This sentence is all about correctly using idioms. The two idioms in this sentence are “the rivalry between x and y” and “not just because of x, but because of y as well.” The only answer choice that correctly employs both of these idioms is "The rivalry between Stanford and Harvard is legendary, not just because of academics, but because of sports as well."

To get this question right, you have to know the difference between "fewer" and "less," as well as the difference between "then" and "than." "Fewer" is used in measuring things that are countable, or have a distinct quantity, such as people, footballs, or days. Less is used to describe something that are not countable, or can’t be measured with a whole number, such as soda, dirt, or sand. "Then" is used to convey the idea of “after” (i.e. "I ate and then went to the movie.") while than is used to compare ideas. Therefore, the only sentence that correctly uses both "fewer" and "less" as well as "then" and "than" is "fewer people die every year from infectious diseases than ever before."

Use of the word "not" in the sentence creates a double negative, and double negatives are grammatically incorrect in standard written English. However, the use of "neither . . . nor" is correct. The correct answer both avoids the use of the word "not" whle also utilizing "neither . . . nor."

The use of a semicolon along with the conjunction "but" is incorrect; two independent clauses can be combined either with a comma followed by a conjunction, or by a semicolon, and the sentence as it is written is mixing these options together in an incorrect manner. The best answer choice adheres to one option, the use of a comma followed by a conjunction. The incorrect answer choices either combine these options incorrectly, or use a semicolon to connect an independent clause to a dependent clause that has no subject.

The use of the word “instead” in the last part of the sentence, given that the beginning part of the sentence begins with the word, “while.” The use of the “while” signals to the reader that there will be a change later in the sentence, and so using the word, “instead” is not necessary. Therefore, the correct answer eliminates use of the word instead, and does not contain any other errors.

If a sentence is describing how “you” should behave, it creates discontinuity to then begin using the word “one” as a pronoun in place of "you." Therefore, “one" should be replaced by the word “you" in the sentence.

This sentence does not comply with the idioms that govern when prepositions should follow verbs. “Attracted” is typically followed by the preposition “to,” or is not followed by a preposition at all. Therefore, the use of the preposition “towards” after the word “attracted” is incorrect, and to correct the sentence, one should change "towards" to "to" or omit "towards" altogether. 

In this sentence, the adjective “careful” modifies the verb “entered.” Given that adverbs can only modify verbs, the proper word would instead be “carefully,” which is an adverb.

“Which” is used to show that there is modification to a phrase when the modification comes after a comma. “That” is used to show that there is a modification to a phrase in which there is not a comma after the subject being modified. Here, the part of the sentence before the comma is being modified by the part of the sentence after the comma. Therefore, “which” is appropriate, not “that.”

“Its” is used to show possession. However, the context of this sentence does not call for a showing of possession. Rather, “it’s,” the abbreviated version of “it is,” is the appropriate word that should be used.