I'm a strong advocate of two counter-intuitive strategies for Logic Games: 1) NEVER use brute force to solve for the answer to a question. This goes against what many of my students do, or think they should do, when they watch YouTube videos or take a prep course. The plus of solving with brute force is that you will eventually get to the right answer. However, the negative is that it takes far too much time. And the trade-off is not worth it. The time you spend solving for all possible worlds to get to the answer means less time for other questions and other games. I encourage students to learn how to NOT use brute force; and 2) NEVER determine inferences you don't need. Many students diagram the rules and then start trying to find as many inferences as they can, even without knowing if they're needed in the game. But it takes too much time, and if you understand the problem and more importantly, the logic behind the problem, you will quickly learn how to take only what you need.
Below I provide an example of this strategy. It does not teach you how to deploy these strategies on all and every game. But it does offer an example of how it works. I'm using a relatively simple game to demonstrate, but it works on every game, all the time.
If you want to follow along, it's a logic game from Preptest 43, section 3, questions 7 - 12.
The set up is very easy. There are six dogs, and there are six slots for the dogs. Two per day, Monday through Wednesday. This is good. It means our diagram is very easy, and it means our inferences are limited. Our basic set-up looks like this:
Very simple. Days of the week, two per day. Six dogs total, so six slots for six variables. Nice and balanced. And just like that, we have our diagram. Nothing complicated, nothing time-consuming. Let's now turn to the rules:
It's important to notice how simply we can diagram our rules. And there aren't a lot of rules. At this point, prep books and courses will tell you to do a bunch of different things. Forget about them. Instead, do one simple thing. Ask yourself, what information MUST the game provide in order for me to solve this game?
Right away, two things stick out: 1) The game will have to help us match pairs of dogs. There are three days, two dogs per day, so there are three pairs of dogs. The game MUST help us establish what those pairs should be, regardless of day. 2) The game must help us know what pairs go to what days. Which two dogs are on Wed, Thurs, Fri?
It should not be at all surprising that all of our rules help us to figure out these two things. And notice: two of our rules deal with the first piece of information (dog pairs). And two of our rules deal with the second piece of information (dog to days).
So when we look for inferences, we now know EXACTLY WHAT WE NEED TO LOOK FOR. We're looking for anything that helps us match dog pairs, and anything that gives us dogs to days. Don't just start looking for inferences! You need to know WHY you're looking for inferences and WHAT inferences you need. Once you've diagrammed your problem, take just a few moments and ask what information the problem must provide you. Usually, it's obvious. Sometimes, it's not so obvious. But asking yourself this question allows you to know what kinds of inferences to expect in the problem.
You'll also notice that I immediately took the contrapositive of every conditional. This is what I consider an "auto-deduction." It should be done automatically, every time, without thought.
Do we need to draw every inference? Absolutely not. Why would we? We don't know what inferences are relevant. So what inferences do we draw? Only the most immediate and obvious inferences! That's it. And in this problem, there is only ONE key inference, and most would identify it right away. Here it is:
See, the first two rules deal with the dog pairs. And they make it very easy to determine which dog is with which other dog. L + P go together. But G and H can't be together. That leaves only K and S. But if G and H can't be together, then K and S have to be paired with G and H. The only thing we don't know is who gets K and who gets S.
This is a powerful (and simple) inference for two reasons. (1) It completely maps out the pairs of dogs, and (2) It is likely that the questions will somehow tell me who gets K and who gets S.
Let's look at the questions...
At this point, it's easy to say, "what about other inferences? That can't be all we have to do!" But it is. Yes, there are other inferences. Yes, we could solve for multiple scenarios. Yes, there are other things to notice about this problem. But the goal is not to find the truth of the logic game. The goal is to answer the questions as quickly as possible. So, why waste time with other inferences? I know the pairs of dogs, and the conditionals will help me determine days. Since the conditionals are the only rules that deal with days of the week, then I know that if the question asks about days of the week, I know just where to go. That's all I need. Why waste time? Altogether, this took us less than a minute, and I know the questions will have to help me determine pairs and days for the dogs. So let's move on...
7. Is a list question. I'm not going to dwell on this. List questions are always the same. They are intended to be easy, and to drain time. The fastest method for every list question? Take the rules, one at a time, in order, and eliminate options until you have the solution. That's it. It's the fastest way, the simplest way, and it saves the most time.
8. A must be true question that is global in nature. These give students fits because it leads them to think they must have missed something. Usually, the answer is not immediately obvious, and it's tough to brute force these questions. After all, it's asking for a deduction that is logically necessary. Logical necessity is tough to brute force. The other reason these questions are tough for most people is because you must read each answer and make a decision. That takes time. So, you have to think about the question. Skim each answer and look for a general pattern. That pattern will usually point you to a series of rules. Here, we should notice something right away: all of the answers deal with possible dog pairs. This is great for us. We KNOW nearly all of the dog pairs. So, we're looking for a logically necessary deduction about dog pairs.
(a) K but not G. Nah. G can have K or S, but there's nothing that says they CAN'T be together.
(b) K and S can't be together. Must that be true? Well, of course! If K and S were on the same day, then G and H would be on the same day, and G and H can't be together. So, it MUST be true that K and S can't be together. Our inference showed us that. Either K or S goes to G and the remaining variable goes to H. No brute force needed.
9. Could be True. Should be renamed for students, "Brute force for truth." But our mantra is "Never brute force!" So what do we do? Convert ALL could be true questions to Must Be True questions! Then plug in the condition, deduce, and eliminate options. Simple.
Poodle on Tuesday. Right away, we know we'll need those conditionals, since the conditionals tell us about days, but let's plug the condition and deduce.
I added the most obvious inference, but let's go over it. Remember that contrapositive? Sure. It said that if G isn't on Tuesday, then K isn't on Monday. So, K must be on Wednesday. Nowhere else for it to go. And the other contrapositive said that if H isn't on Tuesday, then S isn't on Wednesday. So it has to be on Monday. Now, the only thing I don't know is where G and H go. But this should be enough. These are my only deductions. So, let's see how many options we can eliminate: B is out. C is out. D is out. E is out. So our answer must be A. And there was no brute force needed at all!
10. Must be true and local? Money in the bank. Plug the condition, deduce.
The first thing the problem did was give us the pairs of dogs. But what we want to know is what DAY goes with each pair. So, we MUST use our conditionals. Right away, we notice something. Our conditionals state that if G is on Monday, then K is on Tuesday. But, G and K are together. So, G can't be on Monday. Likewise, if S is on W, then H is on Tuesday. But S and H are together. So, S can't be on Wednesday. We end up with this:
Most students would think that they now have to figure out where everything else goes. But remember, this is a Must be True based on the condition we’re given. This is the most immediate and obvious inference from that condition (and actually, the only full inference). So, before we go hunting for more inferences, let’s stop and see if it’s enough.
Lo and behold! E tells us that S cannot be placed on Wednesday. MUST that be true? Yes! So without further work, that’s our answer.
Notice that none of this has involved brute force, and all of our choices have been based on immediate, obvious, and straightforward deductions.
11. This is just a Must Be True with a twist. Cannot be true is essentially the same as Must Be True. Only something is logically impossible rather than logically necessary. What this question does is twofold: it gives us dog pairs and it helps with dog days. That is a huge help. So, let's plug the condition and see what we've got.
The inferences are pretty clear. If H and S aren't on the same day (because H is the day before S), then we have our dog pairs: H must go with K. That leaves G with S. And of course, our rules state L with P. But we know something else: H/K and G/S are a block. H and S are on consecutive days. So, L/P is either Monday or Wednesday, but obviously not Tuesday. Before we go further, why not test and see if that's one of our answers? It is after all a CANNOT be true, and it CANNOT be true that L/P is on Tuesday, so let's see.
We notice right away one particular answer choice: Poodle on Tuesday. That CANNOT be true. Just that quick and we're done.
12. Here's another Cannot Be True. It's also using blocks. Let's plug it in and see:
If G is before P/L, then H is either Monday or Wednesday. Why H? Because it's the one variable that we know cannot go with G. Either K or S can, but G and H are not on the same day. So H must be on a different day than the block G/P/L.
So, H is Monday or Wednesday. What day is it not? Tuesday. Cannot be Tuesday. So, let's see if they made it easy for us. Is H one of the options? Sure. A is our answer.
See? Never brute force an answer. Think intelligently about the information you MUST be given, and think carefully (but quickly!) about the information you ARE given, and you'll never have to brute force a problem again!
Free stuff related to the LSAT. This blog includes reflections, tips, strategies, and problem solving for the LSAT. Feel free to email questions. I'll be happy to answer them on my blog.