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Assumption. The correct answer choice is (E)
The nutritionist explains that vitamins synthesized by chemists are identical to naturally occurring vitamins. The nutritionist concludes that it is a waste of money to pay for vitamins pills made of high-quality or natural ingredients.
The nutritionist assumes that the vitamin element is the only relevant factor in the pills, and you are asked to identify that assumption.
Answer choice (A): The nutritionist does not argue against supplements; the nutritionist argues against choosing expensive instead of inexpensive supplements.
Answer choice (B): The nutritionist does not need to assume that pills with natural ingredients always cost more. The nutritionist merely argues that you should not pay more for natural ingredients. Technically, even if every single natural ingredient product were the cheapest available, the nutritionist could still be correct that you should not be willing to pay more for natural ingredients, so this choice addresses an irrelevant consideration and is incorrect.
Answer choice (C): The nutritionist argues that natural and synthetic vitamins are identical, so the nutritionist does not have to assume that all pills contain some synthetic vitamins. This choice ignores the considerations already in the stimulus.
Answer choice (D): The nutritionist does not need to assume that some producers are guilty of false advertising. It is possible that some pills, as advertised, are made of higher-quality or natural ingredients, but that the quality of those ingredients does not affect the overall quality of the pill. In that case, the readers of pill bottles would be guilty of faulty reasoning; the producers would not be guilty of false advertising.
(You can argue about at what point advertising that experts should anticipate would, though true, mislead someone with an "unengaged" mind becomes false advertising, but since that involves a number of presumptions, that is really not a viable, logical means of justifying this choice.)
Answer choice (E): This is the correct answer choice. The nutritionist has to assume that the non-vitamin ingredients in a pill do not affect how much money the pill is worth. If the factor of non-vitamin ingredients can affect worth, the nutritionist might be wrong.