Q25 - Most serious students are happy

[robowarren]

Hi,

I am working on conditional logic diagramming and am having an issue with this question. Here is what I have, would you mind helping me fix?

Most SS --> HS
Most SS --> GS

SO

Some HS --> GS AND Some GS --> HS

THEN we know that GS --> O

I dont see how we can jump from:
Some GS --> HS
GS --> O

Saying that answer choice B - Some HS --> O

What am I missing here?

Thanks!

[timmydoeslsat]

I think you would have an easier time if you did not use arrows with some and most statements.

Some A's are B's.

A SOME B

And this statement is clearly reversible. A most statement is not reversible to say most again. Rather it is reversible to state some.

For example:

Most A's are B's.

A MOST B

We can flip it to state what we know about B.

B SOME A


As for this stimulus. Once I saw what was going on, that this was a must be true question involving diagramming, I went to work.

I will go line by line with what I did.

Most serious students are happy students

Serious MOST Happy


Most serious students go to grad school

Serious MOST Grad School

At this point I will stop because I believe this is the very heart of your confusion.

We have these two statements diagrammed.

Serious MOST Happy
Serious MOST Grad School

We have two most statements with a common variable of serious. We are able to conclude that the happy and grad school part OVERLAP with each other. In other words, that there will be at least one situation where we have both.

To help see this, here is an example:

We will pretend we have 10 kids in a classroom.

Most of the kids in the classroom have on gloves.
Most of the kids in the classroom have on hats.

To state that most of the kids in this classroom are doing something, it must be the case that we are talking about 6 or more children. We must have more than half, as the definition of most is a majority. 50% is not a majority.

K K K K K K K K K K
G G G G G G

I am illustrating that 6 of the 10 kids have on gloves.
We now want to show 6 of the kids having on hats.

Do you see how there will be an overlap of G and H.

This is what happens when we have two most statements with a common variable.

A MOST B
A MOST C

We know that B SOME C. (Or vice versa of course)

Can you see what is wrong with this one?

A MOST B
D MOST A

We do not have the common variable of the most statements!

The first one is discussing most of A, while the second is discussing most of D. We cannot infer anything from this.

All we could do is this:

A MOST B
A SOME D

I flipped the most statement to show A on the same side, and we CAN NEVER combine some statements to conclude something nor can we ever combine some and most statements, even if the same variable is lined up.

However, with two most statements of the common variable, we know that there will be an overlap.

So back to our stimulus, we have this:


Serious MOST Happy
Serious MOST Grad School

To finish up the diagramming, we can draw a line from grad school to overworked (OW), as every grad school student is overworked.


Serious MOST Happy
Serious MOST Grad School ---> OW

And now is when we can show off our inference ability of knowing that the most statements overlap the Happy and Grad School.

Happy SOME Grad School ---> OW

And now we have proven that Happy SOME OW.

[jamiejames]

I diagrammed this out thusly:
______HS
SS -->
______GS --> OW

How are you able to combine happy student and graduate school?

[timmydoeslsat]

I diagrammed this out thusly:
______HS
SS -->
______GS --> OW

How are you able to combine happy student and graduate school?

I am concerned with your diagram because I am not understanding where your statements use the word most in them?

I would go with:

SS most HS
SS most GS

GS ---> OW

We know that 2 most statements using the same variable (the variables on the left side, if you will) will force the two right variables to have sharing occur. That is, we know from those 2 most statements given, that we will have HS some GS.

Knowing that will give us:

HS some GS ---> OW

And that will allow us to infer that HS some OW.

[ManhattanPrepLSAT1]

We are given three statements:

1. Most serious students are happy students.
2. Most serious students go to graduate school.
3. All students who go to graduate school are overworked.

Correct Answer
Answer choice (B) is the inference that can be drawn after combining all three statements. Combining the first and second statement allows us to infer that some happy students go to graduate school. Combining this with the third statement allows us to infer that some happy students are overworked.

Incorrect Answers
(A) is too strong. While we can infer that some overworked students are happy students, we cannot infer that most are.
(C) is too strong. While we can infer that some overworked students are serious students, we cannot infer that all of them are.
(D) is a common misrepresentation of the inference from the first and second premise. We can establish that students who go to graduate school are happy, but that does not mean that some of them are unhappy. The quantification of "some" has no upper limit.
(E) is too strong. While we can infer that most serious students are overworked, we cannot infer that all of them are.

[mitrakhanom1]

I solved it slightly differently.

SS-m-> HS
SS-m-> GS
HS<-s-> GS

SS-m-> GS
GS---> OW
GS-m-> OW

I then combined HS<-s-> GS and GS-m-> OW

HS-s->GS-m->OW
and then drew the inference
HS-s-> OW

IS that an okay inference? I feel its the same thing as the previous poster. If its not, please let me know so I don't make a similar inference mistake on future problems.

Thanks!

[maryadkins]

Unless "GS-m-> OW" looking to me that you mean MOST graduate students are overworked, it's good. We know ALL graduate students are overworked, not most.