Logical Reasoning

PT141 · S2 · Q21 Most of the students who took Spanish

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Most of the students who took Spanish 101 at the university last semester attended every class session.

Statements

Most Spanish 101 students attended every class.

Each student with a grade lower than B- missed at least one class.

Evaluate

We have a conditional ("each/all/any/every" are all sufficient LEFT side triggers) and a Most statement. Is there any overlapping idea?

Yes, they're both talking about whether or not someone attended every class. Our priority is always the conditional, so let's get that diagrammed with its contrapositive so that we can see if the Most fact triggers either version.

Grade lower than B- → missed at least 1 class

~Miss at least 1 class → ~Grade lower than B-

Let's flip these negatives to positives: didn't miss at least 1 class = attended all didn't get lower than B- = B- or higher

So, it's really Attended all → B- or higher

Most Span 101 students attend all, so Most Span 101 got B- or higher.

Goal

Since they are likely rewarding us for synthesizing the two claims, we should expect something like .

21.

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?

  1. At least some of the

    Illegal Reversal

    We know that Attended every class → B- or higher But this answer is trying to go backwards, acting like if you got an A- or higher then you must have attended every class. It's possible that all the people who attended every class just got B's.

    16% picked this

  2. Most, if not all, of

    Illegal Reversal

    We know that received lower than B- → missed at least 1 This answer is acting like we know that if you missed at least 1, then you got lower than a B minus. We can't make any generalization about Most students who missed at least 1.

    17% picked this

  3. Most of the students received

    Too Strong: higher than B-

    What we were able to infer is that they got a grade of B minus or higher. This is saying they were all above B minus. Since Most attended every class, Most didn't get lower than B minus. But it's possible they all got a B minus.

    28% picked this

  4. At least one student who

    Out of Scope: B- or higher

    We were only told that students who got lower than B minus missed at least one class. We don't know if some students who got B-minus or higher missed at least one class.

    10% picked this

  5. Correct

    More than half of the

    Why this is right

    This is what we prephrased -- most of the students got a B minus or higher. Most = more than half

    Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.

    29% picked this

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