Based on your analysis, let's break down the options:
- Option 1 adds depth to the prediction that start-ups, under the pressure of revenue, will likely expand their product offerings. Since this aligns with the author's prediction, Option 1 is unlikely to weaken the argument.
- Option 2 suggests that start-ups are not exempt from the general trend and may face challenges or need to change. While this doesn't directly contradict the author's prediction, it introduces an element of skepticism about the success of start-ups, which may slightly weaken the argument.
- Option 3, as you mentioned, brings out a point that contradicts the idea that start-ups will necessarily offer more product varieties. This option introduces a counterpoint to the author's prediction, making it a potential weakening factor.
- Option 4 predicts the failure of start-ups, supporting the author's argument about their fate. This aligns with the author's viewpoint and, therefore, does not weaken the argument.
Considering your analysis, Option 3 appears to be the choice that introduces a point contradictory to the author's prediction, potentially weakening the argument.
Correctly identifying the answer involves synthesizing information from various parts of the paragraphs. The provided excerpts highlight the evolution of certain companies:
- "Casper (mattresses), Glossier (makeup), Away (suitcases), and many others have sprouted up to offer consumers freedom from choice."
- "For start-ups that promise accessible simplicity, their very structure still might eventually push them toward overwhelming variety."
- "Casper has expanded into bedroom furniture and bed linens. Glossier, after years of marketing itself as no-makeup makeup that requires little skill to apply, recently launched a full line of glittering color cosmetics."
Considering these statements collectively, both companies, Casper and Glossier, began by offering simplicity and limited choices but eventually expanded their product lines to include a more extensive and varied range. Thus, Option 2 accurately captures this evolution, making it the correct choice.
The author expresses a favorable stance toward two main points: limiting the range of choices and endorsing mid-range pricing.
Evaluating the options, both Option 2 and Option 3 advocate for reduced variety, but only Option 2 aligns with the additional criterion of mid-range pricing. The passage supports this combination, as indicated by the statement,
"The companies have a few aesthetically pleasing and supposedly highly functional options, usually at mid-range prices." Therefore, Option 2 is the accurate choice as it concurs with the author's preferences for limited variety and mid-range pricing.
Based on the provided passage, we are tasked with identifying a statement that cannot be inferred regarding consumer behavior. The passage discusses multiple facets of consumer behavior, particularly in the context of online shopping and the overwhelming plethora of choices available to consumers today.
Let's analyze the options in light of the passage:
1. Too many options have made it difficult for consumers to trust products. The passage discusses choice anxiety and how consumers are faced with numerous options, making decision-making more challenging. This sentiment is consistent with the idea that trust could be undermined in the sea of choices.
2. Consumers tend to prefer products by start-ups over those by established companies. The passage does not state that consumers have a preference for start-ups. Instead, it mentions start-ups offering limited options as a method to ease choice anxiety, but no comparative preference is expressed directly for start-ups over established brands.
3. Having too many product options can be overwhelming for consumers. This is directly stated in the passage through the reference to "choice anxiety," where too many options lead to decision difficulty.
4. Consumers are susceptible to marketing images that they see on social media. The passage mentions the influence of lifestyle influencers and aspirational worldviews on Instagram, a social media platform, indicating that consumers are indeed influenced by such marketing strategies.
Considering the passage and each option's analysis, the statement "consumers tend to prefer products by start-ups over those by established companies" cannot be inferred. The passage highlights a method used by start-ups to ease choice anxiety without discussing consumer preference over established companies. Thus, this is the correct choice for what cannot be inferred from the passage.


When people who are talking don’t share the same culture, knowledge, values, and assumptions, mutual understanding can be especially difficult. Such understanding is possible through the negotiation of meaning. To negotiate meaning with someone, you have to become aware of and respect both the differences in your backgrounds and when these differences are important. You need enough diversity of cultural and personal experience to be aware that divergent world views exist and what they might be like. You also need the flexibility in world view, and a generous tolerance for mistakes, as well as a talent for finding the right metaphor to communicate the relevant parts of unshared experiences or to highlight the shared experiences while demphasizing the others. Metaphorical imagination is a crucial skill in creating rapport and in communicating the nature of unshared experience. This skill consists, in large measure, of the ability to bend your world view and adjust the way you categorize your experiences. Problems of mutual understanding are not exotic; they arise in all extended conversations where understanding is important.
When it really counts, meaning is almost never communicated according to the CONDUIT metaphor, that is, where one person transmits a fixed, clear proposition to another by means of expressions in a common language, where both parties have all the relevant common knowledge, assumptions, values, etc. When the chips are down, meaning is negotiated: you slowly figure out what you have in common, what it is safe to talk about, how you can communicate unshared experience or create a shared vision. With enough flexibility in bending your world view and with luck and charity, you may achieve some mutual understanding.
Communication theories based on the CONDUIT metaphor turn from the pathetic to the evil when they are applied indiscriminately on a large scale, say, in government surveillance or computerized files. There, what is most crucial for real understanding is almost never included, and it is assumed that the words in the file have meaning in themselves—disembodied, objective, understandable meaning. When a society lives by the CONDUITmetaphor on a large scale, misunderstanding, persecution, and much worse are the likely products.
Later, I realized that reviewing the history of nuclear physics served another purpose as well: It gave the lie to the naive belief that the physicists could have come together when nuclear fission was discovered (in Nazi Germany!) and agreed to keep the discovery a secret, thereby sparing humanity such a burden. No. Given the development of nuclear physics up to 1938, development that physicists throughout the world pursued in all innocence of any intention of finding the engine of a new weapon of mass destruction—only one of them, the remarkable Hungarian physicist Leo Szilard, took that possibility seriously—the discovery of nuclear fission was inevitable. To stop it, you would have had to stop physics. If German scientists hadn’t made the discovery when they did, French, American, Russian, Italian, or Danish scientists would have done so, almost certainly within days or weeks. They were all working at the same cutting edge, trying to understand the strange results of a simple experiment bombarding uranium with neutrons. Here was no Faustian bargain, as movie directors and other naifs still find it intellectually challenging to imagine. Here was no evil machinery that the noble scientists might hide from the problems and the generals. To the contrary, there was a high insight into how the world works, an energetic reaction, older than the earth, that science had finally devised the instruments and arrangements to coart forth. “Make it seem inevitable,” Louis Pasteur used to advise his students when they prepared to write up their discoveries. But it was. To wish that it might have been ignored or suppressed is barbarous. “Knowledge,” Niels Bohr once noted, “is itself the basis for civilization.” You cannot have the one without the other; the one depends upon the other. Nor can you have only benevolent knowledge; the scientific method doesn’t filter for benevolence. Knowledge has consequences, not always intended, not always comfortable, but always welcome. The earth revolves around the sun, not the sun around the earth. “It is a profound and necessary truth,” Robert Oppenheimer would say, “that the deep things in science are not found because they are useful; they are found because it was possible to find them.”
...Bohr proposed once that the goal of science is not universal truth. Rather, he argued, the modest but relentless goal of science is “the gradual removal of prejudices.” The discovery that the earth revolves around the sun has gradually removed the prejudice that the earth is the center of the universe. The discovery of microbes is gradually removing the prejudice that disease is a punishment from God. The discovery of evolution is gradually removing the prejudice that Homo sapiens is a separate and special creation.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: