Which one of the following must be true?

AndreaK January 4, 2020

Hi @Anacusk

So, this is a tricky little game. I’ll walk you through how I set it up so that hopefully, why C is wrong will be clarified for you.

Our question stem here doesn’t give us any additional premises. It only asks “What must be true?” That means we have to rely on our game rules to make deductions.

We have five rules here. I chose to use the friends as my game base. I’m sure there are other ways of approaching this game, but this is just one way I feel works well. I also opted for scenarios. I combined rule 5 and rule 4 to start the game boards with, because together, those rules are pretty constricting, making them a good bet for two scenarios.

So, according to rule 5, at least one friend graduated in 93. However, according to rule 4, Ramon and Sue graduated in the same year. So, either Ramon and Sue both graduated in 93’, or just Tom did. They can’t all graduate in 93’ together, because rule 1 says Ramon graduated in the year before Taylor. I would use this deduction to make two scenarios, one where R and S graduate in 93, and one where T does.


1)
G C
R: 93
S: 93
T:

2)
G C
R:
S:
T: 93

Now, floating back to rule 1, we know that R graduated in some year before T. This gives us some insight into both R and S’s graduations in scenario 2, and would help us place a few must be trues down in this scenario. I would start here. Because we know that R and S graduated in the same year, this means that in scenario 2, R and S either both graduated in 91 or 92. But wait, there’s another rule that we can consider that involves the graduation of one of those players. Rule 3, Sue bought her first car in some year *before* the year she graduated.

Because we know based on the above Sue could only graduate (in scenario 2) in 91 or 92, but we also know she bought her first car in some year *before* she graduated....then, because 91 is the earliest year in our game, we know that Sue must have graduated in 92. It has to be that way in order for there to be room to accommodate a year for her to buy her car before graduating. Then by that, we also know she bought her car in 91.

2)
G C
R: 92 l _
S: 92 l 91
T: 93 l _

We can get another deduction for scenario two in rule 2 as well. Since we know T graduated in some year (which we know is 93 in scenario 2) before he bought his first car, that means he must have bought his first car in 94 or 95.

2)
G C
R: 92 l _
S: 92 l 91
T: 93 l 94/95

We have no rules that tell us about what year Ramon bought his first car, so that’s all we can fill out from here. With only the information we have from the rules, that space could be any of our years.

Let’s take a look back at scenario 1 now.

1)
G C
R: 93
S: 93
T:

According to this, we know because of rule 1 that T then graduated in 94 or 95. However, similar to what happened above with S, we can make another close deduction about the year T graduated using rule 2. Because we know he graduated in some year *before* he bought his first car, and because 95 is the latest year in our game, we then know he must have graduated in 94, and bought his car in 95.

1)
G C
R: 93 l
S: 93 l
T: 94 l 95

We can make another further deduction about the year Sue bought her first car using rule 3. Because we know S bought her first car in some year *before* she graduated, and in scenario one, she graduated in 93, that means S bought her first car in 91 or 92.

1)
G C
R: 93 l _
S: 93 l 91/92
T: 94 l 95

Again, we run into the same problem with Ramon in that we don’t have a rule that tells us anything about when he bought his first car. So, with the information we have in the rules, it could be any year in this scenario as well.

Using just the rules provided in the game, we can make the below two scenarios and deductions about what must, can, and can’t happen in the game. Let’s see if one of these is the answer to our must be true question.

1)
G C
R: 93 l _
S: 93 l 91/92
T: 94 l 95

2)
G C
R: 92 l _
S: 92 l 91
T: 93 l 94/95


A) Correct. Looking at our completed game boards above where we have all the possible graduation years filled in, none of the friends can graduate in 91. That must be true.
B) Nope, in scenario 2, R and S both have to graduate in 92.
C) The reason C is wrong is because there are no restrictions on when R could have bought his first car. So, with just these rules, it could be in 93.
D) In scenario 1, T has to graduate in 94.
E) In scenario 1 T must have bought his first car in 95, and in scenario 2, T could have.

Hope this helps! This is a tricky game, and definitely a good one to practice doing more than once.