#21 - Each of the candidates in this year's mayoral election

[Administrator]

Complete Question Explanation

Parallel Flaw—FL. The correct answer choice is (B)

The flaw in this stimulus is one of Formal Logic. The argument attempts to connect a chain relationship using formal logic as follows:

• Premises: Candidate Small Business Owner Competent Managers Skills Necessary
  
  Conclusion: Candidate Skills Necessary

If most small-business owners are competent managers and all competent managers have the skills necessary to be a good mayor, then it is valid to conclude that most small business owners have the skills necessary to be a good mayor:

• Small Business Owner Skills Necessary

However, even though all of this year’s candidates are small-business owners, we cannot conclude that any of these candidates have the skills necessary to be a good mayor. Let’s say there are 100 small business owners, 51 of whom have the skills necessary to be a good mayor. If there are only 5 candidates for the position, all of whom small business owners, it is entirely possible that these 5 candidates are among the 49 who do not have the necessary skills. The correct answer choice should attempt to make this same mistaken connection using Formal Logic as the stimulus.

Answer Choice (A): This answer choice presents valid reasoning, and therefore fails the Validity Test. If most of the company’s management has worked in sales, and anyone who has worked in sales has worked there for at least one year, then most of the management has worked in sales for at least one year. Also, since everyone who has worked for at least one year understands marketing, then it is valid to conclude that most of the management understands marketing. The logic can be diagrammed as follows:

• Premise: Management Work in Sales Work in Sales 1+ years Understands Marketing
  
  Conclusion: Management Understands Marketing

Answer Choice (B): This is the correct answer choice. Since most fat-free foods are sugar-free, and all sugar-free foods are low in calories, it is true that most fat-free foods are low in calories. The stimulus also states, however, that all of the food on Maddy’s menu is fat-free. However, it is unknown whether the fat-free food on Maddy’s menu falls into the majority of fat-free food that is sugar-free. Much like in the stimulus, it is possible that all of the food on Maddy’s menu is fat-free but not sugar-free. Therefore, since it is invalid to conclude that most of Maddy’s menu is sugar-free, it is invalid to conclude that it is low in calories. This answer choice therefore parallels the flawed reasoning in the stimulus. The logic can be diagrammed as follows:

• Premise: Menu at Maddy’s Fat-Free Food Sugar-Free Food Low in Calories
  
  Conclusion: Menu at Maddy’s Low in Calories

Answer Choice (C): This answer choice fails the Conclusion Test. The conclusion in the stimulus was about most of the candidates. Answer Choice (C) concludes that Ed never read the books in less than 3 hours. The language in this conclusion does not match the logical force of the conclusion in the stimulus.

Answer Choice (D): This answer choice fails both the Premise Test and the Conclusion Test. The premises in the stimulus formed a formal logic chain, connecting candidates to small business owners, small business owners to competent managers, and competent managers to skills necessary. The premises in answer choice (D) present multiple facts about films less than an hour long: most do not become commercially successful and none have an intermission. Meanwhile, the conclusion in this answer choice refers to most films. In order to match the conclusion in the stimulus, the conclusion here needs to refer back to most avant-garde films, the subject of the original premise.

Answer Choice (E): Once again, this answer choice fails the Premise Test. Similar to answer choice (D), the premises here present multiple facts about the bicycle helmets sold in this store: all of them contain plastic and most of them contain rubber. The premises here do not link three formal logical statements into a logical chain in the same manner as the stimulus.

[jschruhl]

I was able to answer the question correctly just by matching the stimulus to the answer choices, but my question is regarding why the conclusion is flawed.

Candidates in election > Sme business owners (>Most) Competent managers > Have skills necessary

"Flawed" conclusion: Candidates in election (>Most) have skills necessary

Can you properly infer that "some" candidates have the skills necessary?

When I saw this, I thought back to the Persian cat question where Beautiful Cats (Some>) Persian > Pompous so some beautiful cats are pompous. Therefore, is the error because the conclusion says "most" and not "some" or is it different in some way from the persian cat example in that we cannot make any inferences? Thanks so much, just trying to get the formal logic straightened out before saturday!

[Adam Tyson]

Actually, in this case it is a mistake to assume that ANY of the candidates are competent managers. Jut because MOST small business owners have that characteristic doesn't mean that any of these guys are in that majority. There's the flaw, and all the other statements that purportedly follow from that flaw are also necessarily flawed as well.

The same flaw appears in correct answer choice B - just because most fat-free foods are also sugar-free doesn't mean the ones on Maddy's menu are in that group - they could all be in the minority of fat-free foods that do have sugar in them.

Classic formal logic flaw, assuming that just because two groups CAN overlap that they MUST overlap.

Adam

[lsatprep1215]

Hi
I answered this question correctly but I still have something that I want to ask.
My diagram is Candidates SBO
SBO CM
CM Have skills to be good Mayor

Is it valid if I connect Candidates CM ?

[Adam Tyson]

Your diagram is correct, lsatprep1215, and matches what we've provided earlier in this thread, so good work on that. To answer your question, though, no, we cannot then infer that most of the candidates are competent managers, and in fact we cannot even infer that some of them are. It's entirely possible that these candidates, who are all small business owners, are NOT in the majority of small business owners who are also competent managers. They could ALL be in the minority who are not competent managers! You have to be careful about carrying that idea of "most" over to other parts of the chain. Sometimes it works, but most of the time it does not. Here's one where it works:

Most of my my cousins are married, and all married people wear rings. Therefore, most of my cousins wear rings.

I can carry the "most" forward here in the chain because I know something about everyone who is married. But if we change the placement of the "most" statement, we have a problem:

All of my cousins are married, and most married people wear rings.

Can I now prove that most of my cousins wear rings? No. In fact, it is possible that none of my cousins wear rings. Maybe they are not part of the majority of married people who wear rings, but are instead in the minority that does not.

When in doubt, apply some numbers, as we did earlier in this thread. If there are 100 small business owners, and most of them are competent managers, then at least 51 of them are competent managers. That means as many as 49 might not be competent managers. Perhaps there are just a few candidates for mayor. and they are all part of that group of 49? That would be one possible situation, so we cannot prove that any candidates share the characteristic that most small business owners share.

[Nsaramouni]

Hello,

I am little confused as to how we get this chain from the stim.

Premises: Candidate --> Small Business Owner -- (most)--> Competent Managers ---> Skills Necessary

I am confused primarily because of the competent managers arrow to the skills necessary. The stim states that " no competent manager lacks the skills necessary to be a good mayor. " so how is it that we have an all arrow instead? Why is it that it just switched? Am I missing something in terms of the logic ladder? Can you please explain how it isn't a Not Arrow, amongst anything else you think I have missed?

[Robert Carroll]

Nsaramouni,

The "competent manager skills necessary" diagram of that relationship is logically equivalent to the relationship you're talking about.

Imagine we were to diagram the statement as a "not" relationship. When we have a sentence of the form "No A are B", we'd diagram that "If A then not B". Here, that would amount to "If someone is a competent manager, that person does not lack the skills necessary to be a good mayor." But note that "not lacking the skills necessary to be a good mayor" is the same as "having the skills necessary to be a good mayor"; there was a double negation going on. "Not lacking" = "having". So the necessary condition of that conditional involves a double negation. When the double negation is eliminated, the necessary condition is a positive statement, not a negative one.

Note also that a Double-Not Arrow is always a conditional relationship. "No one who signs up late for financial aid will be eligible for a scholarship" can be diagrammed as follows:

signs up late for financial aid eligible for a scholarship

But it's also equivalent to the English sentence "If you sign up late for financial aid, you are not eligible for a scholarship," which can be diagrammed:

signs up late for financial aid eligible for a scholarship

Whether a conditional arrow or the Double-Not Arrow works better depends on the situation, and, to some extent, personal taste. In the relationship we started discussing about competent managers, the diagram with a conditional arrow will have "positive" statements in both conditions. That's pretty intuitive for a conditional to have. It also makes it easier to see the chain reasoning the author was attempting to use (and which was flawed).

Robert Carroll

[lsatstudy2023]

Hi,

Is it reasonable to knock E out because the first premise is about "Bicycle Helmets" sold in the store, but the conclusion is about "most helmets sold in the store"

[lsatstudy2023]

Hi,

Is it reasonable to knock E out because the first premise is about "Bicycle Helmets" sold in the store, but the conclusion is about "most helmets sold in the store"?

[Rachael Wilkenfeld]

I would say that's similar to the stimulus in that way. There's a difference between small business owners and small business owners who are candidates. Similarly, in answer choice (E), there's a difference between bicycle helmets sold in the store and all helmets sold in the store. The bigger issue with answer choice (E) is that the conditionals don't chain correctly. The premise sufficient conditions are the same, so they aren't going to link like the stimulus was able to link.

Hope that helps!