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PrepTest 78, Game 1, Question 3


The third question of PT78, game number 1, asks, V could be the project leader if which one of the following is true? Now, because technically this question doesn't give us new information and asks us what follows from that new information, it's not a local question. You could think of it technically as a global question. We're looking for which answer allows V to be the project leader.

But logically speaking, because on this problem the wrong answers are gonna be things that don't allow V to be project leader, or in other words, must be false, when V is project leader, you could actually think of this question as a local question, where the new piece of information is V is project leader. This question is basically asking if V is project leader, which one of these answers could be true?

That's another way of saying, if which one of the following is true, V could be the project leader? Which of these answers doesn't prevent V from being project leader? So that's how to solve this question. I'm gonna draw a local diagram on my scratch paper just for this question. And I'm going to make V in and I'm gonna make V the project leader.

I'm gonna go to the rules to see what else follows from that. And then I'm gonna pick an answer choice that could be true when V is project leader. So starting with the first rule, if V is project leader, that means neither Q nor R can be project leader since there's only one project leader. And since if Q or R in they have to be project leader, that means when V is project leader, Q is kicked out, and R is also kicked out.

Now, let's take a look at the second rule, if S is in, then T is in. I'm not sure we can do anything right now because if you put S in, you still have room for T, but I don't know that we have to put S in. So rule number 2 here, I'm not sure we can do anything. Let's move on to rule 3. This is something we can do something with because if V is in right now, that means W has to be out.

So I'm gonna put W in the out group. And at this point, notice that there's only one more space left in our out group. This is actually important because if you go back to rule number 2, you'll notice that the contrapositive is if T is out, then S is out as well. But when you only have one more out group slot left, if we try to make this out group slot T, we're also supposed to put S out as well.

But now, we have five in our out group, and we don't have enough people to be project members. So that's why one of the inferences you can make right now based on rule number 2, is that T must always be in. So we've applied all of our rules and now, let's go ahead and see what letters are remaining.

We've handled Q, R and W, we've handled the V and the T, so the letters that are remaining are the S and the X. That means one of these is gonna go in and the other one is gonna go out. Now, if you're a little bit confused and think that T being in means that S has to be in, that's because you're reading rule number 2 backwards. This is just a one way arrow, if S is in then T is in, but T is allowed to be in without having S in.

T being in doesn't go backwards to force S in. So that's why either S or X could be in right now. So which of the following could be true? Or in other words, which one of these answers, if true, is going to allow V to be project leader? A says, neither Q nor S is selected, and that is going to be our answer.

That is possible cuz you could put Q out and you could put S out and if you just made this X go in, then you could have this combination. You could have VB project leader T in, X in, and then Q and S could be out. But let's take a look at why the other ones are wrong. V says, neither or nor T is selected. Now, this doesn't work, remember, because if you try to put the T out, the T out means S is out as well, and then there's not enough room in the out group to accommodate all the letters that are out.

Now, if it makes it a little bit easier, I'll go ahead and rewind before we made that inference that T had to be in because I don't wanna suggest that you had to make that inference in order to get this question correct. Let's see why these other answers are wrong when you didn't make that inference. As I was saying with answer choice B, if you try to put R and T out, here, the R is already out.

While, if you try to put the T out, well, now, there's no room for the S in the out group. So that's why this is not going to work and it's not going to allow V to be project leader. The same thing is happening with answer choice C. If you try to put S and T out, well, there's not enough room for both S and T out right now.

So that's why C is not going to work. You'll notice the exact same dynamic is occurring with answer choices D and E. In answer choice D, if you try to put S out and X out, well, we don't have enough letters left to be in while allowing V to be project leader. And with answer choice E, if you try to put T and W out, here, the W is already out, but if we try to add the T out, well, based on the contrapositive of rule 2, you have to put the S out.

And again, we don't have enough letters to go in while allowing V to be project leader. So that's why none of these other answers allow V to be project leader.

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