LSAT Analytical Reasoning 4 – Grouping Game

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The following is a free explanation of a Grouping Game. This game can be found as the fourth game in the LSAT Analytical Reasoning Section 1 from the June 2007 exam. If you have not already done so complete the Grouping Game Tutorial before completing this game.

STOP Before you read this get your self a copy of the June 2007 LSAT and do the Analytical Reasoning section. (Free Copy of June 2007 LSAT Here) Then come here for the explanation of how to do the games. Book mark this page and come back when you have completed the June 2007 games section. Click here for some tips on making the most of your practice LSATs.

OKAY – so you have completed the Analytical Reasoning section of the June 2007 LSAT on your own. Now here is a full set of explanations for you to practice from.
If you’re looking for more lessons and explanations try some free LSAT Video Lessons

At the top of the first page of Section one of the June 2007 LSAT you find the title Directions with an explanation of how to do this section. You should read and understand this now but DO NOT read it during the actual LSAT. The directions do not change and this is a waste of 30 seconds. It may not seem like much but in the end it could mean the difference between getting one more question right or one more wrong; and this could mean the difference between getting into your law school of choice or not. Read it now, read it tomorrow but DO NOT read it on the actual LSAT.

Let’s go on to the first game. Each game consists of an introductory paragraph, a set of rules and then a series of questions. As you read the introductory paragraph and set of rules you MUST summarize them all into a simple diagram and if necessary a few short hand rules on the side. We suggest a short hand for you to use here or you can develop your own, just make sure it is neat and easy to understand.

IMPORTANT – when you have completed summarizing the game and rules you must have included everything. You should not have to return to the rules or the introductory paragraph at any time when you are doing the questions. Your diagram and shorthand rules should give you all the information you need. If you find yourself returning to the game description you need to work on your diagram and shorthand rules notations.

Now let’s look at the introductory paragraph which describes the basic set up of the game. In this game we have three groups (the recycling centers) into which we have to place our entities. We have five types of entities to choose from (glass, newsprint, plastic, tin and wood). We call this type of game a [Grouping Selection] game.

Like all our games we start off by developing a master diagram and set of rules to include all the information from the introductory paragraph and rules.

The first piece of information we are given is the list of groups, or three recycling centres. This will be the start of our diagram:

1 2 3

Then we add our entities or materials to be recycled

G N P T W

1 2 3

IMPORTANT NOTE – We are told that EXACTLY FIVE kinds of materials will be recycled. This means that each completed diagram must include at least one of each of our entities: G N P T W. You cannot be missing one. This is very important to remember and is not the same as other games that say you can choose from five entities.

Next we are told the maximum and minimum number of materials that any one recycling center or group can include.

DIAGRAMMING TIP – Whenever you are given a maximum or minimum number of entities for a particular group you can express the minimum as a solid underline and the maximum as a dotted underline. This tells you that you must fill up the solid underlines with entities and you may fill up the dotted underlines.

G N P T W

1 2 3
___ ___ ___
___ ___ ___
_ _ _ _ _ _ _ _ _

Next we add our rules. Rule 1 tells us that any group that includes W must also include N.

G N P T W

1 2 3
___ ___ ___
___ ___ ___
_ _ _ _ _ _ _ _ _

if W then N

Rule 2 tells us that everything in group 2 will also appear in group 1. Note that this is not the same as group 1 and 2 being the same. Items in group 1 need not appear in group 2.

G N P T W

1 <= 2 3
___ ___ ___
___ ___ ___
_ _ _ _ _ _ _ _ _

if W then N

Rule 3 tells us that there is only one P and when there is P there is no G.

G N P T W

1 <= 2 3
___ ___ ___
___ ___ ___
_ _ _ _ _ _ _ _ _

if W then N
Only one P
If P then No G.

DIAGRAMMING TIP – in a game like this you have rules about where you can place many of your entities. Some entities have no rules about them. These entities are “free-floating” and can be placed anywhere in the diagram. It can often be helpful to circle these entities in your master diagram to remind you that they are free floating. In this game our free-floating entity is T. N is included in a rule but is essentially free floating as it can be placed anywhere, the rule only tells us that N is required whenever we have W.
What to do with our free-floating entities? They are the most flexible part of your game because they can go anywhere and you can use them in any group or as many groups as you want. It is often best to leave them until last when filling in your game diagrams. Use them to fill space in your game not otherwise filled with the other entities. Remember it is best to start with your least flexible rules and entities. Then when you have a spot that cannot be filled by another entity you can place your free-floaters there.

We now have our completed diagram with all of our rules included. From our last rule we also can add that there will be no Ps in group 2 because anything in group 2 also has to occur in group 1 and this would give us more than one P.

Question 18:

Like most games the first question is looking for a complete and accurate set of entities. We can completed this question quickly by applying each rule to the answer choices and crossing off an answer choice that violates the rule. We will be left with only the correct answer choice.

Apply our rule if W then N. (A) violates this rule as there is a W with no N in center 3.

Apply the rule that everything in 2 must also be in 1. (C) violates this rule.

Apply the rule that there is only one P and when we have P there is no G in that group. (D) and (E) violate this rule.

We are left only with (B) our correct answer choice.

Question 19:

This question asks us which centers could be the one to recycle P. Whenever you have a question that mentions an entity in particular it is a good idea to look first to any rules that include that entity. Here our rule with P is: Only 1 P & if P then No G.

Check each center or group to see if it can include P. We know from our answer in question 18 that P can be in center 3. Anything that is in group 2 must also be in group 1, so if we put P in center 2 then it must also be in group 1 but we can only have one P, therefore P can not be in group 2. Can P be in group 1? Try it.

G N P T W

1 <= 2 3
P W G
W N T
N

Our diagram here satisfies all of our rules and includes P in group 1. So P can be in group 1 or 3 but not 2. The only answer choice that reflects this is (D). (D) is our correct answer. How did we fill in this diagram? We wanted to check if P could be in group 1. Start by putting P in group 1. Then look to our rule about P. P cannot be with G. We need to have G somewhere but it cannot be in 1 or 2 (if it is in 2 then it must also be in 1). So we put G in 3. Then we need W somewhere and it will be accompanied by N. We try putting WN in 2 which means it will also be in 1. This works so far. Then we check our list of entities. There is only T left and we see that 3 has only one entity in it. It must have a minimum of two entities. Put T in 3. This completes our diagram and we have P in group 1.

Question 20:

This question does not explicitly ask for the answer choice that Must be True, but it is still a must be true question. We are asked which entity must be in group 3. The extra information given in this question is that there must be three entities in group 2. When you are given information about a particular group check any rules that relate specifically to that group and use it to plug in the extra information into your re-drawn diagram. Here our rule about group 2 tells us that any entity in group 2 is also in group 1. note that we can only have one P so P cannot be in group 2. This means P must be in group 3.

1 2 3
P

Also G cannot be with P so G must be in group 1 and 2. Remember that Group 2 has three entities in this question and they all must also be in group 2 because of our rules.

1 2 3
G G P

We could go on and try to fill out our entire diagram like this but it seems we already have our answer. Center 3 must recycle P. The correct answer is (C).

Question 21:

This is a Could be True question so we will test each answer choice to see if it can be true the one that can is our correct answer.

If we look at our answer choices they all ask if it could be true that Only a specific group includes a specific entity, meaning that this entity is not in any other groups. We know that any thing in group 2 must also be in group 1, and since all groups have 3 entities in this question it means that group 1 and 2 must be the same. Therefore, only group 3 could have an entity that does not appear in another group. This narrows our answer choices down to (B) and (D). Test each one.

First of all we must have P somewhere. We already know it cannot be in 1 and 2 as we can only have one P. P must be in 3. Also that means G must be in a different group and since 1 and 2 must be the same G is in 1 and 2.

1 2 3
G G P

Then we try to put N in group 3 and no other group.

1 2 3
G G P
N

We need two other entities to plug into 1 and 2. The only ones left are T and W, however, whenever we have W we must also have N. So this does not work. At this point we have eliminated all answer choices except (D) which is our correct answer. Here we show you why (D) could be true.

1 2 3
G G P
T

Now we have T in group 3 and we need to fill in two more entities in 1 and 2 and one more in 3.

1 2 3
G G P
W W T
N N N

W and N can go together in 1 and 2. And N can go in group 3.
Question 22:

Here we have another Must be True question. Start by plugging our extra information into our diagram and then fill in as much as we can by applying our rules.

1 2 3
G

We have placed G. Look at the rules that apply to G. We know that G and P can not be together so P must be in either 1 or 2, but P can only be in one group so it must be in 1 because anything in 2 must also be in 1.

1 2 3
P G

This question is asking us which entity must be in group 2. We know now that it cannot be P as there can be only one P and it cannot be G as that would also put G in 1 with P and G and P cannot be together. This narrows our options down to N, T or W leaving us with (B), (D) or (E) for possible answer choices.
Because this is a must be true question we will try to prove that each answer choice can be false.

(B)

Try to fill in the diagram without N in 2.

1 2 3
P G

We know that 2 cannot have P or G, it also now cannot have N, and if it has W it must have N so it cannot have W. This leaves us with only T. Each group must have a minimum of two entities so only T is not enough. Group 2 must include N. Therefore (B) is our correct answer.

For learning purposes the following diagrams show how 2 need not include T or W.

(D)

1 2 3
P W G
W N T
N

(E)

1 2 3
P T G
T N W
N N

Question 23:

For this question we are looking for a complete and accurate list of the entities that are found in any one group. Start by plugging in the information we are given and then applying our rules to put as many more entities into the diagram as possible. Then test each answer choice to see if it can be true.

1 2 3
W

It is given that W is in 1, and from our rules we know that W must be accompanied by N.

1 2 3
W
N

If this is all you see at this point you can stop here and test each answer choice. However, there is more that we can fill in. We know that every entity in 2 must appear in 1 and 2 must have a minimum of 2 entities and 1 an maximum of 3 entities. This means that since we already have 2 entities in 1 and there need to be at least 2 in group 2 that one of them must be the same as one of the entities already in 1. This entity cannot be W as our question tells us that 1 is the only group with W. Therefore 2 must include N and one other entity that will also appear in 1.

1 2 3
W N
N ___
___

Also we must have P somewhere and it cannot be in 1 and 2 as P can only occur once. P must be in 3. This also means that G must be in 1 and 2 as it cannot be with 3.

1 2 3
W N P
N G
G

Finally we need a T and the only spots left are in 3.

1 2 3
W N P
N G T
G (N)

Note that we could also include N in 3 but it is not necessary. Now we can test each answer choice to see which one could be a complete list of entities in any group.

Only answer choice (A) matches our completed diagram. P and T could occur in group 3. (A) is our correct answer.

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