Q22 - Only a minority of those who

[rbolden]

I narrowed my choices down to A and B and ended up choosing A but would like more clarification on why B is incorrect.

Part of the flaw I see is a reversal with "engaging in political action" and "a sense of social justice." Just because a minority of those who engage in political action do so out of a sense of justice does not necessarily mean that some people with a sense of social justice do not engage in political action.

With this thought in mind I was able to eliminate C, D, E.

I then took a closer look at the phrases "only a minority" and "some" which were used in the question but in answer choice B there was no indication of this in the first sentence. So this is why I eliminated B.

I am not sure if my thought process is correct. Please provide your explanation!

Thanks!

[noah]

Good question! It's a good one because you got it right, but want to clean up your process regardless. Overall, I think you need to at the formal structure (though you don't necessarily need to represent it formally) or the modifiers. For this problem, the modifiers work.

From reading the stem, I know I'm looking for a flawed structure. Similar to you, I see the flaw being that you can't conclude that some social justice folks don't engage in political action - it's possible that all of them do. To think of it formally:

(less than all) Soc. Just. --> Pol. Action

The only thing we can infer is the reverse:

(some) Pol. Action --> Soc. Just
as well as
(some) Pol. Action --> Not Soc. Just

But "some" is vague, meaning only "1 or more." Perhaps there are 10 people who are politically active because of their sense of social justice and those are the only people who have a sense of justice!

Looking for matches, we can use the fact that we need a "some" conclusion to be illegally drawn from a "minority" statement.

You can quickly eliminate some of the answers - as you did with (C), (D) and (E) - because they don't have both a minority and a some statement.

(B) can be considered incorrect because it does not have a "minority statement" and it concludes with a "most" statement.

Try out that approach on some other matching questions and see how it works. While sometimes a more formal look at the structure is needed, at times the modifiers will get you there.

Tell me how that goes.

[timmydoeslsat]

Just thought I would update this with my thought.

Here is a hypothetical of this stimulus. We are going to have 5 people that do political action. A minority will do so out of a sense of social justice.

P P P P P

Those are my 5 people, the only 5 people that do political action.

Now, a minority of these guys guys do so out of a sense of social justice.

P P P P P
S

I decided to have only one P do so with a sense of S.

As you can see, we cannot conclude that there will be S's out there that do not do P.

You could, but you cannot conclude that you necessarily have a case of an S not doing P.

[lhermary]

Wow, this one was incredibly tricky.

[taaron]

How would you formally diagram the first premise "only a minority of those who engage in political action do so out of a sense of social justice"?

I chose A, but in reviewing, I realized I may be diagramming it backwards...

My diagram was:

Political action --MOST--> Not Social Justice

thank you!!

[zagreus77]

Good question! It's a good one because you got it right, but want to clean up your process regardless. Overall, I think you need to at the formal structure (though you don't necessarily need to represent it formally) or the modifiers. For this problem, the modifiers work.

From reading the stem, I know I'm looking for a flawed structure. Similar to you, I see the flaw being that you can't conclude that some social justice folks don't engage in political action - it's possible that all of them do. To think of it formally:

(less than all) Soc. Just. --> Pol. Action

The only thing we can infer is the reverse:

(some) Pol. Action --> Soc. Just
as well as
(some) Pol. Action --> Not Soc. Just

But "some" is vague, meaning only "1 or more." Perhaps there are 10 people who are politically active because of their sense of social justice and those are the only people who have a sense of justice!

Looking for matches, we can use the fact that we need a "some" conclusion to be illegally drawn from a "minority" statement.

You can quickly eliminate some of the answers - as you did with (C), (D) and (E) - because they don't have both a minority and a some statement.

(B) can be considered incorrect because it does not have a "minority statement" and it concludes with a "most" statement.

Try out that approach on some other matching questions and see how it works. While sometimes a more formal look at the structure is needed, at times the modifiers will get you there.

Tell me how that goes.

Friendly amendment, Noah. Rather than
(less than all) Soc. Just. --> Pol. Action , which does not capture what the argument says nor support the valid inferences you cite from what the argument does say, it should be some but less than all all-- the parallel doesn't follow precisely w/r/t the correct answer, but correct parallel question answer choices are not always exact matches to those in their respective stimuli, as you well know, just the most similar.

[ottoman]

Can you explain why E is wrong?

Thank you!

[dandrew]

Is part of the flaw that the passage claims overlap when there isn't any proof to support it? While reading I visualized the box that the strategy guide uses, with one slice being the minority (aka "some") who are both political action AND social justice. The other slice (also "some") was of people with social justice but no political action. The overlap here is social justice, but since both parties are only "some", there's no proof that they overlap, which is why "A" is the correct answer, right?

Thank you!

[christine.defenbaugh]

dandrew, I'm glad you asked!

I think you're thinking of a different scenario, actually. The box from the strategy guide, with the overlapping (or not) slices, is more useful when you have a category (the box) described in two different ways. It's a way to process two overlapping (or not) statements.

For instance, if most of my cats are gray, and most of my cats have stripes, then you'd know at least one of my cats is gray with stripes. Here we have the category "my cats" as the box. There's a gray slice and a stripes slice that overlap just a bit.

But this situation is different. We only have two groups, being described in relation to each other. So, here the box might look like this:


The box itself is all political action people. There's no overlap in the two 'slices' because something either is social justice or it isn't - it can't be both and it can't be neither.

We know that only a minority of that group does political action for social justice, while the majority do not. The (flawed) conclusion then claims that some social justice people do NOT engage in political action. But we don't have any information about the group "not political action"! There's a whole world outside that box we know nothing about!

Just because "most political action = not social justice" does not necessarily meant that "some social justice = not political action". (A) commits the same error: just because "most scholars = not prize motivated" does not mean that "some prize motivated = not scholars".

I hope this helped clear this up a bit!

[ttunden]

Can anyone explain why D is wrong? It has the some + some like the stimulus does. I don't really understand why A is the right answer. I picked it but may have done so due to doing this problem in the distant past.

Any additional explanation please? Would prefer no diagramming. Thanks.

[christine.defenbaugh]

Thanks so much for posting, ttunden!

On formal quantity logic parallel questions such as this one, there are a few tools that you can use to match up answers to the stimulus. One is to use the quantifier words themselves, which it sounds like you're doing by looking at the 'some' language of (D). Another way is to look at the elements being discussed. Sometimes, just one of these could be enough to zero in on the correct answer, and other times, we'll have to use a combination of the tactics.

First, a note about the quantity words themselves: "a minority" actually gives us a bit more information than just a bare 'some' statement would. To say that "only a minority of the apples are red" would tell me two reciprocal things:

1) Most of the apples are not red
2) some (less than half) of the apples are red

This is a little more specific than a simple 'some' statement!

But let's take a sharp look at the elements being discussed in the stimulus: it's talking about [people engaged in political action] and [people with a sense of social justice]. That's all! It's all about how those two groups of people do or do not intersect!

I know you said that you preferred no diagramming, but at least a little is fairly critical to see the pattern in the stimulus. Let's breakout what we've got:

PREMISE:
only minority [political action people] are [social justice people] -->
so most [political action people] are NOT [social justice people]
CONCLUSION:
Some [social justice people] are NOT [political action people]

A simplified, generic version of this pattern is:

PREMISE: Most A are not B
CONCLUSION: Some B are not A

Only Answer (A) follows this whole pattern. We've got

PREMISE:
Most [scholars] and NOT [prize motivated people]
CONCLUSION:
Some [prize motivated people] are NOT [scholars]

The diagramming helps, because it makes it a little easier to see that these two arguments have the same shape.

Let's take (D) apart: Both statements have 'some' quantifiers, and even though I know my original had an implied 'most', it might be okay. But now we need to check out the elements: The first sentence talks about [parents] and [people who show no interest in school curricula]. Fine. But the second sentence brings up [decisions], which is a totally new category! And suddenly we're talking about how decisions should be made!

Wait a second, this argument isn't about overlapping/intersection groups at all! It's an argument about how decisions should get made! This can't match up with our original argument that was about intersecting groups!

In fact, the only two answer choices that are legitimately about whether groups overlap/intersect are (A) and (C).

(B) brings up the weird issue of 'what voters deserve'.
(D) brings up the above mentioned 'how decisions should be made'.
(E) keeps changing the terms between [profits], [decisions], and [companies], which are categories that can't legitimately overlap.

And while (C) does talk about overlapping groups, it's conclusion is a 'none' statement instead of a 'some' statement. It's pattern is:

PREMISE: Some [corporations] are NOT [concerned w/ env]
CONCLUSION: NO [corporations] are [concerned w/ env]

That's an interesting (flawed) quantity argument, but ours concluded with a 'some' statement - no dice!

Remember, you can't rely solely on the quantifier terms - you've got to look at the elements being compared/overlapping/intersecting as well!

Does this help clear things up a bit?

[canutos]

I did not ask the question but awesome write-up, Christine. It helped a lot. (I got the question right basically because of the quantifiers.)

[magic.imango]

I'm still a little confused about two things.

Firstly, how does the first sentence:
"Only a minority of people in PA do so out of SJ" =
"PA (most) --> ~SJ"

I diagrammed it as: "SJ (most) --> PA".

I took the "only a minority of people in PA" to be the necessary condition. Can you please explain where I am going wrong with this?

[mitrakhanom1]

I picked incorrect answer choice C instead of A. I diagrammed the argument as follows:

SJ-some-> PA
SJ-some-> -PA

I don't understand how you figured out "only a minority" is somewhere between some and most and how am I suppose to know or remember something like this?

I diagrammed the answer choices:
A) S-most-> -W
W---> -S

B) DV -most-> FP
V-most-> FP

C) C-some-> E
C ----> -E

D) P-some-> C
D-some-> -P

E) C---> P
C ---> -P

Can somebody please explain where I went wrong on my diagramming and reasoning? Thanks. I'm so confused on this problem.

[ohthatpatrick]

What is the meaning of the word "a minority"? What is the opposite of "a minority"?

The opposite of 'minority' is 'majority'. What does a majority mean? It means more than half. So a minority means less than half.

On LSAT, there are lots of words used that mean 'more than half'
most
majority
typically
generally
usually
tends to

There are a few terms that mean 'less than half'
a minority
few
rarely
seldom

As you may already know, the technical meaning of quantity words is somewhat different from how we use them in everyday conversation.

True or false:
Most US presidents have been men. Few US presidents have been female.

True! When we say "Most of my friends are Democrats" in real life, we assume the speaker is also saying that "Some of my friends are not Democrats".

But this isn't logically required. 100% is definitely more than half. So if all my friends are Dems, it is true to say that MOST of my friends are Dems. 0% is definitely less than half. So saying "Few US president have been female" is also true.

When you say "A few US presidents have been female", you are saying there have been 3 or 4. So that would be untrue.

But 'few' as a quantity modifier just means "less than half".

Whenever I see "few ppl do", I rephrase it as "most people don't".

Few A's are B = Most A's are ~B

So when I read the first sentence, I rephrase it as
"Most ppl who engage in political action are NOT doing it out of sense of social justice."

How does the 2nd sentence relate? It uses the opposite of both terms ... it talks about people who DO have a sense of social justice and who DON'T engage in political action.

So if the first sentence was
Most A's are ~B.

The second sentence is
Some B's are ~A.

(A) Most A's are ~B.
Thus, Some B are ~A. (looks good. If I'm thin on time for this section, I'll pick this and circle #22 so that I can come back if I have time leftover)

(B) ONLY A's are B? (stop ... it's over. We didn't have a conditional strength idea in the original)

(C) Some A's do B.
Thus, No A's do ~B (this went from Some to None ... not a match)

(D) Some A's are ~B.
Thus, Some C .. (stop, don't want some new idea)

(E) Very little A comes from B.
Thus ~B is usually A. (not a Most -> Some match ... and I'm really cheating in treating both mentions of profit and both mentions of good/bad management as logical opposites/equivalents)

==== In terms of where your diagramming went wrong:
"I diagrammed the answer choices:
A) S-most-> -W
W---> -S"

The conclusion isn't conditional. It says Some W are ~S.

"B) DV -most-> FP
V-most-> FP"

This first sentence is not a most statement. It doesn't say "Most voters are disregarded by foolish politicians" or anything like that.

The word "only" here is conditional. Fooling politicians are THE ONLY ppl who would ignore the wishes of most voters.

If someone is a foolish politican, to we know that they'll ignore most voters' wishes?

Nope.

But if someone is ignoring most voters' wishes, do we know if they're a foolish politician?

Yup.

That first sentence is
FP --> DW of most voters

"C) C-some-> E
C ----> -E"

Excellent!

"D) P-some-> C
D-some-> -P"

Isn't that first sentence saying some parents have NO interest in curricula?

Great job knowing that C and D were two different concepts!

"E) C---> P
C ---> -P"

The 1st sentence isn't really conditional "only". One us of the word only is restrictive, saying "everything else would NOT apply".

Another use of only is just as an adverb, like 'paltry, meager, pathetic quantity". If I say "Only a few people came to my bday party", I'm just whining about low attendance. If I say "Only bankers came to my bday party", I might have had a party of 1000 people, but there is logical certainty between 'attending party' and 'banker'.

So in (E), "only a small %" is really just saying "Just a small percentage". Just a minority (like the original argument).

The conclusion is also not conditional. If I give you a badly managed company, are you SURE it will turn a profit?

Nope. Usually. It's likely, not certain.

Hope this helps.

[robinzhang7]

Hi Moderators,

Thanks for such a thorough lesson on "some, most, etc." I still had something that was bugging me: particularly, the understanding of the word "few" vs. "some"

So does "few" along with "rarely" ALWAYS refer to less than half of the time? As in, "few apples are red."

That means that: some apples are red. But does it preclude the possibility that "most apples are red?" i know you can't 100% infer a "most" statement from a "some" statement but it could still be a possibility. OR, does the word "few" refer to ALWAYS less than half, never MORE.

If it's the latter definition, then it makes perfect sense why we can translate/infer that: "most apples are not red."

For my second question, the "a" in "a few" gives us definite number/proportion so that is why we can't say that "A few US presidents have been female." However, just saying "few US presidents...." is just saying that less than half of US presidents have been female (in this case, none).

Thanks so much!
Robin

[ohthatpatrick]

Yup, you're correct in both cases.

Few/rarely ALWAYS means less than half (0-49%).

"A few" means "a handful", so it refers to an actual number (like 3 or so), not a percentage.

If I bought five oranges and a few of them looked rotten, then most of the oranges look rotten.

[obobob]

How does the 2nd sentence relate? It uses the opposite of both terms ... it talks about people who DO have a sense of social justice and who DON'T engage in political action.

So if the first sentence was
Most A's are ~B.

The second sentence is
Some B's are ~A.

Just a quick Q. Is the following wrong b/c its illegal contrapositive?

So if the first sentence was
Most A's are ~B.

The second sentence is
Some B's are ~A.


Also, just to clarify, is it the case that we can never do contrapositives for some statements and most statements?

[ohthatpatrick]

Yeah, there's no such thing as a contrapositive unless you're talking about conditional logic.

"most" and "some" aren't conditional logic.

You can't infer "shadow quantities":

If we're told "most NFL players are men",
we can't infer "some NFL players are not men".

If we're told "not all humans live on Mars",
we can't infer "some humans do live on Mars"

You can infer an overlap between two qualities if you have one of these two situations:
1. "Most A's are B" + "Most A's are C"

2. "All A's are B" + "Some other fact about A or ~B"


Here's an analogous version of the flawed argument:
Only a minority of US citizens have been President.
Therefore, some Presidents have not been US citizens.

Why is this flawed?
Even though most citizens are not President,
it could still be true that all Presidents are citizens.


Similarly, even though most ppl engaged in political action aren't in it for social justice,
it could still be true that everyone with a sense of social justice is doing political action.