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Objection’s LSAT Tips – “Level Ordering” Games

Question Type: Leveled Ordering Games
Section:
Logic Games

Introduction

Our last type of ordering game is the leveled ordering game. Success on leveled ordering games requires the same clear and neat diagrams and game-breaking inferences that are required on all logic games. However, leveled ordering games have more than two sets of variables, making the construction of diagrams much more difficult.

Method

The difference between multiple sets of independent variables and variables with distinguishing factors is best illustrated rather than explained. Take the following setup:

Five chimps – F, G, H, I, J – and four gorillas – L, M, N, O – are assigned to a row of nine cages numbered 1-9.
A chimp cannot be in cage four.
No two gorillas can be caged next to each other.

Your diagram would be: Chimp/Gorilla _ _ _ _ _ _ _ _ _
                                                             1 2 3 4 5 6 7 8 9

The above case is relatively simple to diagram, even though it does have three sets of variables (cages, gorillas, and chimps).

Now let’s introduce a few additional rules which add further distinctions:

Each primate is a baby or an adult.
Four of the primates have tan fur, three have black fur, and two have red fur.

You now need to add additional rows for fur color and life stage:

Fur Color     _ _ _ _ _ _ _
Life Stage   _ _ _ _ _ _ _
Ape             _ _ _ _ _ _ _
                   1 2 3 4 5 6 7

On the other hand, the following setup is an example of multiple independent variables:

A summer camp is 8 weeks long. Each week, the campers at the camp perform one of eight physical activities and play one of eight board games.

In this case your diagram would look something like: 

PA _ _ _ _ _ _ _ _
BG _ _ _ _ _ _ _ _
      1 2 3 4 5 6 7 8

Otherwise, solve these like you would solve the other ordering games. Inferences and clear diagrams rule the day.

Example

Three boys – A, B, C – and three girls – X, Y, Z – are forming a three week study group. Each week involves three pairs of children – one boy and one girl – studying together, according to the following conditions:

A studies with Y in either week one or week two.
Whoever studies with X in week two must study with Y in week three.

No two children can study together in more than one week.

Let’s think first of how we should diagram this game. The weeks should form the base (on the x-axis) as they have an inherent sense of order. We can put either the girls or the boys on the y-axis. You can work with it either way, so let’s just pick the girls. Here is what your base diagram, before adding any rules, should look like:


 






Let’s analyze the rules and fill out our diagram before we jump into the question. A having to study with Y in either week one or week two means Y is studying with either B or C in week three. This means that B or C must study with X in week two because of the second rule.

Those inferences are fairly simple. There is one more major inference that is a little harder to see. Before I tell you, try to figure it out yourself.

If you figured it out – fantastic! If not, don’t feel bad.

The key inference is that the person who studies with X in week two (and with Y in week three) must also study with Z in week one because everyone must study with each person exactly once. For example, say that B studies with X in week two. By rule two, B studies with Y in week three. B has to study with Z at some point, and since he can’t study with two people in the same week, B studies with Z in week one.

This rule breaks the game wide open, as you will soon see.

Here is my final diagram:










In the explanations that follow, the circled numbers will be referred to as DR# (diagram rule [number]). For example, the rule above that A studies with Y in either week one or two will be referred to as DR1. Let’s get to it.

1. If C studies with X in week 2, which one of the following could be true?

A) A studies with Z in week 1.
B) B studies with Y in week 2.
C) B studies with Y in week 3.
D) C studies with Y in week 1.
E) C studies with Z in week 3.

How to Solve: Inference plus Mini-Diagram plus Process of Elimination

Draw a mini-diagram next to this problem. And remember, “could be true” means the wrong answers must be false. It’s always quicker to identify the “must’s” than the “could’s”.

If C studies with X in week two, then C studies with Y in week three (DR3) and Z in week one (DR4).

A – Must be false. Violates DR4.
B – Correct.
C – Must be false. Violates DR3.
D – Must be false. C is studying with Z in week one.
E - Must be false. C studied with Z in week one and can’t study with someone more than once.

2. If Y studies with B in week three, which one of the following is a complete and accurate list of the girls any one of whom could study with C in week one?

A) X
B) Y
C) Z
D) X, Y
E) X, Z

How to Solve: Inference plus Mini-Diagram

Jot down a quick diagram for this question as well. If B studies with Y in week three, then B also studies with X in week two (DR3), and with Z in week one (DR4). That leaves X and Y as the only people with whom C could study in week one.

This is answer choice D.

3. If C studies with Y in week one, which one of the following is a pair of children who must study together in week three?

A) A & X
B) A & Z
C) B & X
D) B & Z
E) C & Z

How to Solve: Mini-diagram plus Inference

If C studies with Y in week one, B studies with Z in week one (remember DR4 which means that B/M must study with Z in week 1). This means A studies with X in week one and with Y in week two (DR1). Since X studied with A in week one and Y studied with A in week two, A and Z must study together in week three.

This is answer choice B.

It’s interesting to note that you can fill out the entire diagram just from the one piece of information given in this question (C and Y studying together in week one).

4. If B studies with Y in week two, which one of the following is a pair of children who must study with each other in week one?

A) A & X
B) A & Z
C) B & X
D) B & Z
E) C & X

How to Solve: Mini-diagram plus Inference

This is virtually identical to the previous question.

If B studies with Y in week two, that means C studies with X in week two, and consequently with Z in week one (DR4). Since A must study with Y in week one or two, and Y is booked in week two, Y must study with A in week one. This is not an answer choice, however. Thankfully, this game resembles a simple sudoku and you can, again, fill in the entire diagram. Eventually you’ll see that in week one, since Y studies with A and C studies with Z, B must study with X.

This is answer choice C.

5. If C studies with X in week one, which one of the following must be true?

A) A studies with X in week two.
B) A studies with Y in week three.
C) A studies with Z in week one.
D) B studies with X in week two.
E) B studies with Z in week three.

How to Solve: Mini-diagram plus Inference

If C studies with X in week one, B must study with Z in week one, which means that A studies with Y in week one. None of these are answer choices. Let’s move to week two. Because of DR4, B must study with X in week two.

This is answer choice D.

Again, you could fill out the entire diagram here. Of course, once you find the answer you should simply move on.

Final Notes

As you can see, the DR4 inference was key and made this game relatively simple. The two main issues with leveled ordering games are time and making a useful diagram. The best thing you can do is familiarize yourself with as many games as possible. Always strive to create the most efficient diagram possible. With good diagrams comes speed. Don’t be too worried if you’re just starting out and this game type takes you longer than others.

As always, hit the forums for more: 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

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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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