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## #21 - Most of the students who took Spanish 101 at the

• PowerScore Staff
• Posts: 8224
• Joined: Feb 02, 2011
#33829
Complete Question Explanation

Must Be True—FL. The correct answer choice is (E)

This stimulus contains facts involving the use of Formal Logic. The first statement is that most of the university’s Spanish 101 students last semester attended every class session. We can diagram this statement as:
• StudentSpanish 101 attended every class session
Next, we are told that each student with a grade lower than a B- missed at least one session. We can diagram this just like we do with any conditional relationship, recognizing that missing at least one session is logically identical to “did not attend every class session”:
• Studentlower than B- attended every class session
and the contrapositive:
• attend every class session Studentlower than B-

We can connect the first, “most” relationship to the contrapositive of the second relationship across the common term “attend every class session”:
• StudentSpanish 101 attended every class session Studentlower than B-
Based on this connection, we can infer that most students who took Spanish 101 at the university last semester received a grade of B- or higher (i.e., not lower than B-).

The question stem identifies this as a Must Be True question. Our prephrase is the inference made above, that most students who took Spanish 101 at the university last semester received a B- grade or higher.

Answer choice (A): Since the stimulus did not tell us about students who received a grade of A- or higher, we cannot make this inference.

Answer choice (B): This answer choice contains a reversal of what we know from the stimulus. We know that every student who received a grade lower than a B minus missed at least one class session, but we cannot simply reverse that statement to say that most people who missed at least one class session received a grade lower than a B minus. At most, we can say that some people who missed at least one class session received a grade lower than a B minus.

Answer choice (C): This is a tricky answer choice, because it is very close to our actual prephrase. However, this answer choice is incorrect because it leaves out the possibility of those students receiving a B minus, stating that most of the students received a grade “higher than B minus.”

Answer choice (D): The only rule we have that associates grades with attendance is the second rule, which told us about students who received a grade lower than a B minus. We cannot infer anything about the attendance of those students who received a grade of B minus or higher.

Answer choice (E): This is the correct answer choice, and it restates our prephrase, that most of the Spanish 101 students received a grade of B minus or higher.
mokkyukkyu
• Posts: 97
• Joined: Aug 17, 2016
#29163
Hi,

Is A wrong because
It could be true that A students might not exist? Or they might skip a class too?
In real life, usually there are some % As stundets Bs students etc but from the stimuls we only know about B minus students so we don't really know about all other students...right?
Is Be wrong because it is illegal negation? (illegal revese)

And...
At first, I thought in real life, grades consist of test, attendance, and other factors too so I thought E may not be true too...but in this case we only care about class attendance right?
• PowerScore Staff
• Posts: 3813
• Joined: Apr 14, 2011
#29342
A is wrong here because we just cannot know, based on this info, about any A- students. B is wrong because we just don't have enough info about the students that missed some classes.

When I face the word "most", I start by putting numbers into the equation. I imagine that there are 100 students, and at least 51 of them attended every class and also got at least a B-. They had to have gotten at least that grade, because any lower grade would mean they had missed a class. This proves answer E to be correct - more than half the class got at least a B-.

If every student with less than a B- skipped a class, I imagine just one student fitting that description.

Now, I have 48 students about whom I know nothing at all. What grade did they get? Did they miss any classes? It's all up in the air.

It looks like you are trying to bring some causality into this equation, but the author did not do that so you shouldn't either. This isn't about why they got a certain grade, or what effect attending class had - it's just about numbers.
ShannonOh22
• Posts: 70
• Joined: Aug 15, 2019
#71067
Why wouldn't B work as an answer for this question? It says each student who got a B- or lower missed at least one class. Can we not then infer that most students who missed at least one class received a grade lower than B-? I feel like I'm missing how this answer is a Mistaken Reversal...please help
Paul Marsh
• PowerScore Staff
• Posts: 290
• Joined: Oct 15, 2019
#71537
Hi Shannon! Answer Choice (B) is incorrect because the stimulus leaves open the possibility that there could be many students who missed at least one class but still received a grade of a B minus or higher.

The last sentence of our stimulus tells us:
B minus (or lower) Missed a class (or more)

To say that if you missed a class, then you probably got a B minus, (as answer choice (B) does), would be a Mistaken Reversal! We can only read a conditional from left (sufficient condition) to right (necessary condition). So if a student got a B minus, then we know something (in this case, that he or she missed a class). But if a student missed a class, we don't know anything about that student's performance.

For example, say that 3 students in the class received a grade lower than a B minus. From our stimulus, we know that all 3 of those students must have missed at least one class. However, there could be 20 other students that missed a class but all got an A plus! The stimulus never rules out that possibility. So we don't know whether most students who missed a class got a B minus or lower, which means answer choice (B) is incorrect. Hope that helps!

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