## PrepTest 78, Game 2, Question 10

### Transcript

This is the fifth question from PT 78, Game 2, and it's asking if Y is not assigned to the project, which of the following could be true? So here we have a local question. And in our local diagram that we draw for this problem, we'll go ahead and put that new information, Y is not assigned to the project. So there are two ways to go at this point, we could just go to the answers, and essentially just try to visualize each answer in our minds.

Maybe we'll sketch out a couple of these answers to see whether or not they could be true. Eventually we'll get to the right answer, that's one option. The other option is to think a little bit more about the rules we have to see if putting Y out will now result in another inference.. And I'll show you both ways of solving this question.

Let me start with the inference making way of solving the question, because that is generally gonna be the faster method. If Y is out, notice that there's only one more outgroup slot. And that's gonna put a lot of pressure on some of our rules here. Especially rules that tell you one letter brings another letter with it. For example, take a look at rule 3, if t is in, then that means R has to be in.

The contrapositive means if R is out, then T also has to be out. But what do you notice about this situation when you only have one out group slot? If R is out, T also has to be out. If you put an R over here, you're supposed to put a T in the out group, but there's no more room for the T in the out group.

That means that putting R out is actually not possible in this situation. So one inference you can make actually is that R always has to be in. And if R is in, according to rule number 4, you have to put an O immediately before that R. The only place in OR block can go is in 1 and 2 like this. And at this point, the letters that we have left are M, which can go and 4.

And so if M can't go and 4, that means M is going to have to go in the outgroup. And now we're left with just either T or L to go in the fourth spot. So if Yoshio is not assigned to the project, what that means is R has to be in, which means O is in 1, and then that means M is out, which then leads to T or L being in 4. That's why the correct answer here is answer choice E.

L is assigned to 1924. That's something that could be true. None of these other answers could be true. But let's say we didn't make that inference. How could we still get to the correct answer? Well, we'd start by putting y out based on the condition of the problem, and then we take a look at the answer choices.

Could this be true, L is not assigned? Well, if you put L out, that means you're going to have to put T in slot number 3, T brings R with it, right? So that means R is gonna have to go to two because you have to have room for the O immediately before the R. And now the only letter left is your M to go in 4, but M can't go in 4.

So that's why A doesn't work, it leads to a contradiction. Answer choice B says R is not assigned, and so let's see, could that work? If you put R out, that means T also has to go out because of the contrapositive of rule 3, but this is where you realize you couldn't put R out. So that's why B doesn't work. Now at this point, if you were just going down the answer choices and trying them out, hopefully you'd realize that R has to be in, and then you'd be led to all those inferences that we discussed earlier.

But assuming that you weren't able to get that far, let me go ahead and just put up my markings again. But assuming you weren't able to get that far, let's go down to answer choice C. C says T is not assigned. Could that be true when Y is out? Well, if you put T out, that means L is going to have to go in 3.

And now the letters that you have left are the O, the R, and the M. And you're going to be left with the similar situation as answer choice A, the R has to go in 2, cuz the O has to go immediately before it. The M is gonna have to go to 4, but the M can't go in 4. So that's why C doesn't work. And finally answer choice D, O is assigned to 1922.

Well, let's see if Y is out, could you put an O in 1922? If O is in 1922, that means the R has to go out because there's no room to put the R immediately after the O. If you try to put R out however, that means you have to put T out as well and there's not enough room. So that's why answer choice D doesn't work.

Read full transcriptMaybe we'll sketch out a couple of these answers to see whether or not they could be true. Eventually we'll get to the right answer, that's one option. The other option is to think a little bit more about the rules we have to see if putting Y out will now result in another inference.. And I'll show you both ways of solving this question.

Let me start with the inference making way of solving the question, because that is generally gonna be the faster method. If Y is out, notice that there's only one more outgroup slot. And that's gonna put a lot of pressure on some of our rules here. Especially rules that tell you one letter brings another letter with it. For example, take a look at rule 3, if t is in, then that means R has to be in.

The contrapositive means if R is out, then T also has to be out. But what do you notice about this situation when you only have one out group slot? If R is out, T also has to be out. If you put an R over here, you're supposed to put a T in the out group, but there's no more room for the T in the out group.

That means that putting R out is actually not possible in this situation. So one inference you can make actually is that R always has to be in. And if R is in, according to rule number 4, you have to put an O immediately before that R. The only place in OR block can go is in 1 and 2 like this. And at this point, the letters that we have left are M, which can go and 4.

And so if M can't go and 4, that means M is going to have to go in the outgroup. And now we're left with just either T or L to go in the fourth spot. So if Yoshio is not assigned to the project, what that means is R has to be in, which means O is in 1, and then that means M is out, which then leads to T or L being in 4. That's why the correct answer here is answer choice E.

L is assigned to 1924. That's something that could be true. None of these other answers could be true. But let's say we didn't make that inference. How could we still get to the correct answer? Well, we'd start by putting y out based on the condition of the problem, and then we take a look at the answer choices.

Could this be true, L is not assigned? Well, if you put L out, that means you're going to have to put T in slot number 3, T brings R with it, right? So that means R is gonna have to go to two because you have to have room for the O immediately before the R. And now the only letter left is your M to go in 4, but M can't go in 4.

So that's why A doesn't work, it leads to a contradiction. Answer choice B says R is not assigned, and so let's see, could that work? If you put R out, that means T also has to go out because of the contrapositive of rule 3, but this is where you realize you couldn't put R out. So that's why B doesn't work. Now at this point, if you were just going down the answer choices and trying them out, hopefully you'd realize that R has to be in, and then you'd be led to all those inferences that we discussed earlier.

But assuming that you weren't able to get that far, let me go ahead and just put up my markings again. But assuming you weren't able to get that far, let's go down to answer choice C. C says T is not assigned. Could that be true when Y is out? Well, if you put T out, that means L is going to have to go in 3.

And now the letters that you have left are the O, the R, and the M. And you're going to be left with the similar situation as answer choice A, the R has to go in 2, cuz the O has to go immediately before it. The M is gonna have to go to 4, but the M can't go in 4. So that's why C doesn't work. And finally answer choice D, O is assigned to 1922.

Well, let's see if Y is out, could you put an O in 1922? If O is in 1922, that means the R has to go out because there's no room to put the R immediately after the O. If you try to put R out however, that means you have to put T out as well and there's not enough room. So that's why answer choice D doesn't work.