Most of the students who took Spanish 101 at the university last semester attended every class session. However, each student who received a grade lower than B minus missed at least one class session.

Which one of the following statements about the students who took Spanish 101 at the university last semester can be properly inferred from the information above?

A

At least some of the students who received a grade of A minus or higher attended every class session.

B

Most, if not all, of the students who missed at least one class session received a grade lower than B minus.

C

Most of the students received a grade higher than B minus.

D

At least one student who received a grade of B minus or higher missed one or more class sessions.

E

More than half of the students received a grade of B minus or higher.

When I’m given very formal questions like this with “most,” I tend to use real numbers. Here, for example, I imagined a class of ten people.

If “most” of them attended every class, then at least six of them did. And maybe four did not. And if “each” student who got lower than a B- (which is a C+ or lower) missed at least one class, then those six students who attended every class must have gotten a B- or higher.

This does not mean, however, that the four slackers got a C+ or lower. Some of them did, but not necessarily all of them. That’d be a false contrapositive.

The word “each” means “if,” so this last sentence is saying “if C+ or lower, then not attend all classes.” The contrapositive is “if attend all classes, then not C+ or lower (in other words, then B- or higher).” We don’t know what happens if you don’t attend all the classes.

A. We don’t know anything about the A students. Maybe there are none. Wrong.

B. Some of them did, but not necessarily “most” of them. This is the false contrapositive issue.

C. This plays off of the wording in the passage “lower than B minus,” which means C+ or lower. So maybe all the students who came every time got a B-. Wrong.

D. Maybe all of the four slackers got C+ or lower. It doesn’t have to be true, but it could be true.

E. We know that “most” attended all the classes. And that if you attended all of them, you did not get a grade “lower than B minus,” so this must be true. Correct.

E