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Objection’s LSAT Tips – Multiple Group Games

Question Type: Multiple Group Games
Section:
Logic Games

Introduction

Multiple group games are exactly what they sound like: games where you need to place variables into multiple (two or more) groups. It could be students to classes, researchers to research topics, monkeys to cages, or anything else the LSAC wants to dream up.

Like other game types, these can be “less” (e.g., four players for eight slots) or “more” (e.g., eight players for four slots). These can also be “stable” (i.e., the group sizes are known) or “unstable” (i.e., the group sizes are not known). An example of a stable game setup is “eight students will be separated into two, four-person classes.” An example of an unstable game setup is “eight students will be separated into three classes.” If you use PowerScore’s Logic Games Bible, you will recognize these concepts although under different, copyrighted names.

Method

A clean diagram is an absolute necessity here. You will be working with multiple variables (players and groups), and at times, you will be working with quite a few of each (it’s not unheard of for you to be required to put eight or more variables into four or more groups). You must stay focused and organized.

There are a few frequently appearing rules to be aware of in these types of games.

The first is the “must be together” rule. In this, certain variables must always be in the same group. For example, if a rule says, “F and G must study the same subject,” F and G must be together. This helps limit the number of variables, as F and G essentially become one variable (so long as neither is involved in another rule without the other).

Another rule that is similar, but not the same, is what we’ll call the “stalker” rule. This rule will look something like “If F studies Anthropology, G must also study Anthropology.” G is basically stalking F with respect to anthropology. But this does not mean that they always have to be together. Nor does it mean that F must study Anthropology if G studies Anthropology. You should diagram this relationship as follows:

F-anthro -> G-anthro

The contrapositive is:

~G-anthro -> ~F-anthro.

Be careful not to misinterpret the “stalker” rule or diagram it incorrectly, as it will likely cost you several questions.

It is also important to stay focused on the bigger picture. You don’t want to look at rules in isolation. You want them to relate them to the broad scheme of things. For example, if one rule says, “If F studies Anthropology, G must also study Anthropology,” and another rule says, “Only two people can study Anthropology,” then you should realize that if F studies Anthropology, no one else but G can also study Anthropology. So the answer to a question that says “If F studies Anthropology, which cannot be true” will likely be “<non-G variable> studies Anthropology.”

Beyond that, attack them like you should attack every other game: calmly, logically, and with a clear head.

Example Four different people – F, J, K, and M – will perform at least one and at most three of four activities – Q, W, X, and Z. They must perform the activities according to the following specifications:

Any activity performed by F is performed by J.
Any activity performed by K or M is not performed by F.
Exactly two people perform X.
Exactly one person performs Q.
Exactly two people perform W.
Exactly three people perform Z.

Take a second and spot as many inferences as you can. Fill in the diagram as much as you feel is possible. Done?

Here is the diagram I used to complete this game:









Diagram rules explanations:

DR1. Any activity performed by K is not performed by F.
DR2. Contrapositive of DR1.
DR3. Any activity performed by M is not performed by F.
DR4. Contrapositive of DR3.
DR5. Any activity performed by F is performed by J.
DR6. Contrapositive of DR5.
DR7. F cannot be grouped with K or with M, so F cannot be in group Z, as at least one of K or M must be there also (four variables for three slots, yet F can only be with J). This means that the three people performing Z are J, K, and M – the only three left after removing F from consideration.
DR8. Since F must bring along J (J is stalking F), F cannot be in group Q, since there is not enough room for J. We have established that F cannot be in group Z. Therefore, F can only be in group W or group X.

And those are the rules in a nutshell. Rules 7 and 8 are the big rules. They break this game wide open. If you didn’t get those, keep practicing.

1. If F performs exactly two activities, then which of the following could be true?

A) M performs Q.
B) M performs W.
C) J performs Q.
D) M performs exactly three of the activities.
E) J performs exactly two of the activities.

How to Solve: Narrow it Down

If F performs two activities, we know that they are W and X. That means J also performs W and X. Since one person can perform three activities at most, J cannot perform Q. We already know F cannot perform Q. That leaves either K or M to perform Q.

Answer choice A is the correct response.

You could also come to the correct answer by eliminating the incorrect answers:

B – Incorrect. F and J are taking up each spot in W.
C – Incorrect. J is already performing three activities and taking on a fourth would be a violation.
D – Incorrect. Two of the four activities are already taken up completely by F and J.
E – Incorrect. J is already performing Z and it must follow F to W and X as well.

2. If K performs three activities, then which one of the following must be true?

A) K performs X.
B) K performs Q.
C) K performs W.
D) M performs Q.
E) M performs W.

How to Solve: Locate the Violation

You should rarely use process of elimination on “must be true” questions except as a last resort.

If K performs three activities, what must be true? We already know that K must perform Z, and we know that K cannot be with F, and we know that F must be in W or X. Therefore, we can conclude that K can only perform one of W/X, which means her three activity breakdown is: Z, W/X, Q. K must learn Q.

This is answer choice B.

3. Each of the following could be true of the person who performs Q EXCEPT:

A) The person also performs X but not W.
B) The person performs neither X nor W.
C) The person also performs X but not Z.
D) The person also performs both X and Z.
E) The person also performs Z but not X.

How to Solve: Spot the “Must”

Remember, “could be true EXCEPT” questions are “must be false” questions.

The person who performs Q is J, M, or K. Therefore, the person who performs Q is also performing Z.

Answer choice Cviolates this deduction and is therefore the correct answer.

4. Each of the following could be a complete and accurate list of the people who perform both W and Z EXCEPT:

A) J
B) M
C) J, K
D) J, M
E) K, M

How to Solve: Locate the Violation

Again, do not use process of elimination. You’re looking for an answer choice that violates some sort of logical deduction based on your diagram.

Think about this: The question is asking about W and Z. This means F will likely have something to do with it, since W is one of only two places F can be. If M is performing both W and Z, then F must perform X (F cannot be with M), which means that either J or K must occupy the second spot in the W group. However, J and K also both perform Z, so M could not be the only one learning both W and Z.

B is the answer.

5. Which one of the following could be true?

A) K performs exactly three activities – Q, W, and X.
B) K performs exactly three activities – W, X, and Z.
C) J performs exactly three activities – Q, W, and X.
D) J performs exactly three activities – W, X, and Z.
E) M performs exactly three activities – Q, W, and X.

How to Solve: Process of Elimination

A – Incorrect. DR7 establishes K must perform Z.
B – Incorrect. DR8 establishes that F must be in W and/or X. DR1 establishes that F cannot be with K. K performing W and X leaves no room for F.
C – Incorrect. DR7 establishes J must perform Z.
D – Correct. This wouldn’t necessarily present any rules violations, and therefore could be true.
E – Incorrect. M must perform Z, and M performing both W and X leaves no room for F.

6. If J performs exactly two of the activities, then which one of the following must be true?

A) M does not perform Q.
B) F does not perform W.
C) K does not perform Q.
D) J does not perform Q.
E) M does not perform W.

How to Solve: Locate the “Must”

We already know that J must perform Z. We also know that J stalks F, so whatever F does J does. F can only perform W or X (no ‘and,’ in this case, because J can only perform one more activity since the question says only two activities are performed by J). Therefore, J performs Z and W/X.

So D must be true, since J cannot perform Q in this scenario.

7. Which one of the following must be true?

A) J performs fewer activities than M.
B) F performs fewer activities than J.
C) F performs fewer activities than K.
D) M performs fewer activities than K.
E) M performs fewer activities than J.

How to Solve: Locate the “Must”

This problem introduces no new information or rules. This means it can be answered solely on the basis of our original diagram. The question asks who will definitely perform fewer activities than someone else. No rules deal explicitly with that matter, but think about it: from the start, J, K, and M each are each performing one activity (Z), while F has none definite (although we know he must do at least one). Further, F always brings J. So J will always perform at least one more activity than F.

This is answer choice B.

It’s a bit like what many younger siblings say to their older siblings: “When I’m older than you, I’m going to <insert mean activity here>.” Of course, the younger sibling will never be older because they age at the same rate and the older sibling has a head start. F is J’s little brother.

Final Notes

The key to defeating this game was the clean diagram and the broad understanding of the rules. Do not isolate the rules other than to diagram them. Always think of the bigger picture. What are the repercussions of this rule? What restrictions does it bring? What does it allow and what does it not allow? What rules might I be able to combine it with?

As always: http://www.top-law-schools.com/forums/viewforum.php?f=6


Ken's Introduction to the LSAT

Conquering the LSAT

How I Scored a 180 - Article #1

How I Scored a 180 - Article #2

How I Scored a 180 - Article #3

Retaking the LSAT

Logic Fundamentals: A Lesson In Conditional Reasoning

Objection’s LSAT Tips – “Describe” Questions (LR)

Objection’s LSAT Tips – “Main Point” Questions (LR)

Objection's LSAT Tips - "Must Be True" Questions (LR)

Objection’s LSAT Tips – “Role” Questions (LR)

Objection’s LSAT Tips – “Level Ordering” Games

Objection’s LSAT Tips – “In/Out” Games

Objection’s LSAT Tips – “More/Less” Ordering Games

Objection’s LSAT Tips – Simple Ordering Games

Objection’s LSAT Tips – Multiple Group Games

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