June 2007 Game 1

June 2007 LSAT, Game 1 Recap

Having answered all the questions in Game 1 of the June 2007 LSAT, a couple final notes: 1)  There's no scratch paper allowed on the LSAT, so you must write on your test pages in order to solve the games. Here's what my test page for Game 1 looked like when I got done with it:

Game 1 completed test page

2)  I call the approach I took here "Making Worlds," for lack of a better term. This is extremely powerful when applied at the right time, and Game 1 was perfect for such an attack. But when applied at the wrong time, or in the wrong way, this approach can be a colossal waste of time. So before I make Worlds, I look for two criteria: First, I want a limited number of Worlds--preferably just two of them. Second, I want to be able to fill out some stuff, with certainty, in at least one and preferably all Worlds.

Here, in Game #2, I had a perfect opportunity to make only two Worlds which were mutually exclusive (there was no overlap between the two) and encompassed all possibilities (there were no missing ways to complete the product code--any acceptable code had to fit into one of the two Worlds). And in both of my two Worlds, I knew exactly what the first and second digits were--with further soft inferences about the possibilities for the third and fifth spots. So it was a green light to make two Worlds, and I ended up crushing this game.

3)  I think this is a terrific game to study. It's a very common task--putting things in order--and the question types are very manageable/learnable. If games are bothering you, THIS is the game to try to master. Before you can tackle tougher games, you certainly need to understand relatively simple games like this one.

See my class schedule for more opportunities to learn about Logic Games--including my Logic Games Boot Camps. And check out my book Cheating the LSAT on either CreateSpace.com or Amazon.com for a dissection of an entire recent test, including the Games.

June 2007 LSAT, Game 1, #5

Time to wrap up Game 1 of the June 2007 LSAT. To answer question number 5, I'm going to once again lean heavily on the two worlds I made in my setup. Again, those look like this: World 1:   1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

World 2:   2      4     0/1   __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

The question says "Which one of the following must be true about any acceptable product code?" This means the correct answer MUST always be true in not one but BOTH of the two worlds. Let's see:

A)  There does not have to be exactly one digit between the 0 and the 1 in either World 1 or World 2, so there's no way this is the answer.

B)  There are zero digits between the 1 and the 2 in World 1, and there does not have to be exactly one digit between the 1 and the 2 in World 2, so there's no way this is the answer.

C)  In World 1, it's possible to have three digits between the 1 and the 3. This isn't possible in World 2, but that doesn't matter, since the correct answer has to be true in ALL cases. This is out because it doesn't have to be true in World 1.

D)  In World 2, it's possible to have three digits between the 2 and the 3. This isn't possible in World 1, but that doesn't matter, since the correct answer has to be true in ALL cases. This is out because it doesn't have to be true in World 2.

E)  Yep.  In World 1, there are a maximum of two digits between the 2 and the 4. In World 2, there are zero digits between the 2 and the 4. Therefore, in both worlds, there are at most 2 digits between the 2 and the 4. So this is our answer.

June 2007 LSAT, Game 1, #4

Question number 4 in Game 1 of the June 2007 LSAT asks "Any of the following pairs could be the third and fourth digits, respectively, of an acceptable product code EXCEPT:" That's a bit of a mouthful--let's see if we can translate it. The word "respectively," here, means "in that order." And since we're told that any of the pairs of digits COULD be third and fourth, EXCEPT one of the pairs, (the pair we're looking for) that means the correct answer CANNOT be third and fourth. So another way of asking the question would have been "which one of the following cannot ever be the third and fourth digits, in that order?" Dammit, why didn't they just say that?

Because it's a test, of course. They're seeing if you can 1) slow down, 2) be patient, and 3) decode some far-less-than-perfectly-written English. That's exactly what you're going to have to do to make sense of Court opinions, contracts, and especially statutes--the LSAT is making sure you have the reading chops that will be required at the next level. Okay, now let's answer this question.

If you don't already have the June 2007 LSAT, you'll find it here. To answer question number 4 in Game 1, I'm going to once again lean heavily on the two worlds I made in my setup (this probably won't make any sense if you didn't read that post):

World 1:   1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

World 2:   2      4     0/1   __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

For question #4, any answer choice that will work in either (or both) of the two Worlds will not be the correct answer. The answer choice that won't work in either world will be our answer.

A)  In World 2, it's possible to have 0, 1 as the third and fourth digits. So this is out.

B)  In World 1 and World 2, it's possible to have 0, 3 as the third and fourth digits. So this is out.

C)  In World 2, it's possible to have 1, 0 as the third and fourth digits. So this is out.

D)  In World 1, it's possible to have 3, 0 as the third and fourth digits. So this is out.

E)  It's impossible to have 3, 4 as the third and fourth digits in either World 1 or World 2. So this is the correct answer to a "could be true EXCEPT" question.

June 2007 LSAT, Game 1, #3

Here's our setup for Game 1 of the June 2007 LSAT, and if you don't already have the test, you'll find it here. Question 3 says "If the third digit of an acceptable product code is not zero, which one of the following must be true?" Just like Question 1, this question requires us to make a new diagram that incorporates the new condition (third digit can't be 0) with all of the original conditions. The question couldn't be easier, if we simply apply the two worlds we developed in the initial setup. Remember, the initial rules conspired together to leave us with only two templates for completing the game. Those two templates looked like this:

World 1:   1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

World 2:   2      4     0/1    __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

The new condition says the third spot CAN'T be 0. Let's apply that first to World 1.  If the third spot can't be 0, then the only alternative for the third spot in World 1 is 3.  And we can go further. If the third spot in World 1 has to be 3, then the last spot in World 1 can only be 4 (because the fifth spot has to be higher than the third spot). And we can go further still. If the third spot is 3 and the last spot is 4, then only 0 is left for the fourth spot. So it looks like this:

Revised World 1 (where the third spot can't be zero):   1      2      3      0      4  

We can do the same thing for World 2. If the third spot can't be 0, then the only alternative for the third spot in World 2 is 1. And we can go further. If the third spot in World 2 is 1, then the last spot in World 2 can only be 3 (because the fifth spot has to be higher than the third spot). And we can go further still. If the third spot is 1 and the last spot is 3, then only 0 is left for the fourth spot. So it looks like this:

Revised World 2 (where the third spot can't be zero):   2      4      1      0      3  

Now we just have to pick the answer choice that must be true in BOTH of these worlds.

A)  The second digit has to be 2 in our revised World 1, but not in our revised World 2. So it's not our answer.

B)  The third digit has to be 3 in our revised World 1, but not in our revised World 2. So it's not in our answer.

C)  The fourth digit has to be 0 in our revised World 1, and also has to be 0 in our revised World 2. So this is going to be our answer.

D)  The fifth digit has to be 3 in our revised World 2, but not in our revised World 1. So it's not our answer.

E)  The fifth digit can't be 1 in either revised World 1 or revised World 2. So it's not our answer. Our answer is C.

 

 

 

 

June 2007 LSAT, Game 1, #2

Two days ago, I discussed the setup and rules for Game 1 in Section 1 of the June 2007 LSAT. (You'll find these explanations most useful if you print yourself a copy of the test and have it handy.)  And yesterday, I took a look at Question 1. Question 2 asks "Which one of the following must be true about any acceptable product code?" Unlike Question 1, Question 2 doesn't give us any new information.  So we have to answer Question 2 solely based on the initial requirements of the game. (Important:  The new rule that was in play for Question 1 doesn't apply for subsequent questions.) The starting conditions implied two templates for completing the game. We learned, before we even looked at the questions, that any acceptable product code MUST be in one of the following two forms:

World 1:

  1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

World 2:

  2      4     0/1    __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

For question 2, we're asked to identify an answer that "must be true." This means the correct answer must always be true in both World 1 and World 2. If it doesn't have to always be true in every scenario, then it can't properly be called "must be true."

If there's one correct answer that must be true, then there are four incorrect answers that could be false. (The incorrect answers might be false in all circumstances, or might be true sometimes and false sometimes. Only the correct answer will be true in all circumstances.)  Let's see what we've got in the answer choices.

A)  This does have to be true in World 1, but it does NOT have to be true in World 2. (In fact it can't be true in World 2.) Since we need to find an answer choice that must always be true, this one is out.

B)  This does have to be true in World 1, but it does NOT have to be true in World 2. (It could be true, or could be false, in world 2.) Since we need to find an answer choice that must always be true, this one is out.

C)  Yep. In both World 1 and World 2, the digit 2 has to be used before any possible spot where 3 could be used. So no matter where the digit 3 goes, in either world, 2 will always be before 3. This is going to be our correct answer, but I'll look at D and E just to be sure.

D) This doesn't have to be true in either world.  Not even close.

E) This does have to be true in World 2, but it could be true or false in World 1. So this is out, and our answer is C.

 

 

 

June 2007 LSAT, Game 1, #1

Yesterday, I discussed the setup and rules for Game 1 in Section 1 of the June 2007 LSAT. It's a fairly straightforward and very familiar game--all we're asked to do is put five things in order. This is the type of game that you've simply got to master if you're going to do well on the Logic Games. One game similar to this appears on nearly every LSAT. The rest of the games in the section will tend to be harder than this. So there's no use in rushing through or skipping this game. For students who are just starting out, I recommend spending your entire 35 minutes, if necessary, on this first game. The point is this: Speed, on the LSAT, comes from accuracy. You need to be able to get each of the questions on this game right with certainty. Once you can do that (no matter how long it takes) you'll eventually be able to go faster. I've seen students go from the low single digits on the Logic Games (getting 3 or 4 questions correct) to scoring perfectly on the Games (23 or 24 correct). But you have to walk before you can run. So slow down, make some inferences (see yesterday's post  for my definition of "making inferences") and answer the questions with certainty. It's easier than you think.

Question 1 says "if the last digit of an acceptable product code is 1, it must be true that..."

So here, we're given a new additional rule: The last digit has to be 1. Note that this rule only applies to this question... on later questions, the last digit does NOT have to be 1. Furthermore, note that all the rules that we were given in the initial setup DO apply to this question.

Yesterday, I made the realization that there were really only two different templates for figuring out the five-digit code: The code must start 1-2, or the code must start 2-4. There's just no other way to do it without breaking the rules. But for Question 1, we have the new rule that the last digit must be 1. Therefore, the code must start 2-4. So I make a new diagram, that applies to question 1 only, that looks like this:

  2      4    __  __    1  

But I'm not done yet. The last rule in the game says that the third digit must be less than the fifth digit. This rule means that, if the last digit is 1, that makes the third digit 0. Which, in turn, would make the fourth digit 3. So the completed code looks like this:

  2      4      0      3      1  

And now, the question will be extremely easy to answer.

A) Yes, the first digit has to be two. I'm 99.9% sure this will be our answer. But because it's the first question, I'll definitely check all five answer choices just to be sure.

B)  No, the second digit does not have to be 0. In fact it can't be 0.

C)  No, the third digit does not have to be 3. In fact it can't be 3.

D)  No, the fourth digit does not have to be 4. In fact it can't be 4.

E)  No, the fourth digit does not have to be 0. In fact it can't be 0. So our answer is A.

One of the most important things I can teach you about the logic games is that the questions can be answered with 100% certainty. On the Logical Reasoning, there are some questions that require a balancing test. Sometimes on LR I'll make a case for B, and a slightly stronger case for D, and I won't be entirely sure, but I'll pick D because I think it just "feels" better. This never happens on the Logic Games. On the Logic Games, there is a single, objectively correct answer to every question. Your goal should be to pick an answer where, even with a gun to your head, you'd be confident that your answer was correct. Here, with a gun to my head, I'm still confident that A is the answer. There's no way around it.

June 2007 LSAT, Game 1 Setup

Logic Games are troubling for nearly every LSAT student I've ever met--on the first day of class. But Games are also, by far, the most teachable section of the test. On Logical Reasoning and Reading Comprehension, improvements tend to happen slowly, incrementally... like a long uphill march. On Logic Games, improvements tend to happen all of a sudden, in jumps and spurts... like launching off a trampoline. I've seen a zillion students walk into my classroom getting their asses kicked by Games. And I've seen a zillion students walk out of my classroom scoring perfectly on the Games. (It's by far the most commonly fucked-up section. And it is also, by an even wider margin, the most common section where perfect scores are achieved.) This is the most fun section of the test, and it's also, in large part, where I make my money.

Games are easy to teach in class, but I've been skeptical about trying to teach them in writing. Luckily, Game 1 of the June 2007 LSAT  is fairly straightforward, so if explaining logic games in the blog format is ever going to be possible, it's got to be possible on this game. I promise I'll give it my best. You're probably going to want to print yourself a copy of the test, if you haven't already. And take 5-10 minutes attempting Game 1 (questions 1-5) on your own before reading these explanations. That's the best way to learn. When you've done that, come back.

The game simply asks us to put five things in order: the numbers 0, 1, 2, 3, and 4. There are five digits, and they can go in any order, subject to a few rules. Here we go.

--Each digit goes exactly once. --The second digit is twice the first. --The third digit is less than the fifth.

If you've prepared at all for the LSAT, you've been told repeatedly that the key to Logic Games is "making inferences." This is true, of course, but it's unhelpful without an explanation of what "making inferences actually means. Drumroll, please.

The Super-Secret Magical Definition of "Making Inferences":  

...

Uhm. Well. Yeah. All this means is "combine the rules together and see what you've learned."

Sorry to disappoint you, but this shit is simply not rocket science. The LSAC knows that the reason most people end up taking the LSAT is that they basically sucked at their science and math classes in high school and college. Most of the inferences you're going to make on the LSAT's logic games are very simple combinations of two, or maybe three, rules. If you blink, it looks like magic. But if you pay close attention, you'll realize that each baby step is basically obvious. All you have to do is simply look at each rule in the context of every other rule, and see if the two (or three) rules in combination teach you anything else that's new. Here, let me show you:

There's a rule that says the second digit has to be exactly twice the first. And there's a rule that says that each digit (0, 1, 2, 3, and 4) are each used exactly once.

Okay, so:

If the first digit is 1, then the second digit has to be 2:

  1     2    __  __  __

And if the first digit is 2, then I guess the second digit has to be 4:

  2     4    __  __  __

And if the first digit is 3, then the second digit has to be 6. But there IS no 6. So the first digit can't be 3. Likewise, the first digit can't be 4, because there is no 8. And the first digit can't be 0 either, because two times 0 is 0, and we can only use 0 once.

So really, there are only two ways to do this game. (The two ways I've drawn out, above.) And that, my friends, is the magic of making inferences. Easier than you thought? I hope so.

And we don't want to stop there. We need to reconsider what we've just learned (there are only two ways to do the first two digits) with the REST of what we know about the game. (The other rules.) This is like playing solitaire. In solitaire, every time you make a move, no matter how small, you get to go back through the entire deck to see if anything has changed. In Logic Games, every time we make an inference, we need to consider that inference in light of all the other stuff we know about the game, to see if we learn anything ELSE that's new.

Here, I'm thinking about the rule that says the third digit has to be less than the fifth. Let's consider the world that looks like this:

  1     2    __  __  __

What can go third and what can go fifth? Well, I'm thinking that 4 could never go third there (because that's the highest number) and 0 could never go last (since that's the lowest number). So it's this:

  1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

Likewise, let's consider the world that looked like this:

  2      4    __  __  __

I'm pretty sure in that world, the third spot can't be 3 (since that's the highest remaining number) and the last spot can't be 0 (since that's the lowest number). So it's this:

  2      4     0/1  __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

I'm left with two templates for solving this game:

World 1:

  1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

World 2:

  2      4     0/1    __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

And that's about enough for today. Tomorrow, I'll start answering the questions for this game. But believe it or not, we've already done all the heavy lifting. From here, the questions will be easy. We're in position to crush this game. And that's your first, most important, lesson on the Logic Games: Do as much work as you can BEFORE you even look at the questions. I bet we've already answered some of the questions, before we've even seen them. This should be fun.