Most serious students are happy students, and most serious students go to graduate school. Furthermore, all students ...

Naz March 17, 2015

Let's diagram:

"Most serious students are happy students."

Q1: SS-most-HS
HS-some-SS

"most serious students go to graduate school."

Q2: SS-most-GS
GS-some-SS

"Furthermore, all students who go to graduate school are overworked."

P1: GS ==> OW
not OW ==> not GS

So, we know that we cannot combine a "most" statement with a "some" statement. And we can only combine a Sufficient & Necessary statement with a Quantifier statement if the sufficient condition of the Sufficient & Necessary statement and the right-hand-side variable of the Quantifier statement are the same.

Therefore, we can combine "Q2" and "P1," like so: SS-most-GS ==> OW to conclude: SS-most-OW, i.e. most serious students are overworked. However, as you can see, none of the answer choices give us: "SS-most-OW."

Well, what else can we combine? We know that we can combine two "most" statements if their left-hand-side variables are the same into a "some" statement with their respective right-hand-side variables. So, we can combine "Q1: SS-most-HS" with the new inference: "SS-most-OW," to conclude: "HS-some-OW," i.e. some happy students are overworked, which is answer choice (B): "Some happy students are overworked."

Hope that clears things up! Please let us know if you have any other questions.

yababio May 21, 2015

Theres no video

Naz May 21, 2015

There is no need for a video explanation to this question since it has no major visual components. Please refer to the written explanation above for a breakdown of the problem.

Hope that helps! Please let us know if you have any other questions.

brenthorn July 24, 2017

Could we have combined Q1 and Q2 straight off the bat, since they are both most and both have SS on the left to state that HS -some-GS, therefore HS -some -GS ==>OW; HS-some-OW?

Mehran July 28, 2017

@brenthorn absolutely!

P: SS-most-HS
P: SS-most-GS

C; HS-some-GS
GS-some-HS

Unfortunately, this was not an answer choice but it is definitely a valid deduction.

Notice, however, that this deduction is then combined with the S & N statement to arrive at the correct answer choice here:

HS-some-GS ==> OW

HS-some-OW

This is exactly what (B) says, i.e. "Some happy students are overworked."

Hope that helps! Keep up the great work!

:)) April 22, 2020

How does SS-most-HS and SS-most-OW combined make "some"? Why can't it still be "SS-most-HS" SS-most-OW" = "HS-most-OW"?