tobyna
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Q22 - In Sheldon most bicyclists

by tobyna Fri Oct 19, 2012 2:58 pm

I really have trouble understanding this one...can someone please explain the logic (or lack thereof) and answer choices? Thank you!
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Re: Q22 - In Sheldon most bicyclists

by ohthatpatrick Fri Nov 09, 2012 10:06 pm

Hey, there.

This is a "Match the Flaw" question, so our first job is to understand the flaw in the original argument.

Our second job is to think about how to express the flaw in the abstract and to characterize the type/strength/order of claims in the premise(s) and conclusion.

The argument is trying to use a statistic that says:
most bikers who are A (18+) are B (have lights on their bikes)
+
most bikers who are ~A (under 18) are ~B (don't have lights)
====
thus, most B are A

You may notice that the first premise and the conclusion make an illegal move.

Most A are B ==does not tell us that==> Most B are A

Most criminals are men, but that doesn't mean that most men are criminals.

In fact, we could run with this example even more to mimic the original argument:

Most people who are criminals are men, whereas most people who are not criminals are not men. It follows that most men are criminals.

It's true, in the real world, that most criminals are men.
It's true, in the real world, that there are more women than men, so it's true that most non-criminals are not men (women).

But obviously this conclusion is silly. The reason this is a flaw is you are not allowed to equate Most A are B with Most B are A. The 2nd premise, which says that Most ~A are ~B doesn't do anything to help prove Most B are A.

So we know our flaw (Most A are B does not prove Most B are A), and we can describe the premise and conclusion ingredients in an abstract way:
P1: Most A are B
P2: Most ~A are ~B
Conc: Most B are A

Now we just need to scan the answer choices for this structure (these three ingredients can be in a different order, as long as the conclusion is still saying the same thing).

(A) is worth considering since it has three "most" statements ("most", "almost everyone", and "fewer than half" -- which can be translated into "most")

P1: Most A (ppl in Sheldon) are B (buy gas on Mondays)
P2: Most A (ppl in Sheldon) are C (buy groceries on Tuesdays)

This already fails to match the original, so we should eliminate and move on.

(B) This is not worth analyzing. There are no "most" statements. Furthermore, there's only one premise, whereas the original argument had two.

(C) This looks promising.
P1: Most A (voted) are B (on Conservative mailing list)
P2: Most ~A (didn't vote) are ~B (not on C-list)
Conc: Most B (on C-list) are A (voted)

On a test, I would commit to this answer and move on, while circling the problem, so that if I have extra time at the end of the section I can check the two choices I didn't consider.

(D) Not worth analyzing. There are not three "most" statements. The first premise is "all", the second is "most, and the conclusion is "at least two".

(E) Not worth analyzing. There are not three "most" statements. The first premise is "all", the second is "not all", and the conclusion is just comparative "X more than Y".

Notice how the extra time I spent initially categorizing the type/strength of the premise(s)/conclusion is allowing me to not have to carefully read all the answer choices.

It's a good example of how a little extra time on the front-end can save you tons of time on the back-end.

Let me know if you have questions about any of this. Hope this helps.
 
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Re: Q22 - In Sheldon most bicyclists

by taaron Sat Nov 10, 2012 7:28 am

Great answer - thank you!

A follow-up question: Is A correct or flawed logic?
 
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Re: Q22 - In Sheldon most bicyclists

by griffin.811 Thu Jul 11, 2013 8:59 am

I went with E on this one. I think I understood the flaw a little differently though.

The stim says most A are B, and most C are not B, therefore, most B are A.

I saw the flaw as failing to consider the fact that there may be many more B than A. If there are 10 A's (and lets say 9 of them are B) but there are 1000 C's (and say 100 are B's) then we would have an issue...

I think E fits this flaw: If assumes there are more people that knit, or at least not so many more people that sew and do not not knit.

Was this question flawed? (more likely my reasoning has the flaw)

Thanks!
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Re: Q22 - In Sheldon most bicyclists

by ohthatpatrick Fri Jul 12, 2013 3:44 pm

To answer a stale question a couple posts back, yes, (A) appears to be sound logic.

Griffin, you're definitely right about how you were thinking about the original flaw.

There's no reason to use C (as you did in another post I just saw) to describe "under 18", because that would just be not-A.

Not only does this simplify how many variables we're keeping track of, it also correctly represents the idea that A and not-A are mutually exclusive groups (whereas A and C could have overlap).

But you're reasoning is right.

Let's say there are 10 ppl over the age of 18 and 9 of them have bike lights. (fits the first idea)

Let's say there are 100 ppl under the age of 18 and 49 of them have bike lights. (fits the second idea)

Well, a total of 58 people in this town have bike lights, and MOST of them are UNDER 18, so clearly the original conclusion is flawed.

(E), meanwhile, is actually valid logic.

If you're over 60 and knit, then you also sew.

Whereas there ARE people over 60 who sew but don't knit.

If you can picture concentric circles, draw a big circle and label it "people over 60 who sew"; then draw a smaller circle inside of that circle and label it "people over 60 who also knit". THAT is what those first two facts give us.

Thus, there MUST be more people over 60 who sew than there are people over 60 who knit.

So you would want to eliminate (E) because it is CORRECT, not FLAWED logic.

You might also have seen a problem because the two facts it gives us are not about mutually exclusive groups.

In the stimulus, fact 1 was about "bikers 18 and over" and fact 2 was about "bikers under 18". No possible overlap.

In (E), fact 1 is about "people over 60 who knit" and fact 2 is about "people over 60 who sew". There is possible overlap, so this is not a good match for the original.

Hope this helps.
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Re: Q22 - In Sheldon most bicyclists

by WaltGrace1983 Sat Feb 07, 2015 3:23 pm

I eliminated (E) for its conclusion but, upon reviewing, I see that it is actually valid! Thanks for the tip, Patrick. I was a bit confused by your explanation so I'll try and see if I got this one correct:

We are just going to ignore the whole "over 60" thing because we are ONLY talking about people over 60, no need to make this more complicated!

In this world, you can either Knit or ~Knit, (K) or ~(K).

If you K, you must also S.

Therefore, for every K, there absolutely must be be (at least an) equal amount of S. Why? Because K --> S and so if you count 75 K's, you must at least count 75 S's according to our rules in the stimulus.

However, there are some S's that don't K!

If you push these two rules together, you'll see that the first rule gives you an equal amount of K's and S's while the second rule gives you some S's that don't K, thereby entailing that there are actually MORE S's than K's.

Pretty cool. I don't think I would be able to do that kind of thinking under pressure though.
 
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Re: Q22 - In Sheldon most bicyclists

by seychelles1718 Thu Feb 18, 2016 11:58 am

Thanks for your explanation Patrick!

Just to be clear, I don't think "fewer than half" of A is translated to "most" because "most" means more than 50%.
I eliminated A because I knew "fewer than half" does not match to the "most" in the conclusion of the original argument.

Am I correct?
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Re: Q22 - In Sheldon most bicyclists

by ohthatpatrick Sun Feb 21, 2016 7:53 pm

Thanks for the follow-up … I never reached the point of explaining what that meant.

Statements about “few”, “a minority”, “less than half” allow you to translate into “most”, just as statements about “all” allow you to translate into “none”.

All NFL players are men = No NFL players are women

Most NFL players are at least 200 lbs = Fewer than half of NFL players are under 200lbs.

So if we hear that “fewer than half of the ppl in Sheldon buy gas and groceries on the same day”, we can translate that into “most ppl in Sheldon do not buy gas and groceries on the same day”.

That’s all I meant. If you really NEEDED to, you could make it work. I wouldn’t suspect we’re on the right track, but I can’t get rid of it for not providing three “most” claims.
 
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Re: Q22 - In Sheldon most bicyclists

by AshleyT786 Fri Sep 24, 2021 9:53 pm

How would I go about diagramming aged 18 and over? I feel that 18+ isn't enough because that is only talking about 18 and older, isn't it? Is this stimulus an example of illegal reversal of a most statement? Doesn't that mean the second half of the first sentence (whereas most...) is just fluff?