Ordering setup | Video lesson

- [Instructor] Let's take a look at an ordering setup together. We'll start by examining the introductory passage and that will help us understand what we're being asked to do. So we're told that exactly five objects, J, K, L, M, and N are to be stacked one on top of the other. Their resulting positions are numbered from one through five, from bottom to top. The resulting stack must meet the following restrictions. All right, so the first thing we can notice is that the primary players are five objects. We'll make a list of them here, so that we can keep track of them. We've got J, K, L, M, and N. Now, what are we doing with these objects? Well, they're stacked vertically and we're basically meant to determine what order they're stacked in. We're not seeing any kind of grouping action happening, so that means this is a classic ordering setup. Let's make a diagram that looks like our situation. Five objects stacked one on top of another and that can look like five spots in the vertical column. And, we're told that the bottom is number one and the top is number five. Gosh, can you imagine getting this part backwards on test day? It would be a nightmare, so it's a good idea to never rush just for the sake of time, because it is so much more costly to have to go back and fix mistakes, than it is to just take your time with important details. At this point, we have a basic diagram and we can move on to the rules. Our first rule is that L is immediately above K in the stack. There's always various ways to notate different kinds of rules. We like putting a pair in a box, like this. Our second rule is that J is not in position one. Whenever we can mark a rule directly in our diagram, it's a good idea to do so, instead of noting it off to the side. This way, it's clearer, we see it all the time. We can show that J isn't in position one by writing J with a line through it. The third rule tells us that M is not immediately below K in the stack. We can illustrate this in a similar way as we did in Rule One, except this time we can put a line through it to show that this situation doesn't happen. So, M below K, but with a line through it to show that it can't ever happen this way. Finally, the fourth rule tells us that N is either in position one, or else in position five. Just like with Rule Two, we can mark this directly into our diagram. You can use arrows like this or whatever makes the most sense to you and is clear and consistent. Okay, we've notated all the rules either directly into the diagram or off to the side so that we don't forget them. We've set ourselves up for one of the most important aspects of analytical reasoning now, which is making deductions. So what definites can we deduce that weren't explicitly told to us? Well, Rule One is that L is immediately above K. If we think about combinations for where these two could go, there's just too many of 'em, so we don't want to sit there on test day and think, where are all the places L and K could go? What we know for sure is, where L and K can't go. So, if L is always immediately above K in the stack, then L can't be first and K can't be fifth. We weren't explicitly given that information, but we know that it must be true, because if L is immediately above K, then L can't be on the bottom and K can't be on the top. Since we know that it's true, that is what a deduction is, something that we weren't told, but we can infer. J can be in four different spots so that doesn't help us. The only thing we know about K and L is that there's one place each that they can't be. We know next to nothing about M, only that it can't be below K and we don't know where K is, and N is so far the most restricted object, because there are only two places N can go. So, having checked for more deductions and not finding any, we can move to the questions. To recap, we just set up an ordering task, using dashes for the spots. We noted some rules off to the side and some directly in the diagram and we made one deduction based on Rule One. Even though we don't know where any of the objects go for sure, we're in a really good 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. It's likely that some of the questions will give us extra information to use that will allow us to make more deductions for those questions, so don't get worried on test day, if you finish a setup and you don't have any of the spots determined. That will happen sometimes. Have confidence that you've made the deductions that you can and now you can move to the questions.