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Prep Test 5 - Logic Game 1 Setup

Video Transcript:

0:06
This question reads: "Jon receives one grade for each of the following six courses: Economics,
0:13
Geology, History, Italian, Physics, and Russian.
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From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing
0:27
grade.
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Two letter grades are consecutive if, and only if, they are adjacent in the alphabet."
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We've got a lot of information here.
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We have our first set of variables, which are Jon's classes.
0:43
We've got Economics, Geology, History, Italian, Physics, and Russian, and we have 5 possible
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grades.
1:00
We have A, B, C, D, and E. Remember, so far, we haven't been told that Jon has to receive
1:14
one of every grade.
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These are just the possible grades he can receive.
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Let's go into our rules.
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Rule #1.
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Jon's grades in Geology and Physics are consecutive.
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Remember from the prompt, it says "two letter grades are consecutive if, and only if, they
1:34
are adjacent in the alphabet," so they have to be next to each other.
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Jon's grades in Geology and Physics are consecutive.
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So we've got Geology and Physics.
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Instead of putting a box around them, because we don't know if Geology is going to come
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before Physics or Physics is going to come before Geology as in, if Geology is a better
2:07
grade than Physics, or Physics is a better grade than Geology, we can kind of put a little
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handlebar here with arrows, showing that 1 is going to be flipped, or 1 could be flipped,
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but they're next to each other.
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Now let's go to Rule #2.
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His grades in Italian and Russian are consecutive.
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Same idea.
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We have Italian and Russian.
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Okay, now Rule #3.
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He receives a higher grade in Economics than in History.
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Here we have our nice little classic sequencing rule.
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He receives a higher grade in Economics than in History.
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Rule #4, he receives a higher grade in Geology than in Physics.
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We see he receives a higher grade in Geology than in Physics, and if you note Rule #1,
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Geology and Physics are next to each other, which means that we can deduce from Rule #1
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and Rule #4 that Geology is going to have a better grade, and they're going to be right
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next to each other.
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Now we can box them.
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You have to see the difference between boxing Geology and Physics and not boxing Italian
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and Russian, because we don't know if Italian is a better grade than Russian or Russian
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is a better grade than Italian.
3:45
This question reads: "Jon receives one grade for each of the following six courses: Economics,
3:46
Geology, History, Italian, Physics, and Russian. From highest to lowest, the possible grades
3:47
are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if,
3:48
and only if, they are adjacent in the alphabet."
3:49
We've got a lot of information here. We have our first set of variables, which are Jon's
3:50
classes. We've got Economics, Geology, History, Italian, Physics, and Russian, and we have
3:51
5 possible grades. We have A, B, C, D, and E. Remember, so far, we haven't been told
3:52
that Jon has to receive one of every grade. These are just the possible grades he can
3:53
receive.
3:54
Let's go into our rules. Rule #1. Jon's grades in Geology and Physics are consecutive. Remember
3:55
from the prompt, it says "two letter grades are consecutive if, and only if, they are
3:56
adjacent in the alphabet," so they have to be next to each other. Jon's grades in Geology
3:57
and Physics are consecutive.
3:58
So we've got Geology and Physics. Instead of putting a box around them, because we don't
3:59
know if Geology is going to come before Physics or Physics is going to come before Geology
4:00
as in, if Geology is a better grade than Physics, or Physics is a better grade than Geology,
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we can kind of put a little handlebar here with arrows, showing that 1 is going to be
4:02
flipped, or 1 could be flipped, but they're next to each other.
4:03
Now let's go to Rule #2. His grades in Italian and Russian are consecutive. Same idea. We
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have Italian and Russian.
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Okay, now Rule #3. He receives a higher grade in Economics than in History. Here we have
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our nice little classic sequencing rule. He receives a higher grade in Economics than
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in History.
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Rule #4, he receives a higher grade in Geology than in Physics. We see he receives a higher
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grade in Geology than in Physics, and if you note Rule #1, Geology and Physics are next
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to each other, which means that we can deduce from Rule #1 and Rule #4 that Geology is going
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to have a better grade, and they're going to be right next to each other. Now we can
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box them.
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You have to see the difference between boxing Geology and Physics and not boxing Italian
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and Russian, because we don't know if Italian is a better grade than Russian or Russian
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is a better grade than Italian. All we know is that they are different grades because
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they're consecutive, and they're going to be next to each other in the grade, so it's
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either going to be an A or a B, a B or A C, a C or a D, or a D and an E.
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Now let's make some deductions. We know from Rule #4 that Physics can't get an A because
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then what would Jon get in Geology? Because Geology's going to be a better grade than
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Physics.
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Then likewise, Geology, Jon can't fail because he has a better grade in Geology than in Physics,
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and they're next to each other.
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Likewise with Rule #3. Jon cannot get an A in History because Economics is a better grade
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than History, and Jon cannot fail Economics because he gets a better grade in Economics
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than he does in History.
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We don't know where I and R are, Italian and Russian, so we can't make any deductions that
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way. We just know that Italian and Russian are different grades and they're going to
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be consecutive grades.
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Alright, so now let's go ahead and hit the questions.