otherwise, an error known as a "dangling modifier" is created and the sentence becomes confusing and ambiguous.

Only the answer choice "Central Park was the subject of many of Edward Hooper's paintings" places the subject "Central Park" immediately after the modifying introductory clause and avoids confusion and ambiguity.

All of the other answer choices make it sound as though Edward Hooper is a popular tourist destination, which is somewhat silly and definitely incorrect.

With the sentence phrased the way it is, the thing that is "caring for a pet" appears to be "responsibility." This dangling modifier needs to be changed to make it clear that "children" are "caring for a pet." The correct answer choice is "Responsibility is something children can learn by caring for a pet."

The infinitive verb “to sharpen” should not be split in half by the adverb “quietly,” or any other word. The adverb must be moved elsewhere so the infinitive is not split. The “-ly” ending on the adverb is necessary because without it, “quiet” remains an adjective and is grammatically incorrect.

The problem with the original sentence is that the phrase “even though she was mortally afraid of sharks” interrupts the flow of the main clause. The sentence runs more smoothly when it is placed at the beginning. It is important to preserve the coordinator “even though” in this sentence, because it is key to the logic of the statement. This answer choices that change this are incorrect.

The underlined phrase has a problem with the phrase "most learning." The phrase is describing the word "scholars." While the scholars might have "the most learning," this would make them "the most learned." The correct answer is "even the most learned of scholars."

The insertion of "that" between "studies" and "have" makes the sentence unclear and strangely incomplete, as the sentence essentially becomes a dependent clause. By placing "that" after "shown," the sentence becomes much more clear and appropriately makes the dependent clause after the main body of the sentence. The correct answer choice is "Studies have shown that pets can help people with problems such as depression and anxiety."

The insertion of "only" at the beginning of the sentence creates confusion as to exactly what it is modifying. The word should be moved to make it clear it is modifying "time," which is the way the sentence makes the most sense. Therefore, the correct answer choice is "The only time that will work."

The placement of "exactly" in the sentence is confusing, as placing it after "like" makes it seem as though the manner was almost exactly or kind of exactly. By placing "exactly" after "was," the comparison between the two manners of speech is more clear, making the correct answer "His manner of speech was exactly like his grandfather's."

The word "merely" is dangling in the middle of the sentence, seemingly modifying nothing and making little sense in the sentence. The word should be moved to indicate a clearer usage of the adverb. The place where the word makes most sense is between "information" and "confused," so it is clear that it is modifying the verb "confused."