## PrepTest 73, Logical Reasoning 1, Question 21

### Transcript

Question 21. Question 21 asks you what is properly inferred from the information you've been given, which no surprise means we're doing an inference question. On an inference question, we're looking for something that we can prove with the information that we've been given. This question is fairly simple if you understand formal logic, and a little bit hard if you don't, although there is one sneaky answer choice.

So speaking of what we know, we know two facts. The first thing we know is that most of the students who took Spanish 101 at the university, attended every class session, they had perfect attendance. And the second thing we know is our formal logic rule. Each student who received a grade lower than B minus missed at least one class session.

So if we were to write that in formal logic it'd look like this, less than B minus means that you missed one or more classes. Anytime you write a formal logic rule into shorthand and you definitely should be writing these into shorthand, you want to write the contrapositive right underneath it. Remember to form the contrapositive, you reverse and negate the elements.

So, less than a B minus means missed one or more classes turns into didn't miss one or more classes means that you didn't get less than a B minus. Now, remember the question is asking us to make an inference about students who took Spanish 101 last semester. We know something about students who took Spanish 101 last semester. They attended every class.

And if they attended every class that means they didn't miss one or more classes. And we know if they didn't miss one or more classes, then they didn't get less than a B minus. So most of the students who took Spanish 101 didn't get less than a B minus. With an inference question that's heavily dependent on formal logic, we can often say exactly what the answer is going to look like.

So let's look at the answers to see what we can prove answer choice A, at least some of the students who received a grade of A minus or higher will notice our rule is not about people who got an A minus or higher. Our rule only tells us something about people who got less than a B minus. So I can't prove anything about people who got an A minus or higher. A is not my answer.

Answer choice B. Most if not all the students who missed at least one class session and say, well, I don't have a rule about people who missed at least one class session. I have a rule about people who didn't miss any class sessions. So the answer choice C then, most of the students received a grade higher than B minus.

Now, this is the clever trick. We know that those people didn't get less than a B minus. That doesn't mean that they got higher than a B minus, because a B minus is also not less than a B minus. So we know that they got a B minus or higher not they got higher than a B minus. And yeah, that is kind of an unfair trick, but that is what makes a choice C wrong.

It's so close to what we wanted, but not quite there. Now answer choice D, on the other hand, at least one student who received a grade of B minus or higher. Remember, our rule isn't about people who got a grade of B minus or higher, it's about people who got less than a b minus. So answer choice D is not my answer.

And if we look at E, well, it's got to be the answer because it's the only one left, but more than half the students received a grade of B minus or higher. Yeah because most of the students who took Spanish 101 attended every class session. If you attended every class session, then you didn't miss any classes. And if you didn't miss any classes, then you didn't get less than a B minus. It is exactly what we wanted and thus it is our answer.

Read full transcriptSo speaking of what we know, we know two facts. The first thing we know is that most of the students who took Spanish 101 at the university, attended every class session, they had perfect attendance. And the second thing we know is our formal logic rule. Each student who received a grade lower than B minus missed at least one class session.

So if we were to write that in formal logic it'd look like this, less than B minus means that you missed one or more classes. Anytime you write a formal logic rule into shorthand and you definitely should be writing these into shorthand, you want to write the contrapositive right underneath it. Remember to form the contrapositive, you reverse and negate the elements.

So, less than a B minus means missed one or more classes turns into didn't miss one or more classes means that you didn't get less than a B minus. Now, remember the question is asking us to make an inference about students who took Spanish 101 last semester. We know something about students who took Spanish 101 last semester. They attended every class.

And if they attended every class that means they didn't miss one or more classes. And we know if they didn't miss one or more classes, then they didn't get less than a B minus. So most of the students who took Spanish 101 didn't get less than a B minus. With an inference question that's heavily dependent on formal logic, we can often say exactly what the answer is going to look like.

So let's look at the answers to see what we can prove answer choice A, at least some of the students who received a grade of A minus or higher will notice our rule is not about people who got an A minus or higher. Our rule only tells us something about people who got less than a B minus. So I can't prove anything about people who got an A minus or higher. A is not my answer.

Answer choice B. Most if not all the students who missed at least one class session and say, well, I don't have a rule about people who missed at least one class session. I have a rule about people who didn't miss any class sessions. So the answer choice C then, most of the students received a grade higher than B minus.

Now, this is the clever trick. We know that those people didn't get less than a B minus. That doesn't mean that they got higher than a B minus, because a B minus is also not less than a B minus. So we know that they got a B minus or higher not they got higher than a B minus. And yeah, that is kind of an unfair trick, but that is what makes a choice C wrong.

It's so close to what we wanted, but not quite there. Now answer choice D, on the other hand, at least one student who received a grade of B minus or higher. Remember, our rule isn't about people who got a grade of B minus or higher, it's about people who got less than a b minus. So answer choice D is not my answer.

And if we look at E, well, it's got to be the answer because it's the only one left, but more than half the students received a grade of B minus or higher. Yeah because most of the students who took Spanish 101 attended every class session. If you attended every class session, then you didn't miss any classes. And if you didn't miss any classes, then you didn't get less than a B minus. It is exactly what we wanted and thus it is our answer.