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Analytical Reasoning – Worked examples

Current time:0:00Total duration:7:15

Ordering setup | Overview | Rules and deductions

Analytical Reasoning – Worked examples

Video transcript

- [Instructor] Let's work through this setup by first reading the introductory paragraph so that we can orient ourselves to the situation. Historical records show that over the course of five consecutive years, 601, 602, 603, 604, and 605, a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established. Before we look at the rules, let's make a rough sketch to reflect what's involved here. It's always a good idea to make a list of the players, and in this case we have six monuments, F, G, H, L, M and S. What are we doing with these monuments? Well, we're trying to determine the years in which the construction of each individual monument was begun. This is a classic ordering setup. So let's show the years in this way. If you'd like, you can shorten the years to save a little bit of time. Instead of 601 and 602, for example, let's just use the last digits, one, two, three, four, and five. Hmm. Only five years, but six monuments. That's a bit unusual for an ordering setup, but let's not panic. It just means that two of the monuments were probably begun in the same year. And if we take a super quick peak at the rules, we can see that the last rule tells us that there are two monuments in 601, and no other monument was begun in the same year as any of the other monuments. So we can add a spot to 601 to that second monument. Now we have a decent diagram, and can go through the remaining rules and note the additional information that we're given. Rule one tells us that L was begun in a later than G, but in an earlier year than F. We can note that in a number of ways, but let's use dashes to show relative order. Take it one piece at a time. L is later than G, and L is earlier than F. We don't know how many monuments are between G and L, if any, or L and F, but this shows a loose relationship among the three players. Let's start making some deductions right away. We don't know exactly where G, L, or F go, but we have determined where each can't go. For example, G can't be fourth or fifth, because G is earlier than L and L is earlier than F. Likewise, L can't be first, since it's in a later year than G, and L also can't be fifth, since it's earlier than F. Finally, F can't be first or second, because F is in a later year than L, which is in a later year than G. It's often useful to know where players can't go, because it might help you determine where certain players do go based on process of elimination once you get more information. Rule two is that H was begun no earlier than 604. We can rephrase this as H was begun in 604 or later, so H cannot be first, second, or third. And we can note it this way. And for good measure, if we want to, we can indicate that H has to be in 604 or 605. H is now restricted to only one of two years. Before we move on to the third rule, can we use this information and combination with rule one at all? We know that H has to be fourth or fifth, and we have this G, L, F chain here. Let's ask ourselves, could H be earlier than G? No, because there wouldn't be room for G, L, and F to be later than H. Could H be earlier than L? Nope, because again, with H being in only four or five, there could only be at most one monument that's later than H. So that means that H has to be later than L. It's possible that H is earlier than F if H isn't four and F isn't five. It's also possible that H is later than F. So, we'll make a separate chain going off of L like this. It's great to make chains bigger, if you can, because then you know more about how players relate to each other. For example, we also now know that L can't be fourth, because L is now earlier than two monuments, H and F. Finally, rule three tells us that M was begun earlier than 604. That means that M cannot be in four or five. What does this tell us when we look at it in the context of all the other rules? Well, if M is earlier than 604 and H is 604 or later, that means that M has to be earlier than H. There's no way they can be in the same year, since the year with two monuments is 601, so we can make our chain even bigger and show that M has to be earlier than H. Next, it's worth noting that we learn something about each of the monuments except for S. So just keep in mind that S isn't restricted at all. We can also see that in 601, we've moved out L, F, and H along the way. That leaves only G and S as candidates for 601. Since there are two monuments in 601, then two of G, M, and S are in 601. So if any of the questions place G, M, or S elsewhere, we'll automatically know who's left to be in 601 for that question. As we're still looking at what we can see by process of elimination. In both years 604 and 605, we've ruled out G, M, and L. You could leave it like that, if you like. But some students like to turn those deductions about what can't go there into deductions about who's left, especially when the options are down to only two or three. So, if G, M, and L are out, that means that F, H, and S are the only candidates for 604 and 605. This is a fantastic start for tackling the questions. And if you're worried that you didn't see all of the deductions on your own, it takes practice. And the questions are solvable, even if you didn't make all of these deductions, they may just take longer. So keep working on combining rules to deduce what must be true, and you'll start to see that more quickly and more easily.