Logic Game | Grouping: Selection Defined Diagram | Explanation

This week, I'm doing a blog post to explain my approach to solving last week's Free LSAT Logic Game | Grouping: Selection (Defined).

Again, here are the categories and topics:

P - ABE
R - HLO
W - STY


I'd put a "1-" next to each category because of the rule that we have to have at least one from each category. "1-" indicates that there's "at least one" from each, but we don't know the maximum number of variables we can have from each, so I'm not "closing" the range.

P - ABE - 1-
R - HLO - 1-
W - STY - 1-


Main Diagram
I'd draw it on paper like this:



I put a P, R, and W in parentheses to the side of three of the "in" slots because we know "at least one from each category is in." It just makes that rule a bit more concrete and visual by reserving a slot for everything we know so far.

However, it's just easier to type horizontally (and some of you read this on mobiles that can't see picture files, so whenever you see a diagram I've typed, just think of it being draw vertically):

6 In: _ _ _ _ _ _
3 Out: _ _ _


1st Indented Rule:

If S is in, E and L are out.

Contrapositive: If E or L is in, S is out.


Summary:

S <--+--> E
S <--+--> L

That's a "double-not" arrow. It means that at least one of the things on either side of the arrow CANNOT be in. Looking at the S-E double-not arrow (in isolation), it means that:

(1) S is out

OR

(2) E is out

OR

(3) S and E are both out.


Same goes for the S-L double-not arrow.

We can summarize the two double-not arrows as:

S <--+--> E, L



2nd Indented Rule:

If L is out, Y is in.

Contrapositive: If Y is out, L is in.

Summary:

(1) Y is in

OR

(2) L is in

OR

(3) Y and L are both in.

See Conditional Reasoning for an explanation of this type or rule (and the double-not arrow, as well).


By combining the 1st and 2nd indented rules, we can form the chain:



At this point, we should think something along the lines of, "Wow, that S is pretty powerful stuff. Let's see what happens when I place it 'in'. "

Putting S "in" means E and L are "out," and Y is "in" (we inferred from that conditional chain I just made, above):

6 In: S Y _ _ _ _
3 Out: E L _

That's all we can do with S right now, but let's look at the...


3rd indented rule:

At least one topic on war will not be selected.

This means we'll always have either 1 or 2 war topics "in", but never all 3. At this point, I'd draw a "(W)" to the side of one "out" slot, just to reserve it for a War topic.

(Remember: we can't have 0 war topics "in" because we always have to have at least one topic from each category "in.")

Here are the categories and topics from before, but I'd now add in the number of topics we can have from each category:

P - ABE - 1-3
R - HLO - 1-3
W - STY - 1-2

***

If we JUMP back to that little "S-in" diagram we made just a moment ago...

6 In: S Y _ _ _ _
3 Out: E L _

we'll see that we already have 2 Ws "in" (S and Y are both from the War category).

Because we can't have all 3 Wars from this category, T will have to be "out".

6 In: S Y _ _ _ _
3 Out: E L T

If we now have 3 "out", and 6 have to be "in" total, this means that everyone but E, L, and T has to be "in." Our "S-in" diagram is now complete, giving us:

6 In: S Y A B H O
3 Out: E L T

I'd write this off to the side and circle "S" to indicate that "S-in" is what started everything.

I'd then make another main diagram with S "out" and leave all the other slots blank.

***
I'm not going to explain ALL the questions because that just spoils the fun...but I will give a hint for this type of game in general.

The 1st question is a typical "List / Acceptability" question regarding specific topics. You can solve this simply by applying the rules.

However, the 2nd, 3rd, and 4th questions refer to the general categories as well.

Once you hit the 2nd question, the reference to the religion category should make you start thinking about numerical distributions (the various combinations of numbers of variables you can select from each category).

If you're decent or better with numbers, or you think you can get better by practicing, try to list all the combinations quickly.

The War category is the most limited because you can only have 1 or 2 from that category.

If we have 1 from war, that leaves 5 remaining that we'll need to pick (6 total - 1 from War = 5).

How can we make 5?

5+0, 4+1, and 3+2

However, there's no category with 4 topics, and we need at least one topic from each category (which means having 0 "in" isn't okay), so it's either going to be 3 from Politics and 2 from Religion or 2 from Politics and 3 from Religion.

This gives us the distributions:

3 Politics, 2 Religion, 1 War

2 Politics, 3 Religion, 1 War


BUT

If we have 2 from War, that leaves 4 remaining that we'll need to pick to be "in" (6 total - 2 from War = 4)

How can we make 4?

4+0, 3+1, and 2+2.

Again, there's no category with 4 (and again, we also can't have 0 from any category "in"), so it's either going to be 3 from Politics and 1 from Religion, or 1 from Politics and 3 from Religion, or we'll have 2 from Politics and 2 from Religion:

3 Politics, 1 Religion, 2 War

1 Politics, 3 Religion, 2 War

2 Politics, 2 Religion, 2 War


Of course, you don't want to take up all that space by writing so much.

Instead, I'd write the numerical distributions like this:

P-R-W
3-2-1
2-3-1
3-1-2
1-3-2
2-2-2

(I'd write them spaced-apart without a dash, but I don't want the formatting to get messed-up here.)

Recognizing numerical distributions is good stuff, but I'm not getting a kick out of it just because it's fun.

It also helps us answer the question because it becomes obvious that only the 3P-1R-2W distribution has 1R, so we know that we'll have to have 3P and 2W.

We know that the variable S will be "out" because we already have the complete "S-in" scenario (which is 2-2-2, by the way).

If S is "out", the 2Ws "in" will be T and Y, and all 3 Ps "in" means ABE are "in"... (you can take it from here)

***

What if you're not good with numbers and don't think you can get better at them?

Then, instead of trying to list all the combinations, just start with the 2nd question's limitation, that we have exactly 1 Religion topic and figure out that specific distribution instead of taking the time to list them all.

However, it makes the game much easier if you know all of them, so it's worth practicing how to do this.

I hear you saying, "but it's not fair that I have to be good at math..."

I feel your pain. I couldn't stand precalculus or calculus, but this is just addition. It's about recognizing all the ways to get to 4 and 5.

You can do addition, can't you?

The LSAT is all about thinking of all the possibilities, not just the obvious ones.

So make your 2nd grade math teacher proud and beat everyone at craps.

Photo by wisse / CC BY-NC-ND 2.0

Free LSAT Logic Games | Grouping: Selection (Defined)

I posted my Grouping: Selection / In-Out Logic Game on the blog a month ago, but that one was "Undefined," meaning that we didn't know how many variables were in (voted for) and how many were out (voted against).

The game I've written for this week, on the other hand, is "Defined," which means that we know exactly how many variables are selected and how many are not selected.

Please post your thoughts and questions in the comments!

***

Here's this week's Logic Game:

From among nine topics, a student will select six to debate at a tournament. The topics are organized into three categories. Of the topics, three-A, B, and E-are on politics, three-H, L, and O-are on religion, and three-S, T, and Y-are on war. At least one topic will be selected from each category. The student selects the topics according to the following conditions:

If S is selected, neither E nor L is selected.
If Y is not selected, L is selected.
At least one topic on war will not be selected.

1. Which one of the following could be a complete and accurate list of the topics that the student selects?

(A) A, B, E, H, L, O
(B) A, B, E, H, L, T
(C) A, B, E, H, O, T
(D) A, B, E, H, S, Y
(E) A, B, H, S, T, Y


2. If exactly one of the topics on religion is selected, then which one of the following is a complete and accurate list of the other topics that must also be selected?

(A) A, B, E, T
(B) A, B, E, H, Y
(C) A, B, L, T, Y
(D) A, B, E, S, T
(E) A, B, E, T, Y


3. Which one of the following must be true?

(A) A is selected.
(B) E is selected.
(C) T is selected.
(D) Of at least one of the three categories of topics, exactly two topics are selected.
(E) Of at least one of the three categories of topics, exactly three topics are selected.


4. If exactly two topics from each category are selected, then which one of the following must be true?

(A) B is selected.
(B) H is selected.
(C) Y is selected.
(D) L is not selected.
(E) T is not selected.


5. Each one of the following is a pair of topics that could be among the topics selected EXCEPT:

(A) A, Y
(B) B, H
(C) B, O
(D) S, T
(E) S, Y


6. Each of the following, if known, would fully determine the selection of the six topics EXCEPT:

(A) B and E are not selected.
(B) B and T are not selected.
(C) E and O are not selected.
(D) L and T are not selected.
(E) O and Y are not selected.


The text below contains the answers to the above Logic Game.


1. B
2. E
3. D
4. C
5. D
6. D

***

Can't figure out how to do the game? Not to worry - leave a comment!

See my tips on how to solve this game in Logic Game | Grouping: Selection Defined Diagram | Explanation.

***

For some LSAC-written Logic Games similar to this one, check out:

PrepTest 24, Section 4, Game 4 (page 213 in 10 More)
PrepTest 33, Section 4, Game 3 (page 178 in Next 10)
PrepTest 40, Section 2, Game 2

Photo by ennuiislife / CC BY-NC 2.0

Logic Game Grouping: Matching Templates Diagram | Explanation

As promised, I'm doing a blog post to demonstrate the templates (multiple main diagrams) for last week's Grouping: Matching Templates Logic Game, so here goes.

So, in the game, we have 7 projects. 2 in April, 3 in May, and 2 in June, giving us this layout of slots for each month:

Depending on whether you choose to make your templates refer to specific variables or simply to the categories of variables, you might want to put a "D" with a slash through it under June.

Our variables are:

Classifieds: C C
Electronics: A B
Weapons: D L R

So we can diagram our rules like this:

The options for the game are more limited than they might appear at first. The key is figuring out which rule or block to use to create your templates. You want to go from the most restricted variables and work your way towards the least restricted variables.

The vertical WW block and the vertical WE block could go on any of the 3 months, so they're actually pretty "loose," so we don't want to start there. We also don't want to make those the first variables we work with because there are 3 "W" variables: DLR, and 2 "E" variables: AB.

However, there are only 3 main possibilities for the Classifieds.

They could be on April and May:


on May and June:


or on April and June:


These are our 3 main possibilities, and every possible scenario will fall into one of these 3. You could leave off here, but I prefer to get more specific.

Let's start with the first - the 2 Classifieds on April and May.

In this possibility, we could have EW on May, and WW on June:


OR we could have WW on May and EW on June:


Now the 2nd main possibility - the 2 Classifieds on May and June.

In this possibility, we could have EW on April and WW on May:


OR we could have WW on April and EW on May:


Finally, 3rd main possibility - the 2 Classifieds on April and June.

In this possibility, we're forced to put EWW on May together (which satisfies the EW block and the WW block simultaneously).

The remaining E and the remaining W are interchangeable. One will go on April, and the other will go on June. Here's this possibility with W on April and E on June:


Here's the same possibility, only with E on April and W on June:


Of course, you can easily combine these two into one diagram with E/W on April and W/E on June:




In fact, you can also combine the 2 main possibilities for when we have 2 Classifieds on April and May. The only difference between these two possibilities is whether we have 2Ws in May and E on June or 2Ws in June and E on May. Combining them gives us:





We can also combine the 2 main possibilities for the 2 Classifieds on May and June in the same way:





These become our 3 main diagrams.


Just don't forget that D (the drone) can never be on June. Place D with a slash through it below June in each diagram.

If you prefer to diagram things more literally, you can diagram the game's main possibilities in the same way I've done throughout, only whenever you see "E", you can write "A/B", and whenever you see "W", you can write "D/L/R" (only don't forget that when "W" is on June, it's only "L/R" because D can't be there.

I actually prefer to do the game's templates (main setups/diagrams) by writing the categories rather than the specific variables. As you might imagine, diagramming the specific variables takes longer to write and looks a bit more cluttered. However, it might save you time by allowing you to avoid referring back to which variables fall within each category.

What's best? Try it both ways to determine your personal preference.

Leave your questions and thoughts in the comments!

Photo by donsolo / CC BY-NC-SA 2.0

Free LSAT Logic Games | Grouping: Matching | Templates

Two weeks ago, I published a Grouping: Matching Logic Game I'd written. That one was a difficult type of Matching game because the number of "prayer-answerings" per deity was not fully determined.

In other Grouping: Matching games (such as the one I've written for this week - see below), the number of slots is fully determined for you. In these types of games, drawing multiple templates, possibilities, or limited options is often incredibly useful.

What are templates, possibilities, and limited options? They're all different terms describing the same technique - drawing a few main diagrams instead of only one. Each main diagram you draw will represent a different potential placement of the variables.

The key to drawing templates is to identify a variable or rule that has only a few different possibilities. Once you've found that variable or rule, draw multiple diagrams based upon every different major possibility for it, and fill in the other variables around it.

Please post your thoughts and questions in the comments!

***

Here's this week's Logic Game:


Compu-Global-Hyper-Mega-Net presents seven projects to the military over the course of three months- two in April, three in May, and two in June. Two of the projects are classified. Two others are electronics-active camouflage and a ballistics computer. The remaining three are weapons-a drone, a laser cannon, and a ray gun. The projects are presented in accordance with the following conditions:

The drone is not presented in June.
The classified projects are not both presented in the same month.
At least one of the weapons is presented in the same month as one of the electronics projects.
At least two of the weapons are presented in the same month as each other.

1. If the laser cannon is the only weapon presented in June, which one of the following must be true?

(A) A classified project, an electronics project, and a weapons project are presented in May.
(B) The ballistics computer is presented in May.
(C) A classified project is presented in May.
(D) An electronics project is presented in May.
(E) The ray gun is presented in May.


2. If two weapons are presented in April, which one of the following CANNOT be true?

(A) The drone is presented in April.
(B) The active camouflage is presented in May.
(C) A classified project is presented in May.
(D) The ballistics computer is presented in June.
(E) The laser cannon is presented in June.


3. If the electronics projects are not presented in consecutive months, which one of the following must be true?

(A) A weapon is presented in April.
(B) The laser cannon is presented in May.
(C) A classified project is presented in June.
(D) A weapon is presented in June.
(E) The classified projects are presented in consecutive months.


4. Which one of the following CANNOT be true?

(A) Both electronics projects are presented in the same month.
(B) Two weapons are presented in the same month as a classified project.
(C) Two weapons are presented in the same month as an electronics project.
(D) The active camouflage and the drone are presented in April.
(E) Two weapons are presented in June.


5. If neither of the electronics projects is presented in June, which one of the following must be true?

(A) A classified project is presented in May.
(B) The drone is presented in May.
(C) The ray gun is presented in May.
(D) A classified project is presented in June.
(E) Exactly one weapon is presented in June.


The text below contains the answers to the above Logic Game.

1. E
2. E
3. E
4. A
5. B

***
Can't figure out how to do the game? Not to worry - leave a comment!

You can also see my explanation and diagrams / templates of this game in Logic Games Grouping: Matching Templates Diagram | Explanation.

***
For some Logic Games similar to this one, check out:

PrepTest 37, Section 3, Game 3 (page 306 in Next 10)
PrepTest 38, Section 2, Game 3 (page 332 in Next 10)

Also see my Logic Games Categorization.

Photo by epicfireworks / CC BY-NC 2.0

Logic Games Pure Sequencing Diagram | Explanation

I've received several requests for a diagram of my Pure Sequencing LSAT Logic Game, so here goes.

This blog post includes my version of the main diagram for this Logic Game. It also includes modified versions of the diagram for questions 4 and 5, which introduce new limitations to the main diagram.

***

Also see my explanation of this game's set-up in Logic Games Pure Sequencing Step-by-Step Diagram.

***

I don't normally write "earlier" and "later" on the diagram because linear/sequencing games usually involve putting things in order from earlier -> later.

For this reason, left -> right usually means earlier -> later, and it's come to feel natural. However, some of you are still learning, so I included it in the below diagrams.

Here's the main diagram (click to enlarge):


Here's the diagram for Question 4 (click to enlarge):




Here's the diagram for Question 5 (click to enlarge):




Photo by dannysullivan / CC BY 2.0

(It's from the episode "Sword of Destiny" in the TV show Arrested Development. GOB and Buster perform a magic act together, and Buster accidentally cuts off GOB's fingers. I can't believe someone actually made Lego scenes based on a TV show either. I love Arrested Development, but Lego scenes are a bit much.)

Logic Games Matching Diagram | Explanation

I've received several requests for a diagram of my Grouping: Matching Logic Game, so here goes.

This blog post includes my version of the main diagram for this Logic Game. It also includes my diagram of the rules and some thoughts on making an effective diagram for this game (and games like it).

Here's the main diagram:



Here are the rules that I would've put to the side because they can't be placed easily on the main diagram:



Explanation of why and how I chose GHLRSV (the deities) as the base:

Many of you asked how I knew to put the deities as the "base", rather than the students.

Because the rules tell us more about specific deities than about specific students.

Deities: GHKLRSV
Students: ABJP

Let's look at the rules (which I've numbered below to reference easily):

1. Neither Lakshmi nor Rama answers Bobby's prayers, but Ganesha and Krishna both answer Bobby's.
2. Hanuman, Krishna, and Shiva answer Puja's prayers.
3. Hanuman answers at least three students' prayers, but Krishna and exactly one other deity each answer exactly two students' prayers.
4. If Vishnu answers a particular student's prayer, Hanuman does not answer that student's prayer.
5. If Ganesha answers a particular student's prayer, Rama does not answer that student's prayer.
6. Lakshmi answers at least one of the same students' prayers as Vishnu does.
7. Any deity who answers Puja's prayers also answers Bobby's but does not answer Arjun's.

Rules 1 and 2 tell us equal amounts about deities and students.
Rules 3-7 tell us more about specific deities than about specific students.

For this reason, it's much easier to use the deities as our base, rather than the students. As I mentioned in my hint in the game's initial blog post, choosing the right base can allow you to make inferences more easily.

***

What makes this Logic Game hard?

Two things:

1. Its general ambiguity.

We don't know exactly how many prayers each deity will answer, so this game is "loose." In other words, there are many possibilities (in contrast to PrepTest 35, Game 2 - page 237 in Next 10 - in which 4/6 cars are fully determined).

(This is also unlike Grouping: Matching games such as PrepTest 37, Game 3 - page 306 - and PrepTest 38, Game 3 - page 332 - where the number of slots is explicitly given.)

In my Hindu deities game, only 3/7 deities "prayer-answerings" are fully determined: H, K, and V.

The other deities' "prayer-answerings" are partially, but not fully, determined. I've used a dotted line (----------) to indicate ambiguity in the number of prayer-answerings.

Any letters below the dotted line are fixed. This means they will always be there in any valid scenario.

The letters above the dotted line might be there, but they also might not be there.

On the diagram, this means:

G might answer B only, but G could also answer the prayers of one or two other students as well.

L definitely answers A, but L might also answer J's prayers as well.

R will answer at least A or J, but R might also answer the other one of those two as well. This is why I wrote A/J with the potential of the other (J/A) as well.

S definitely answers B and P, but there's no reason S couldn't also answer J.


2. The third rule

Particularly, this part of it:

"Krishna and exactly one other deity each answer exactly two students' prayers."

The entire game revolves around which "other deity" answers exactly two.

That "other deity" could be G, L, R, or S.

If G answers 2, then L answers 1, R answers 1, and S answers 3.

If L answers 2, G answers 1 or 3, R answers 1, and S answers 3.

If R answers 2, G answers 1, L answers 1, and S answers 3.

If S answers 2, G answers 1 or 3, L answers 1, and R answers 1.


***

Are all Grouping: Matching games like this?

No. You can breathe a sigh of relief. Some are much easier and can be solved by using templates / possibilities / limited options (whatever you call it, it's the same thing).

PrepTest 37, Game 3, and PrepTest 38, Game 3 (both mentioned above) can be solved efficiently by using templates. See the Logic Game I wrote this week for a (difficult) example of this type of game.

Photo by iskcondesiretree
("Krishna kills the bird demon, Bakasura." He's the one standing in its mouth.)

Logic Games Tips | Conditional Reasoning

The following two rules are extremely common in Grouping: In-Out / Selection games, but they give test-takers a lot of trouble.

These rules come up in other types of Logic Games, too. Make sure you can recognize them at a glance and instantly know what they mean.

Please note: "~" is a symbol meaning "not." I'd use a slash ("/" ) through a letter in the below examples to indicate "not."

However, it doesn't come out well when typed, so I'm not using any slashes in this blog post. If you prefer the slash (I do), use it instead.


Rule #1:

Positive Variable -> Negative Variable = + --> -



Original: X -> ~Y
Contrapositive: Y-> ~X

Meaning: at least one does NOT occur, and maybe both will not.


Example:

If I eat cookies, then I don't eat donuts.

If I eat donuts, then I don't eat cookies.

Therefore, I cannot eat at least one of them, but perhaps I'll eat neither.


Whenever you see a positive sufficient condition (the one before the arrow), and a negative necessary condition (the one AFTER the arrow), this means you can never select both, so at least one will not be selected.

(See LSAT Logic: Necessary vs. Sufficient Conditions)

In other words, you must always lack at least one of the two. However, there's no reason you can't lack both.


LSAT Examples:

PrepTest 33, Game 2 - birds in the forest (December 2000 - in Next 10 Actual, page 177):

Original: Harriers -> ~Grosbeaks
Contrapositive: Grosbeaks-> ~Harriers

Meaning: The forest cannot contain both Harriers and Grosbeaks - it will always lack at least one of the two, and maybe it will lack both.


PrepTest 36, Game 1 - fruit stand (December 2001 - in Next 10 Actual, page 278):

Original: Kiwis -> ~Pears
Contrapositive: Pears -> ~Kiwis

Meaning: The fruit stand cannot carry both Kiwis and Pears - it will always lack at least one of the two, and maybe it will lack both.


Rule #2:

Negative Variable -> Positive Variable = - --> +

Original: ~X -> Y
Contrapositive: ~Y-> X

Meaning: at least one MUST occur, and maybe both will occur.

Example:

If I don't eat peas, then I must eat carrots.

If I don't eat carrots, then I must eat peas.

Therefore, I must always eat at least one of the two, but there's no reason I can't have both.

At this point, students often ask, "Why is it possible to have both?"

Answer: Because the rule has no policy for what happens when you already have one of the two.

This rule only has a policy for what happens if I don't eat one (I must eat the other). It has no policy for what happens when I already ate one (or am going to eat). This is why nothing stops me from eating both. There's simply no rule against it.

The only thing this rule means is I can't LACK both.

LSAT Examples:

PrepTest 33, Game 2 - birds in the forest (December 2000 - in Next 10 Actual, page 177):

Original: ~Jays -> Shrikes
Contrapositive: ~Shrikes -> Jays

Meaning: The forest cannot lack both Jays and Shrikes - it will always have at least one of the two, and maybe it will have both.



PrepTest 36, Game 1 - fruit stand (December 2000 - in Next 10 Actual, page 278):

Original: ~Tangerines -> Kiwis
Contrapositive: ~Kiwis -> Tangerines

Meaning: The fruit stand cannot lack both Kiwis and Tangerines - it will always have at least one of the two, and maybe it will have both.


For the birds in the forest game, I would summarize the rule as:

J
S
JS

Every valid list of birds in the forest will fall into one of those three categories - one is in, the other is in, or both are in.


For the fruit stand game, you might summarize the rule as:

K
T
KT

Every valid list of fruits in the fruit stand will fall into one of those three categories - one is in, the other is in, or both are in.

***

You can also see my approach to Birds in the Forest Logic Game.

Photo by _sk / CC BY-NC-SA 2.0

Free LSAT Logic Game | Pure Sequencing

UPDATE: You can get this game, along with several others I've written, in a free book.


This Logic Game I've written is what some would categorize as Pure Sequencing, Loose Sequencing, or Relative Ordering.

Whatever you call it, this type of game requires you to put variables in order, just like Basic Linear games do.

So what's the difference between Pure Sequencing and Basic Linear?

In Pure Sequencing, most of the rules involve the relationship between one variable and another. They'll say things like "A is before B" or "C is after D."

In Basic Linear games, you'll have a few rules that refer to specific and defined "slots" or places within the ordering.

Because the rules for Pure Sequencing games differ from those in Basic Linear games, the most efficient diagrams for these types of games differ a bit from those you'd use for Basic Linear games.

Instead of using slots, I recommend using short lines or "branches" to represent the relationships between variables. In other words, draw lines between variables to indicate their relationships.

Represent something like "A is before B" as "A-B."

Please post your thoughts and questions in the comments!

***

Here's this week's Logic Game:

At the annual meeting of the Magicians' Alliance, 8 magicians-L, M, N, O, P, Q, R, and S- perform their latest illusions, one magician at a time. The order in which the magicians perform their illusions is consistent with the following conditions:

L and Q each perform at some time after P.
S performs at some time before O and L.
M performs at some time before S.
P performs at some time after N.
S and N each perform at some time after R.

1. Which one of the following could be the order in which the magicians perform their illusions?

(A) M, N, R, S, P, Q, L, O
(B) S, M, R, N, P, L, Q, O
(C) R, N, M, P, O, S, Q, L
(D) R, M, S, L, N, P, Q, O
(E) M, R, S, N, O, P, Q, L


2. Which one of the following magicians CANNOT perform third?

(A) M
(B) N
(C) O
(D) P
(E) S


3. If O is the fourth magician to perform, then which one of the following must be true?

(A) M is the second magician to perform.
(B) L is the fifth magician to perform.
(C) P is the sixth magician to perform.
(D) Q is the seventh magician to perform.
(E) L is the eighth magician to perform.


4. If P performs before S, then each of the following must be false EXCEPT:

(A) R is the third magician to perform.
(B) S is the fourth magician to perform.
(C) P is the fifth magician to perform.
(D) Q is the sixth magician to perform.
(E) S is the seventh magician to perform.


5. If R performs after M and O performs before P, then which one of the following could be true?

(A) M is the second magician to perform.
(B) O is the third magician to perform.
(C) N is the fourth magician to perform.
(D) S is the fifth magician to perform.
(E) L is the sixth magician to perform.


***

The text below contains the answers to the above Logic Game.

1. E
2. C
3. C
4. D
5. C

***

See my explanation and diagrams of this game in Logic Games Pure Sequencing Diagram | Explanation.

***

Also see my explanation of this game's set-up in Logic Games Pure Sequencing Step-by-Step Diagram.

***

For some LSAC-written Logic Games like this one, check out PrepTest 33, Game 1 and PrepTest 38, Game 1 in The Next 10 Actual, Official LSAT PrepTests.

Photo by dannysullivan / CC BY 2.0

(The above photo is from the episode "Spring Break" in the TV show Arrested Development. GOB makes the Bluth family's yacht "disappear." I can't believe someone actually made Lego scenes based on a TV show either. I love Arrested Development, but Lego scenes are a bit much.)

Free LSAT Logic Game | Grouping: Matching

You might not know this, but a version of the LSAT has come to India. It's called, appropriately enough, LSAT-India.

In honor of the LSAT's arrival in India, this week's Logic Game is about Hindu deities.

Disclaimer: This Logic Game is in no way meant to imply that all Indian students taking the LSAT are Hindu, nor is it meant to imply that Hindu students would ever pray to deities for LSAT assistance (or that they're the only students who'd pray to Hindu deities for assistance). I've simply given the game this topic because I think Hindu deities are cool, and because I promised I'd write a logic game about non-Greek deities.

Please post your thoughts and questions in the comments!

***
Here's this week's Logic Game:

Exactly four students-Arjun, Bobby, Jason, and Puja-pray to exactly seven Hindu deities-Ganesha, Hanuman, Krishna, Lakshmi, Rama, Shiva, and Vishnu-for assistance in achieving top LSAT scores. No deity answers the prayers of all four students, but each deity answers at least one student's prayer. The deities answer the students' prayers according to the following conditions:

Neither Lakshmi nor Rama answers Bobby's prayers, but Ganesha and Krishna both answer Bobby's.
Hanuman, Krishna, and Shiva answer Puja's prayers.
Hanuman answers at least three students' prayers, but Krishna and exactly one other deity each answer exactly two students' prayers.
If Vishnu answers a particular student's prayer, Hanuman does not answer that student's prayer.
If Ganesha answers a particular student's prayer, Rama does not answer that student's prayer.
Lakshmi answers at least one of the same students' prayers as Vishnu does.
Any deity who answers Puja's prayers also answers Bobby's but does not answer Arjun's.

1. For how many of the seven deities can one determine exactly which students' prayers are answered by each?

(A) two
(B) three
(C) four
(D) five
(E) six


2. If Shiva does not answer Jason's prayers, which one of the following could be true?

(A) Ganesha and Krishna answer exactly the same students' prayers as each other.
(B) Lakshmi answers both Arjun's prayers and Jason's prayers.
(C) Both Lakshmi and Rama answer Jason's prayers.
(D) Exactly three of the seven deities answer Jason's prayers.
(E) Exactly four of the seven deities answer exactly one student's prayers.


3. Which one of the following, if known, would allow one to determine exactly which students' prayers are answered by each deity?

(A) Ganesha answers the prayers of exactly one student.
(B) Ganesha answers the prayers of exactly three students.
(C) Lakshmi answers the prayers of exactly two students.
(D) Rama answers the prayers of exactly two students.
(E) Shiva answers the prayers of exactly three students.


4. Which one of the following could be a pair of deities both of whom answer the prayers of exactly three students?

(A) Ganesha and Krishna
(B) Ganesha and Lakshmi
(C) Ganesha and Shiva
(D) Hanuman and Rama
(E) Hanuman and Vishnu


5. Each of the following could be a pair of deities both of whom answer the prayers of exactly two students EXCEPT:

(A) Ganesha, Krishna
(B) Krishna, Lakshmi
(C) Krishna, Rama
(D) Krishna, Shiva
(E) Krishna, Vishnu


6. Which one of the following is a complete and accurate list of deities, any one of whom could be a deity who answers Arjun's prayers?

(A) Ganesha, Hanuman, Lakshmi, Rama, Shiva, Vishnu
(B) Ganesha, Krishna, Lakshmi, Rama, Vishnu
(C) Ganesha, Lakshmi, Rama, Vishnu
(D) Hanuman, Lakshmi, Rama, Vishnu
(E) Lakshmi, Rama, Vishnu


7. Which one of the following CANNOT be true?

(A) Exactly three of the seven deities answer exactly the same students' prayers as each other.
(B) Exactly three of the seven deities answer Arjun's prayers.
(C) Exactly three of the seven deities answer Jason''s prayers.
(D) Exactly four of the seven deities answer Arjun's prayers.
(E) Exactly four of the seven deities answer Jason's prayers.


Here's one more question, just for fun:

8. Each of the following could be a complete and accurate list of students whose prayers are answered by Ganesha EXCEPT:

(A) Arjun, Bobby
(B) Bobby, Jason
(C) Bobby, Puja
(D) Arjun, Bobby, Jason
(E) Bobby, Puja, Jason

***

Read the below if you have no idea how to set up this game, and you want a hint.

Make the deities your "base" - not the students. This will allow you to make inferences more easily.

***

The text below contains the answers to the above Logic Game.

1. B
2. E
3. D
4. C
5. E
6. C
7. D
8. D

***

See my explanation and diagrams of this game in Logic Games Matching Diagram | Explanation.

***
If you want to try several LSAC-written Logic Games that are similar to the one above, check out the 4th category of games in 7 LSAT Logic Games That Repeated on Future PrepTests.

Photo by pingu1963

Reading Comprehension Questions | Inference and Main Point

You've probably noticed much of the LSAT is about presenting simple things in a confusing way. The LSAT is all about hiding what's staring you right in the face. Reading Comp is no different.

If you've done more than a few Reading Comp passages, you've probably noticed by this point that RC passages tend to have a few of the following:

-main point/main idea questions
-primary purpose/function questions
-inference questions

This blog post will give a few quick tips on main point and primary purpose/function questions. I'll then go into detail with some tips for the more difficult types of RC inference questions.

Main Point Questions
Most of the time, these questions ask about the author's viewpoint or whichever viewpoint is given more attention and space in the passage.

In other words, this is often the aspect of the topic covered in the majority of the passage, not only in one paragraph. LSAT-takers often fall for choices that describe specific parts of the passage, rather than the majority of the passage.


Primary Purpose/Function Questions
These questions are very similar to main point questions. The difference? The answer choices are worded a bit more generally. In other words, they use more abstract language. Pay very close attention to the verbs used in each answer choice.


Inference
Inference questions don't actually ask for new information. They'll often require you to take the contrapositive of something in the stimulus or passage or to simply connect different parts of what's already there. This means you simply have to read a little deeper into relevant lines of the passage. Reading "between the lines" can obviously be difficult to do, but there's a common "trick" LSAC often uses in more difficult RC inference questions.

For these questions, the passage gives you the information you need (as it does for all inference questions). However, the passage simply presents this info in a way that makes it difficult to see and extract this info. This information is presented indirectly. The passage tells you something the author (or a person within the passage) doesn't believe. As a result, if you read carefully, you'll indirectly learn about what the author (or person within the passage) does believe.


Example #1:
PrepTest 37, Section 1, Question 19 (page 292 in "Next 10").

The passage describes Ellison's views on the audience's relationship to works of art by describing his criticism of an opposing viewpoint.

What do I mean by this? I mean that it describes Ellison's interpretation of the criticisms, and then it says Ellison doesn't like these things.

In lines 20-28 of the passage, Ellison says the critics' view makes "the narrow assumption that audiences are capable of viewing the world only from their own perspectives."

If Ellison considers their opinion to make a narrow assumption, then Ellison must disagree with this narrow assumption and whatever directly follows from it.

If the critics think audiences can't view the world from other perspectives, Ellison must think audiences are capable of viewing the world from other perspectives. In other words, as we see in choice C, "audiences have the capacity" to view the world from another perspective (or "appreciate" different art).


Example #2:
PrepTest 36, Section 2, Question 11 (page 265 in "Next 10").

"Would be most likely to agree" means they're asking another Inference question. The passage in full of info about Binns' opinions, so there's no need to guess at what Binns "might" think.

In lines 33-37 of the passage, Binns says the scholars treat the writings as "an autonomous and coherent whole, underestimating the influence on English writers..."

Binns believes these scholars underestimate the influence on English writers, so we can conclude Binns does not actually believe these writings are an autonomous and coherent whole. If Binns thinks they're not as simple and clear as the scholars have implied, Binns must think they're actually more complicated.

In other words, as choice C suggests, Binns thinks these scholars have done a "superficially coherent reading."


Example #3:
PrepTest 35, Section 2, Question 26 (page 235 in "Next 10")

This example isn't quite the same as the other 5, but I included it simply because it's a good opportunity to demonstrate another way LSAC masks content. In this passage, LSAC tells us about legal positivism in the middle of presenting Dworkin's opinion.

The legal positivists believe laws' meanings are all about judges' interpretations of the law. Paragraph 2 talks a lot about legal positivists' belief in "underlying convention," so you could potentially answer the question o n the basis of that paragraph. However, LSAC's trick is to tell what legal positivists most clearly believe in lines 45-49 through Dworkin's eyes.

In order to learn what the legal positivists themselves believe, we need to put aside Dworkin's opinions and focus on the views of the legal positivists themselves. If we ignore Dworkin for a moment and focus on legal positivism itself, we'll learn they're focused on meaning as convention, rather than innate (core) meaning, so choice D fits.


Example #4:
PrepTest 29, Section 2, Question 10 (page 26 in "Next 10")

The people with the view in lines 51-54 believe "the attempt to write down traditional languages is misguided and unnecessary." To phrase this in a positive form, we can describe their viewpoint by saying they believe traditional languages will be okay even if we don't write them down.

As choice A suggests, they believe the languages will survive without being written down.


Example #5:
PrepTest 22, Section 1, Question 15 (page 121 in "10 More")

In lines 49-52, we learn the "anti-objectivist" personal narrative can bridge the gap between those who are "legal insiders" and people excluded from legal discourse and the accompanying power.

In these lines, we're indirectly learning legal insiders have the power, so choice B fits.


Example #6:
PrepTest 19, Section 3, Question 6 (page 29 in "10 More")

Lines 45-50 describe P.D. James' "determination to leave areas of ambiguity...and to distribute guilt..." as a "conscious rebellion against the traditional neatness of detective fiction."

By describing P.D. James' crime novels in contrast to the norm, the author of the passage tells us traditional detective fiction doesn't leave areas of ambiguity or distribute guilt. Thus, choice D fits because it describes the neatness of detective fiction with a synonymous statement: "straightforward assignment of culpability for the crime."

Photo by maynard / CC BY-NC-SA 2.0

Free LSAT Logic Game | Grouping: Selection / In-Out

I've enjoyed forcing you to think about a spaceship with 8 monkeys and 7 Greek deities in a power struggle as you completed my first two LSAT Logic Games.

However, it's time to get back to the real world, at least for a little while, so the Logic Game I've written for this week has a more standard topic.

Please post your thoughts and questions in the comments!

***
Here's this week's Logic Game:

On Wednesday, a legislator remembers that she must vote on seven bills-defense, environment, free trade, gun control, health care, immigration, and judicial activism-by the end of the week. Because the legislator wants to align herself with a major political party, she will vote on the seven bills in accordance with the following conditions:

She votes for the gun control bill only if she votes against the environment bill.
Unless she votes against the judicial activism bill, she will vote for the immigration bill.
She will vote for either the environment bill, the judicial activism bill, or both.
She votes for the gun control bill if she votes for both the health care bill and the defense bill.

1. Which one of the following could be a complete and accurate list of the bills the legislator votes against?

(A) free trade, gun control, immigration, judicial activism
(B) defense, free trade, gun control, health care, immigration
(C) free trade, health care, immigration, judicial activism
(D) environment, gun control, health care, judicial activism
(E) defense, environment, gun control, health care


2. If the legislator votes against the judicial activism bill, then which one of the following CANNOT be true?

(A) She votes against both the defense bill and the gun control bill.
(B) She votes against both the gun control bill and the health care bill.
(C) She votes for both the health care bill and the defense bill.
(D) She votes for both the health care bill and the environment bill.
(E) She votes for both the environment bill and the free trade bill.


3. Which one of the following CANNOT be true?

(A) The legislator votes for neither the gun control bill nor the immigration bill.
(B) The legislator votes for neither the environment bill nor the immigration bill.
(C) The legislator votes for neither the gun control bill nor the health care bill.
(D) The legislator votes for neither the health care bill nor the free trade bill.
(E) The legislator votes for neither the free trade bill nor the immigration bill.


4. If the legislator votes against the immigration bill, then which one of the following is the minimum number of the seven bills she must also vote against?

(A) one
(B) two
(C) three
(D) four
(E) five


5. If the legislator votes for the gun control bill, then which one of the following must be true?

(A) She votes for the health care bill or the defense bill.
(B) She votes against the health care bill or the defense bill.
(C) She votes against the judicial activism bill.
(D) She votes for the immigration bill.
(E) She votes against the immigration bill.


6. If the legislator votes against the judicial activism bill, then each of the following could be true EXCEPT:

(A) She votes against the health care bill and the defense bill.
(B) She votes for the health care bill and the defense bill.
(C) She votes against the health care bill and the gun control bill.
(D) She votes against the free trade bill and the gun control bill.
(E) She votes for the environment bill and the free trade bill.


7. Suppose the condition is added that if the legislator votes for the free trade bill, then she will vote against the judicial activism bill. If all other conditions remain in effect, then each of the following must be true EXCEPT:

(A) If she votes for the free trade bill, then she votes against the gun control bill.
(B) If she votes against the environment bill, then she also votes against the free trade bill.
(C) If she votes against the immigration bill, then she votes for the free trade bill.
(D) If she votes against the judicial activism bill, then she also votes against the gun control bill.
(E) If she votes against the immigration bill, then she also votes against at least three other bills.


The text below contains the answers to the above Logic Game.

1. E
2. C
3. B
4. C
5. D
6. B
7. C

***

See my tips on how to solve this game in Logic Games Selection | In-Out Diagram Explanation.

***


If you want to try several LSAC-written Logic Games that are similar to the one above, check out the first category of games in 7 LSAT Logic Games That Repeated on Future PrepTests.

The 3rd game listed in 10 Hardest Logic Games is a similar Grouping: Selection / In-Out game as well.

Photo by rexandsharkey / CC BY 2.0 (from the Schoolhouse Rock song "I'm Just a Bill")"

Free LSAT Logic Game | Advanced Linear

I promised that my future Logic Games wouldn't be as easy as the Basic Linear game I wrote last week. (Yes, I know that game had a twist aside from the variables' names. Gotcha!)

Well, I've kept that promise. The Logic Game I created for this week is significantly harder than last week's, and that's not only because it's an Advanced Linear game. In fact, some Advanced Linear games are easier than Basic Linear games.

Of course, it's best to practice with actual LSAT Logic Games. However, some of you are concerned about running out of Logic Games in your prep (despite the fact that there are over 60 released LSAT PrepTests). Maybe you haven't ordered your LSAT books yet, don't have them with you at work, or maybe you just can't take out your LSAT books with coworkers and bosses watching.

Also, I enjoyed writing last week's Logic Game and reading your responses, so I've decided to write a Logic Game based on each of the major types of Logic Games. I'll post them on the blog over the next few weeks, along with more LSAT tips, of course.

Check out my categorization of LSAT Logic Games for info on the various types of Logic Games.

You can now see a complete explanation for the below Logic Game's setup.

***
Here's this week's Logic Game:

Eight monkeys-A, B, C, D, E, F, G, and H-ride a spaceship to Mars together. Each monkey sits in a different one of the spaceship's eight seats. The seats are in consecutive rows that are numbered 1, 2, 3, and 4 from front to back. Each row contains exactly two seats: a seat with a window facing the sun and a seat with a window facing the moon. The following conditions must apply:

E's window never faces the sun, but D's window always faces the sun.
F sits in row 1 or row 2, but neither row 2 nor row 3 can contain D.
B sits in the row immediately behind D's row.
If B's window faces the sun, then A's window faces the moon.
If D sits in row 1, then G sits in row 4.
If B sits in the same row as F, then G's window faces the sun.

1. Which one of the following could be an acceptable assignment of monkeys to seats, beginning with the seats in each row whose windows face the sun?

(A) Row 1: D, C; Row 2: B, F; Row 3: A, E; Row 4: G, H
(B) Row 1: D, E; Row 2: F, B; Row 3: H, A; Row 4: C, G
(C) Row 1: D, F; Row 2: B, A; Row 3: G, E; Row 4: H, C
(D) Row 1: D, H; Row 2: C, B; Row 3: F, A; Row 4: G, E
(E) Row 1: D, F; Row 2: B, E; Row 3: C, A; Row 4: H, G


2. If E sits in row 2, which one of the following is a complete and accurate list of monkeys, any one of whom could be among the monkeys who sit in row 4?

(A) A, G, H
(B) C, G, H
(C) A, C, F, H
(D) A, C, G, H
(E) A, C, F, G, H


3. If F's window faces the moon, but F does not sit in row 1, which one of the following CANNOT be true?

(A) A's window also faces the moon.
(B) C's window also faces the moon.
(C) E's window also faces the moon.
(D) G's window also faces the moon.
(E) H's window also faces the moon.


4. If G and H sit in the same row, each of the following could be an accurate list of monkeys whose windows face the moon from row 1 through row 4 EXCEPT:

(A) F, A, E, G
(B) F, E, A, G
(C) E, F, A, H
(D) F, B, E, H
(E) F, C, E, G


5. If A's window faces the sun, but F does not sit in row 1, which one of the following could be true?

(A) C and G sit in the same row.
(B) A and B sit in the same row.
(C) A and F sit in the same row.
(D) E's window faces in the same direction as G's.
(E) G's window faces in the same direction as B's.


6. If B's window and F's window face in opposite directions, which one of the following could be true?

(A) G's window faces the moon, and F sits in row 2.
(B) F sits in row 2's seat with a window facing the moon, and A's window faces the sun.
(C) D and F sit in the same row.
(D) G sits directly in front of H.
(E) F sits in row 2, and E's window faces the same direction as G's window.


The text below contains the answers to the above Logic Game.

1. E
2. D
3. D
4 .E
5. A
6. C

***

You can now see a complete explanation for this Logic Game's setup.

***

If you want to try an LSAC-written Logic Game that's similar to the one above, check out:

PrepTest 36, Section 4, Game 3 (page 280 in The Next 10 Actual, Official LSAT PrepTests).

I included that game in the "10 Hardest Logic Games" blog post.