CB Style Rhetorical Analysis MC Practice #3

26. Which of the following best describes the passage as a whole?

Correct Answer: (C) A reflection on certain key features of mathematical proofs

Textual Evidence: The passage discusses the nature of mathematics as both a science and an art, highlighting the logical certainty of mathematical proofs as well as their aesthetic qualities and the quest for insight.

Distractor: (A) An analysis of rival viewpoints among mathematicians - While there may be mentions of different viewpoints, the passage primarily focuses on the features and nature of mathematical proofs rather than the rival viewpoints themselves.

27. The author includes a reference to Bill Clinton in lines 8-10 primarily to

Correct Answer: (A) provide an example of how a syllogism works

Textual Evidence: The reference to Bill Clinton serves as an example to illustrate the concept of a syllogism, where the conclusion follows logically from the premises provided.

Distractor: (E) develop an analogy to illustrate the difference between politics and math - While there is an analogy being made, it's not about the difference between politics and math; rather, it's about illustrating a logical concept.

28. For the mathematicians cited in lines 10-21, a proof would lack beauty if it were

Correct Answer: (E) completely predictable

Textual Evidence: The passage discusses how a proof should have a high degree of unexpectedness and surprise, indicating that it would lack beauty if it were completely predictable.

Distractor: (B) free of nonessential steps - While a proof lacking nonessential steps might be desirable, the passage emphasizes the importance of unexpectedness and surprise in a beautiful proof.

29. In paragraph one, all of the following pairs illustrate contrasts EXCEPT

Correct Answer: (E) “odd” and “surprising” (line 18)

Textual Evidence: The other pairs in the passage illustrate clear contrasts, such as science and art, obvious and unexpected, trivial and beautiful, and surprising and straight from the Book.

Distractor: (B) “obvious” and “unexpected” (line 12) - This pair indeed illustrates a contrast, so it's not the correct answer.

30. Paragraph two presents which of the following?

Correct Answer: (D) II and III only

Textual Evidence: Paragraph two discusses the Four Color Map Theorem and the tenacity of mathematicians in their pursuit of its proof.

Distractor: (A) II only - While the paragraph does discuss the Four Color Map Theorem, it also includes information about the mathematicians' perseverance, so it's not the best choice.

31. In context, the word “contrarians” (line 34) means those who

Correct Answer: (C) approach a topic from an unorthodox perspective

Textual Evidence: The passage describes how these individuals were searching for a counterexample to the Four Color Map Theorem, which would go against the commonly held belief, indicating an unorthodox perspective.

Distractor: (A) take an old-fashioned view - While contrarians may go against commonly held beliefs, the passage doesn't suggest that they hold old-fashioned views.

32. The phrase “mathematical Mount Everest” (line 53) refers to

Correct Answer: (C) “Four Color Map Theorem” (line 54)

Textual Evidence: The passage discusses the difficulty and significance of proving the Four Color Map Theorem, likening it to conquering a mountain, hence the reference to "mathematical Mount Everest."

Distractor: (E) “1,500 fundamental cases” (line 62) - While the 1,500 fundamental cases are mentioned in the same paragraph, they are not referred to as a "mathematical Mount Everest."

33. In context, the phrase “fundamental cases” (line 62) means

Correct Answer: (A) basic patterns

Textual Evidence: The passage discusses how the computers painted variations of these fundamental cases, suggesting that they are basic patterns.

Distractor: (D) historical illustrations - While the fundamental cases may have historical significance, the passage doesn't primarily emphasize their historical aspect.

34. At the end of paragraph three, the author includes a quotation from Erdős (lines 69-73) primarily to

Correct Answer: (D) dislike some aspects of the proof

Textual Evidence: Erdős expresses dissatisfaction with the beauty and insight provided by the proof of the Four Color Map Theorem, indicating that he dislikes some aspects of it.

Distractor: (C) reserves judgment on the proof - Erdős' statement expresses a clear opinion about the proof, so it's not the best choice.

35. In context, paragraphs two and three (lines 22-73) primarily serve to

Correct Answer: (D) illustrate the shortcomings of a mathematical proof without beauty

Textual Evidence: These paragraphs discuss the use of high-speed computers to prove the Four Color Map Theorem, which while valid, is not regarded as beautiful or providing insight, illustrating the shortcomings of such a proof.

Distractor: (B) explain how both humans and computers rely on syllogisms - While the passage mentions the use of computers in mathematical proofs, it doesn't primarily focus on how both humans and computers rely on syllogisms.

36. Paragraphs two and three are developed primarily by

Correct Answer: (E) narration and analysis

Textual Evidence: These paragraphs narrate the story of the Four Color Map Theorem's proof and then analyze its implications, including the use of high-speed computers and the perception of the proof's validity.

Distractor: (A) definition - While there may be some definitions provided in the passage, the primary focus is on narrating events and analyzing their significance.

37. The sense of the last paragraph depends mainly on which of the following?

Correct Answer: (A) Analogy

Textual Evidence: The last paragraph uses an analogy between the beauty of mathematical proofs and the beauty of Beethoven's Ninth Symphony to convey Erdős' perspective on the aesthetic aspect of mathematics.

Distractor: (C) Irony - While there may be elements of irony in the passage, the main emphasis in the last paragraph is on the analogy between mathematics and music.

38. On the whole, the tone of the author is best described as

Correct Answer: (B) objective

Textual Evidence: The author presents information about mathematical proofs, their beauty, and the challenges involved without expressing personal bias or emotion, maintaining an objective tone.

Distractor: (C) skeptical - While there may be elements of skepticism expressed by some mathematicians in the passage, the author's tone overall is not skeptical but rather informative and analytical.

39.The author’s presentation makes use of all of the following EXCEPT

Correct Answer: (B) dictionary definition

Textual Evidence: The passage provides direct quotations, historical summaries, extended anecdotes, and comparisons with the arts, but it does not make use of dictionary definitions.

Distractor: (E) comparison with the arts - While the passage does compare mathematics with art, it doesn't utilize dictionary definitions, making it the correct answer.