Mixed setup | Video lesson

- [Instructor] We're now going to work through a mixed setup together, so make sure that you've already completed the ordering videos and the grouping videos before you tackle this one, because we're going to be combining the two here. Alright, we'll start by examining the introductory passage to understand what we're being asked to do. The passage tells us each of six tasks, harvesting, milling, plowing, spinning, threshing, and weaving will be demonstrated exactly once at a farm exhibition. No two tasks will be demonstrated concurrently. Three volunteers, Frank, Gladys, and Leslie, will each demonstrate exactly two of the tasks. The tasks must be demonstrated in accordance with the following conditions. There is a lot going on here, so it's a good idea to stay very focused and organized. The first thing we can note is that we have two types of elements at play. We have people, and we have tasks. So let's make a list of them here, so that we can keep track of them. I like to make one set of elements capital letters, and the other set lower case letters, so that you're not just swimming in the same kind of letters all over the place. We've got Frank, Gladys, and Leslie. And not only that, but we have each of them demonstrating exactly two of the tasks. So we'll have two Franks and two Gladyses, and two Leslies. Then we have one each of these tasks: harvesting, milling, plowing, spinning, threshing, weaving. Now what are we doing with these people and tasks? We're trying to determine which two tasks each person demonstrates, and we're also trying to figure out which order they demonstrate them in. If the ordering part wasn't obvious to you, we do have one clue when they tell us that no two tasks will be demonstrated concurrently. And we have some more clues if we peek at the rules. So in this setup, there's a grouping portion, because we're grouping people with their tasks, and there's also an ordering portion, since we're essentially sequencing the demonstrations. That means that this is a mixed setup. We have more than one action happening in our setup. So how do we make our diagram when there are two actions like this? For a mixed setup that involves grouping and ordering the way we see here, it can be really helpful to treat it like it's a double ordering setup. This is what I mean. We put our people in order, and we put our tasks in order. Now it's true that if we got a rule that said something like Gladys demonstrates harvesting, we wouldn't have anywhere to put that in our diagram, and that's okay. We would note it off to the side and incorporate it when we can later on. It's just really important to show the ordering part, because ordering involves the arrangement of elements. At this point we have a basic diagram, and we can move on to the rules. Our first rule is that Frank demonstrates exactly one task before Gladys demonstrates any of the tasks. They're kicking us off with a difficult role right off the bat. This is an ordering rule. We have total two Frank tasks and two Gladys tasks, so let's think about how to do this. If we only had one Frank and one Gladys task, the rule would be F sometime before G. Since there are two of each, though, and this rule is telling us that Frank demonstrates exactly once before Gladys demonstrates her first task, then where does the second Frank task have to go? It has to go after the first Gladys task. Finally, where does that mean the second Gladys task is? Sometime after the first Gladys task, that's all we know. Well let's not jump to the next rule quite yet. We can actually start making deductions right away. Who can't be first, based on this rule? Gladys can't be first, because Gladys has to be sometime after Frank. The first Gladys has to be sometime after Frank. So that means that Frank or Leslie must be first. Great. Our second rule is another ordering rule, and it tells us that Frank performs neither the first nor the last demonstration. Whenever we can mark a rule directly in our diagram, it's a great idea to do so instead of noting it off to the side. Normally, we would write a not Frank above spots one and six. But the beautiful part of this rule and this setup is that we only have three people to work with. So eliminating even one person allows us to make some positive deductions. If Frank can't be first, that leaves only Leslie to be first. And if Frank can't be last, then we know that either Gladys or Leslie is last. This is great, we have a positive deduction that Leslie must demonstrate first. And what does that mean now for the person who demonstrates second? It can't be Gladys. Remember, Gladys is after Frank. So now we know that the second demonstration is either Frank or Leslie. The third rule is our first grouping rule. It tells us that Gladys demonstrates neither harvesting nor milling. Let's turn that negative into a positive. It means that harvesting and milling is done by either Frank or Leslie. Since this is a purely grouping rule, we can note it off to the side. Now we don't know any spots that Gladys does demonstrate in so far, so we can't do more than this right now. So we'll just have to come back to this rule when we have a little more information. This fourth rule is another grouping rule. Leslie demonstrates neither harvesting nor threshing. We can make deductions from this. First of all, we can use the harvesting from rule three to rule out Leslie, and now we know that Frank must demonstrate harvesting. That's another big deduction. We can also not that either Frank or Gladys must demonstrate threshing, because Leslie can't. Okay, now we know that Leslie demonstrates first, so that means that harvesting and threshing can't be first. And because Frank demonstrates harvesting, that means that harvesting can't go anywhere that Frank can't go, and that's spots one and six. So we knew no harvesting in one, and now we can add no harvesting to six. The last rule is an ordering rule. It tells us that milling is the next task demonstrated after threshing is demonstrated. Let's note this off to the side. What can we deduce from this? Well, we can deduce that threshing can't be last, since milling has to be after it. And we know that milling can't be first, because threshing is before milling. Okay, where else do we see threshing mentioned? We see in spot one that threshing can't be there, so that means that milling can't be in spot two. Alright, take a deep breath. If you felt like that was an intense setup, I promise they're not all like that. Some analytical reasoning tasks have a ton of deductions up front, which take a while, even after you've had a lot of practice. But that means that you should get rewarded with some quicker points in some of the questions. Other analytical reasoning tasks have hardly any deductions up front, but then they give you more work to do in the questions, like with questions that give you new conditions to consider. The spectrum of how many deductions you'll make up front is pretty wide, so definitely be prepared for a variety of experiences on test day. So to recap, we just set up a mixed task that involved ordering and grouping. We made a diagram that looks a bit like two ordering tasks, and noted a lot of rules to the side, a lot of which we eventually integrated with our main diagram. We took our time and looked at the implications of each rule, making sure to include deductions about where elements can't go, not just where they can go. So we are in a really excellent position to move to the questions, because we have an initial diagram that we'll use for support, as well as a solid understanding of the rules.