Quantifiers Questions - - Question 15

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

Papri-Basu August 25, 2019

A vs. B

I understand why B is the answer, but why couldn't A also be the answer? Since OW-m-HS can be transformed into HS-s-OW, isn't that technically the same answer as B?

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Victoria August 25, 2019

Hi @Papri-Basu,

Let's start by determining what we can conclude from the passage.

"Most serious students are happy students."

SS-m-HS

"Most serious students go to graduate school."

SS-m-GS

"All students who go to graduate school are overworked."

GS - > OW
Not OW - > Not GS

We can use the transitive property to conclude:

SS-m-OW

From this, we can also conclude...

P: SS-m-HS
P: SS-m-OW
- - - - - - -
C: HS-s-OW

This is directly restated by answer choice B making it the correct answer.

Notice that we cannot conclude that 'most overworked students are happy students.'

We can conclude that most serious students are happy students. We can also conclude that most serious students are overworked because all students who go to graduate school are overworked and most serious students go to graduate school.

However, we cannot take the above information to conclude that most overworked students are happy students. Although most serious students who are overworked at graduate school are happy students, we cannot conclude that most students who are overworked in general are happy students.

We can simply conclude that some happy students are overworked and, as 'some' statements are reversible, some overworked students are happy students.

Hope this helps! Please let us know if you have any further questions.