## PrepTest 78, Game 2, Question 9

### Transcript

This is the fourth question from PT 78. Game number 2, and it's a global question asking how many of the students are there, who could be the one assigned in 1921? So to solve this question, what we have to do is we have to figure out how many of these six students could ever go in slot number 1, now if you've done prior work on other questions you may already know a couple of students who could go in the first slot.

And so you could already add those as part of your accounts. But let's pretend like we don't have any prior work to rely on. In that case, we just have to try each of these letters to see can they go in 1921, now if we made the inference that R can't go number 1, because O has to be immediately before it, then that cuts out R right now so we don't have to try R, but we may have to try the other letters.

Let's start with L. If we put L in number 1, then that means T is going to be third. And if T is in, according to rule number 3, that means R has to be in. But now we run into a contradiction because if you put R in, you're supposed to put an O immediately before that R, but there's no room to put this OR block right now.

L is in 1, T is in 3, RO, OR is not gonna fit in 2 and 4. So that's why L actually doesn't work as someone who can go in 1921. What about M, could M go in 1921? You could put an M over here. Maybe we could put a Y over here, and then we could put an L in number 3, and then we could put an O in 1924.

And this will work because you could put both R and T out. So M is gonna be part of our count. What about O, well, we could put an O in 1. And then you could put an R in 2 because now R gets to go in 2 when there's an O immediately before it. And then you could make this one a T or an L.

And you can make this one a Y. This is something that will work because you could put M out and then you could put either T or L out, so all works in 1921 that's added to our account. What about T? Can I put T in 1? Well, if T is in 1, then that means that L is going to have to go in 3.

In addition, if T is in that means R has to be in. And you know what here we run into that same contradiction we ran into with the L Because if R is in you have to see O immediately before it's but there's no room to fit this OR block when T is in 1 and L is in 3. If R goes in 2 there's no room for O before it, if R goes in 4 there's no room for O before it.

So that's why T is not part of our counts. Finally, what about Y? Could I put a Y in 1? What if I just put an M in 2 and then I could put an L in 3, I think L or T would work. And I'll just put an O over here.

And this is totally fine because you could put an R and a T out, so why works in 1921? That means it's part of our count. That means 1, 2, 3 different students could go in 1921. That's answer choice D. If you were confused on this question you probably picked answer choice B or C.

And that's probably because you didn't realize that L couldn't go in number 1. And the T couldn't go in number 1. The reason they can't go in number 1, is because then R would be forced in, and then you have no room for the OR block.

Read full transcriptAnd so you could already add those as part of your accounts. But let's pretend like we don't have any prior work to rely on. In that case, we just have to try each of these letters to see can they go in 1921, now if we made the inference that R can't go number 1, because O has to be immediately before it, then that cuts out R right now so we don't have to try R, but we may have to try the other letters.

Let's start with L. If we put L in number 1, then that means T is going to be third. And if T is in, according to rule number 3, that means R has to be in. But now we run into a contradiction because if you put R in, you're supposed to put an O immediately before that R, but there's no room to put this OR block right now.

L is in 1, T is in 3, RO, OR is not gonna fit in 2 and 4. So that's why L actually doesn't work as someone who can go in 1921. What about M, could M go in 1921? You could put an M over here. Maybe we could put a Y over here, and then we could put an L in number 3, and then we could put an O in 1924.

And this will work because you could put both R and T out. So M is gonna be part of our count. What about O, well, we could put an O in 1. And then you could put an R in 2 because now R gets to go in 2 when there's an O immediately before it. And then you could make this one a T or an L.

And you can make this one a Y. This is something that will work because you could put M out and then you could put either T or L out, so all works in 1921 that's added to our account. What about T? Can I put T in 1? Well, if T is in 1, then that means that L is going to have to go in 3.

In addition, if T is in that means R has to be in. And you know what here we run into that same contradiction we ran into with the L Because if R is in you have to see O immediately before it's but there's no room to fit this OR block when T is in 1 and L is in 3. If R goes in 2 there's no room for O before it, if R goes in 4 there's no room for O before it.

So that's why T is not part of our counts. Finally, what about Y? Could I put a Y in 1? What if I just put an M in 2 and then I could put an L in 3, I think L or T would work. And I'll just put an O over here.

And this is totally fine because you could put an R and a T out, so why works in 1921? That means it's part of our count. That means 1, 2, 3 different students could go in 1921. That's answer choice D. If you were confused on this question you probably picked answer choice B or C.

And that's probably because you didn't realize that L couldn't go in number 1. And the T couldn't go in number 1. The reason they can't go in number 1, is because then R would be forced in, and then you have no room for the OR block.