## PrepTest 79, Game 4, Question 23

### Transcript

This is the last question of PT 79, Game number 4. And it's a local question asking if P is the only computer that transmits the virus to two other computers, which must be true? So if P is the only one that gets to go to two other computers, that means P has to transmit to R and S. You couldn't put anything else in the spot where P is going right now, because then some other computer would be transmitting to two other computers.

So the first deduction is that P must go to both R and S. Now at this point we have some options with rule number 4 and rule number 5. I wanna start with rule number 5, because that mentions the P, which is mentioned in the condition of the problem. We know that before this P, you're either gonna have T go to P or U go to P. So let me just go ahead and sketch out both of those options.

These are the two possibilities right now for rule number 5. Now let's turn to rule number 4, either R goes to Q or T goes to Q. Now in the first world here, where T goes to P, it seems like you could have R go to Q like this, in which case the S would have to transmit to the final computer, which is U. Or the other option here is T goes to Q, in which case T would transmit to Q like this.

And since S still has to transmit to someone, that means S would have to transmit to U. So I'll just sketch out both of those possibilities, since that's what I'd be doing on my scratch paper. One option is R goes to Q here, with S to U. The other option is over here, remember, where T goes to Q.

And S still has to transmit to someone, so S goes to U. These two possibilities are how rule 4 plays out when you're in the world where T is before P. Now what if you're in the world where U is before P? Again, you have an option about R going to Q or T going to Q. If R goes to Q, then it would look like this, and S would have to transmit to the final letter left, which is T.

And I'll just sketch out the final possibility here. If T goes to Q in this world over here, then that means T has to go over here, followed by the Q. That's because the S must transmit to somebody, and the only person left to transmit to would be the T. So these are the four possible chains for this question.

We're looking for what must be true. A says S transmits to T, clearly that doesn't have to be true, cuz S could go to U. B says T transmits to P, that doesn't have to be true, because it could be U going to P. C says Q does not transmit to anyone else.

And this is going to be our answer, because in every single world here, the Q is at the end. The Q is not transmitting to anyone else, that's why C must be true. Let's eliminate the other answers, D says R doesn't transmit to anyone else. Now that is true over here and over here, but you can see that the R could pass to Q in these worlds.

That's why D does not have to be true, R could transmit to someone else. And finally, E says U does not transmit to anyone else. But that doesn't have to be true, because U could transmit to P, so that's why E is wrong.

Read full transcriptSo the first deduction is that P must go to both R and S. Now at this point we have some options with rule number 4 and rule number 5. I wanna start with rule number 5, because that mentions the P, which is mentioned in the condition of the problem. We know that before this P, you're either gonna have T go to P or U go to P. So let me just go ahead and sketch out both of those options.

These are the two possibilities right now for rule number 5. Now let's turn to rule number 4, either R goes to Q or T goes to Q. Now in the first world here, where T goes to P, it seems like you could have R go to Q like this, in which case the S would have to transmit to the final computer, which is U. Or the other option here is T goes to Q, in which case T would transmit to Q like this.

And since S still has to transmit to someone, that means S would have to transmit to U. So I'll just sketch out both of those possibilities, since that's what I'd be doing on my scratch paper. One option is R goes to Q here, with S to U. The other option is over here, remember, where T goes to Q.

And S still has to transmit to someone, so S goes to U. These two possibilities are how rule 4 plays out when you're in the world where T is before P. Now what if you're in the world where U is before P? Again, you have an option about R going to Q or T going to Q. If R goes to Q, then it would look like this, and S would have to transmit to the final letter left, which is T.

And I'll just sketch out the final possibility here. If T goes to Q in this world over here, then that means T has to go over here, followed by the Q. That's because the S must transmit to somebody, and the only person left to transmit to would be the T. So these are the four possible chains for this question.

We're looking for what must be true. A says S transmits to T, clearly that doesn't have to be true, cuz S could go to U. B says T transmits to P, that doesn't have to be true, because it could be U going to P. C says Q does not transmit to anyone else.

And this is going to be our answer, because in every single world here, the Q is at the end. The Q is not transmitting to anyone else, that's why C must be true. Let's eliminate the other answers, D says R doesn't transmit to anyone else. Now that is true over here and over here, but you can see that the R could pass to Q in these worlds.

That's why D does not have to be true, R could transmit to someone else. And finally, E says U does not transmit to anyone else. But that doesn't have to be true, because U could transmit to P, so that's why E is wrong.