The modifier “wishing for a new doll” applies to Polly, so it must appear next to “Polly” in the sentence. “Wishing for a new doll, Polly blew out the birthday candles enthusiastically” is the best choice, since the modifier is in the correct place and the sentence doesn’t rely on the passive voice or awkward phrasing.

In the original sentence, the clause "Writing about a family that tours as a freak show" incorrectly modifies "Katherine Dunn's novel." As a novel cannot write itself, the clause is actually meant to modify "Katherine Dunn," the novel's author. All of the incorrect answers maintain this error in some form. "Having written" and "writing" both modify "Katherine Dunn's novel." "A family that travels as a freak show" modifies "Katherine Dunn's novel" as well, when it is meant to refer to the characters in the novel, rather than the novel itself. "Being written about a family that tours as a freak show" modifies "Katherine Dunn," when it should modify "Katherine Dunn's novel." The correct answer, then, must be the sentence, "Katherine Dunn's novel Geek Love, which depicts a family that tours as a freak show, was a finalist for the National Book Award." In this sentence, the clause "which depicts a family that tours as a freak show" correctly modifies "Katherine Dunn's novel."

The phrase "Unlike the other programmers" is intended to relate to another programmer, Nathan, not "Nathan's code." The current sentence also uses passive voice in stating that "Nathan's code was made." The best answer uses both active voice and correct modifier-word modified agreement: "Unlike the other programmers, who were disillusioned and bored, Nathan made code that was consistently full of inventive and exciting ideas."

“Looking at the mannequin” is a modifier that refers to an action performed by the speaker of the sentence. Because a modifier should always appear as close as possible in the sentence to the thing it modifies, “Looking at the mannequin, I thought the dress seemed much smaller than the salesman claimed it was” is the most correct and concise answer.

“Cascading to the floor in a rainbow-colored shower” is a modifier that refers to an action performed by the beads, not the speaker, so the modifier must be placed immediately before or after “my bead collection” in the sentence. Here, the most correct and concise choice is a completely rewritten sentence with clear modifiers.

The phrase "oozing with four kinds of melty cheese" is intended to modify "[the writer's] wife's homemade bacon mac & cheese."; therefore, it should be placed at the end of the sentence to be as close as possible to the noun phrase it is describing. The participle "oozing" could still be easily attributed to either the subject "I" or the "mac and cheese," but changing the phrase "oozing with four kinds of melty cheese" to "which oozed with four kinds of melty cheese" removes the possibility of the phrase referring to the subject "I," making the sentence less ambiguous.

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 first part of this sentence, "stretching her arm out as far as she could," necessarily modifies the subject of the sentence. The only possible subject that could do this action of "stretching" is Ramona - therefore Ramona needs to be in subject position. The example sentence thus features a dangling modifier error.

"Stretching her arm out as far as she could" cannot modify a "shelf", so this creates a dangling modifier.