## #22 - In Sheldon most bicyclists aged 18 and over have

PowerScore Staff

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Complete Question Explanation

Parallel Flaw. The correct answer choice is (C)

This is a fantastic question for paralleling key terms in the premise(s) and conclusion. The premise uses the term “most” twice, and the conclusion uses “most” once. Hence, the correct answer choice must mirror this logical structure/language by containing three “most” (or synonymous terms, such as “almost all,” “more than half,” etc.) terms.

The flaw here is a numbers and percentages error: you cannot conclude that most bicyclists that have lights on their bicycles are at least 18 simply because most bicyclists who are at least 18 have lights, whereas most under 18 do not. Consider the following example that meets the premises but yields a different conclusion:

There are 400 bicyclists in Sheldon: 100 are at least 18, and 300 are under 18.

60 out of 100 bicyclists 18+ yrs old have lights (most have lights).

100 out of 300 bicyclists under 18 yrs have lights (most do not have lights).

In this case, most bicyclists with lights are under 18 (100 vs. 60).

Answer choice (A): The conclusion uses the phrase “fewer than half,” which is not the same as “most.”

Answer choice (B): The conclusion in this answer choice is causal, so it does not match the stimulus.

Answer choice (C): This is the correct answer choice. Note that it also contains three “most” statements, and it contains the same error as the one in the stimulus (numbers and percentages, as described above).

Answer choice (D): The first premise says “every,” which does not parallel the “most” premises in the stimulus.

Answer choice (E): The first premise says “everyone,” which does not parallel the “most” premises in the stimulus.
taxstonefromthefeds
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When I diagrammed this question, I also noticed a mistaken reversal flaw. I was wondering if my thought process was right.

1) B18+ lights on bike
2) not B18+ not lights on bike
3) Conclusion: lights on bike B18+

Depending on how this is analyzed, the conclusion is a mistaken reversal of statement number one. This flaw is captured in AC C.
Jonathan Evans
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Hi, Taxstone!

You're right that this is very similar to a Mistaken Reversal flaw! With these "most" statements you cannot travel backwards against the direction of the arrow, with the following exception:

Most children like ice cream. Most children like pizza. Therefore, there is at least one child who likes both ice cream and pizza.

Children like ice cream
Children like pizza
Children like ice cream and pizza

Strictly speaking, Mistaken Reversal refers to the formal conditional fallacy of the converse (or affirming the consequent) and not to quantity statements such as these, but your reasoning is valid.

Good job!