Hi there! —

Welcome to Lsatters and thanks so much for the kind comments — great to hear that you are finding the Trainer helpful thus far —

These complex or rules are some of the most challenging you will see in the LG section — most test takers would prefer not to see them appear on a game, but, as I discuss in the Trainer, once you get comfortable with them, they can be a big positive for you, because when they appear they are often the most important rules for determining where the various elements of a game can go —

So, hope this helps, and if you have any follow-up just let me know —

To start, let’s break down and make sure we have clarity on the different issues that we are dealing with here —

**1) It’s important to keep in mind that the scenario dictates that all elements are to be placed in order, and there cannot be ties. **

And so one inference we can constantly draw is that if one element is not in front of another, it must be behind it. For example, if we know K is not before M, it must be behind it. Similarly, if we know K is not after M, we know it must be before it.

**2) The lines between the elements represent order**, with things on the left going earlier than things on the right (see lesson 10 if u want to brush up on diagramming ordering rules). When you have two elements drawn to the left or to the right of another element (for example, when you have both K and J drawn to the left of M, with lines from K and J to M, that means you know both are before M, but you don’t know which of them is first).

**3) Note that almost all of the rules specifically mention the term “but not both” — **

Keep in mind that without the “but not both,” (or other ways of saying the same thing), “or” statements could allow for both possibilities to occur at the same time —

So, if we have the statement “K is before M or N,” K could be before both M and N without violating the rules.

However, if you have the rule “K is before M or N, but not both,” we know that when K is before M, it can’t be before N, and when it’s before N, it can’t be before M, because the rule specifically tells us it can’t be in front of both at the same time – it has to be in front of exactly 1 of the 2.

Again, that’s what’s very important about the “but not both” — it tells us that when one thing is true, the other thing cannot be.

This too, when coupled with what I mentioned in #1, allows us to make certain inferences.

**So, if we get the statement “K is before M or N, but not both,” —**

If K is before M, it can’t also be before N, and so it must be after N. This gives us the chain N – K – M, where K is before M, but after N.

If K is before N, it can’t also be before M, and so it must be after M. This gives us the chain M- K – N, where K is before N, but after M.

And thus, when given a statement like “K is before M or N, but not both,” —

We know there are exactly 2 ways this can play out:

N – K – M or M – K – N, and so you would write out those two chains as possibilities.

Okay – hope that makes sense — with that laid out, let’s take a look at a few of the specific rules from the drill.

**“L will go after K or before M, but not both.”**

This rule tells us that one of two things must be true — L will go after K or L will go before M, and it tells us that when one of these things is true, the other must be false.

Let’s think this through one possibility at a time:

1. L can go after K.

If this is the case, L can’t go before M (because the rule tells us those two things can’t happen together).

If L don’t go before M, that means L must go after M.

So, when L goes after K, L also goes after M.

And you can draw that as I did in the solution with L to the right of both K and M.

2. L can go before M.

If this is the case, L can’t go after K (because, again, the rule tells us it can’t do both this these things at the same time) — and if L can’t go after K, L must go before K.

So, when L goes before M, L must also go before K.

This is represented with L to the left of both M and K, as I wrote in the solution.

**“Either K or J, but not both, will go after F.”**

Again, the rule gives us two possibilities — either K is going to go after K, or J is going to after F — one of these two things has to happen, but they can’t happen at the same time.

So, let’s break down our options:

1) If K goes after F —

That means J cannot go after F. From this, we can infer that J must go in front of F.

So, when K goes after F, J must go before F, and we get the chain J – F – K.

2) J goes after F.

If J goes after F, K can’t, and so K must go before F.

So, when J goes after F, K must go before F. This gives us the chain K – F – J

So, the rule “Either K or J, but not both, will go after F” gives us two possibilities:

J – F – K or K – F – J.

**“If F goes before L, F will go after H.
If F goes after L, F will go before H.”**

Notice the combination of rules gives us all possible relationships between F and L — F can either go before L, or F can go after L, and again, we have rules for both situations.

1. If F goes before L, F will go after H.

We can represent the part as F – L, and the second as H – F, and those combine to give us H – F – L.

2. If F goes after L, F will go before H.

We can represent the first part as L -F, and the second as F – H, and those combine to give us L – F – H.

…

Hope you found at least some of that helpful — if you are confused about any part or have any follow-up, just let me know — otherwise, if those explanations make sense, hopefully you can apply the same methods to the rest of the rules you had trouble with —

Mike