Lesson Nine: Logical Reasoning and Logic Games

Question 1

– LOGICAL REASONING –

Question 2

LSAT test makers use to their advantage a number of widely-accepted _________________ regarding ______________ and _____________ against test takers that you need to be aware of (namely 7)

Answer 2

misconceptions; numbers; percentages

Question 3

Misconception #1:
Increasing percentages leads to increasing numbers.

Answer 3

Just because the percentage (of a given group of things in discussion) increases, does not mean that the numbers related to those percentages should have also increased.

Ex. Percentage of DUI related car crashes has increased from last year (10%), to this year (30%).

Imagine that the number of DUI related car crashes last year was 50, and this year is 20.

Perhaps the number of DUI related crashes went down as the number of all different car crashes went down, and DUI’s happen to be the larger portion of all crashes.

Question 4

Misconception #2:
Decreasing percentages leads to decreasing numbers.

Answer 4

Opposite Misconception #1.

Just because the percentage (of a given group of things in discussion) decreases, that does not mean the number of things related to that percentage also decreases.

Ex. Let’s take the car crash example again and simply reverse it.

• The percentage of DUI related car crashes decreased from 30% last year, to 10% of all crashes this year.
• Now let’s say the NUMBER of DUI car crashes during last year was 20, and this year was 50.
• The reason we have a greater NUMBER of DUI crashes yet a lower PERCENTAGE is that other types of car crashes increased along with DUI cases, but the other types of crashes increased more, and so DUI cases make up a smaller slice of the pie.

Question 5

Misconception #3:
Increasing numbers lead to increasing percentages.

Answer 5

This reverses the elements of the first two misconceptions.

Just because the number increases does not mean the percentage increases.

Ex. Let’s try a road accident example.

• The number of bicycle-related accidents has increased from 10 last year, to 30 this year.
• The number of total road-related accidents has increased from 100 last year, to 600 this year.
• Yet, the percentage of all bicycle - related accidents has decreased from 10% to 5%.
• We saw an increase in numbers, but not percentages, and this is because All types road related increased increased in number by 500. So while all types of road accidents had this huge increase, bicycle related accidents increased, but not as nearly as much, and so that’s going to be reflected as a significantly smaller percentage (slice of the pie).

Question 6

Misconception #4:
Decreasing numbers lead to decreasing percentages.

Answer 6

Opposite Misconception #3:

Just because the number decreases does not mean the percentage of those things decrease.

• let’s take the road accidents example and reverse it.
• Number of bicycle related accidents decreased from 30 last year to 10 this year.
• Number of total road-related accidents decreased from 600 last year to 100 this
  year.
• Percentage of bicycle related accidents increased from 5% to 10%.
• There’s a decrease in numbers and an increase in percentage because all types of road accidents have decreased by 500 in number, while bicycle related accidents only decreased by 20 in number, as so that decrease is going to be reflected as a larger slice of the pie because they didn’t face near the decrease all other types of road accidents did.

Question 7

Misconception #5:
Large numbers automatically means large percentages.

Answer 7

Just because you have a large number, doesn’t mean the percentage that large number constitutes is also large.

Ex. in 2017, Mercedes Benz sold 55,000 vehicles. 55,000 is a large number (nothing to be overlooked), yet that amount of car sales only made up 1/3 of 1% of all car sales that happen in 2017 (the total amount of car sales that year ended up being around 17 million).

Question 8

Misconception #6:
Large percentages mean large numbers.

Answer 8

Large percentages do not automatically translate to having large numbers.

Just because you have large percentages does not mean you have large numbers.

Ex. 90% sounds like a quite large percentage. But 90% of $5, is not going to be a very large number.

Question 9

Misconception #7:
Seeing reports of something and saying it corresponds to the overall number of occurrences of that thing.

Answer 9

Just because one thing, that is apart of family of things, occurs does not mean all things within that family correspond to the occurrences of that thing.

• Ex. “Violent crime in this town is becoming a serious problem. Compared to last year, local law enforcement agencies have responded to 17 percent more calls involving violent crimes, showing that the average citizen of this town is more likely than ever to become a victim of a violent crime.”

Which one of the following, if true, most seriously weakens the argument?

Between these two answers, which one do you think is right (and for what reasons), and which one commits the misconception (explain how it commits the misconception).

(B) In general, persons under the age of 65 are less likely to be victims of violent crimes than persons over the age of 65.

(C) As a result of the town’s community outreach programs, more people than ever are willing to report violent crimes to the proper authorities.

Answers:
(B) is wrong, and follows the misconception of seeing a report of something and saying is corresponds to the overall number of occurrences of that thing.
- 65 year old people are simply one class of people from the family that is “average citizens,” and this answer choice.

If we prephrase, we quickly realize the author is taking the increase in the number of calls to be consistent with a corresponding rise in crime. So, a weaken answer is one that shows the calls increasing without the crime increasing, and C was the closest answer choice to that.

Question 10

You will see _____________ and ______________ in several if not most logical reasoning stimuli, so when you do, use knowledge of these _______________ to your advantage. Remember, the presence of ______________ and ______________ doesn’t take away from the fact that you’re still dealing with all the different question types you’ve encountered before (Must Be True, Must Be False, EXCEPT, strengthen, weaken etc…). So when this happens, use the same approach to these problems as you normally would, coupled with your knowledge on these ______________.

Ex. When attacking a Must Be True question, what test do we use to find the correct answer choice: ___________ ____________.

Ex. When finding the incorrect answer to a Must Be True question, we’re looking for answers that are…
- an _____________
- ______ __________
- ___________
- ___________

Answer 10

numbers; percentages; misconceptions; numbers; percentages; misconceptions; Fact Test; exaggeration; new info; reverse; opposite

Question 11

– LOGIC GAMES –

Question 12

Numerical Distributions

Answer 12

Numerical distributions are made by distributing one variables set over another.

(Numerical distributions usually take place with 2 variables sets only).

Question 13

What is the “one-to-one” distribution?

Answer 13

when the number of variables (being allocated) = the number of slots available.

Ex.
“During a period of 6 consecutive days–Monday through Saturday–each of exactly six stores – B, C, D, E, F, G, and H will be reviewed. During this period, each of the stores will be reviewed exactly once, one store per day.”

• Each store is reviewed once, one store per day; so it’s quite easy to see the distribution here is 1-1-1-1-1-1.
• The Receiving variable set will be the 6 days (serving as the base; inherent order)
• The allocated variable set will be the six stores being reviewed : B, C, D, E, F, G, H

Question 14

Most distributions are easy-to-understand and can be recognized fairly quickly without the need to write them down (specifically, one-to-one distribution). But, there will be games that present more _____________ situations in which you need to understand how to make these new distributions.

Answer 14

complex

Question 15

Try an example problem:

“An office complex has 6 available offices spread over four different floors of the building. Each floor has either one or two available offices.”

Identify your receiving variable set /base.

Identify the variable set being placed in the receiving variable set.

Answer 15

The 6 available office spaces will be distributed across the four floors. So the 4 floors is your receiving set.

F1 F2 F3 F4
__ __ __ __

The six office spaces are the allocated variable set, we were told there will either be 1 or 2 offices on each floor. So we need a distribution of 1 office and 2 offices on each floor that will total the 6 minimum.

F1 F2 F3 F4
__ __ __ __ =
1 1 1 1 4

right now we have a minimum of four, we need more office spaces. And remember the rules. WE CAN ONLY HAVE ONE OR TWO OFFICE SPACES ON EACH FLOOR.

So the only thing we can do is distribute the 2 remaining spaces among the floors.

F1 F2 F3 F4
__ __ __ __ =
1 1 1 1 4
2 2 1 1 6

(2-2-1-1)

Question 16

Numerical Distributions follow these 2 rules:

1) The numbers add up to an amount equal to the total number of variables in the set being allocated.

• Let’s break it down: The numbers in your distribution should total to the number of things in your allocated variable set (ex. 2-2-1-1 = 6; 6 office spaces in the allocated variable set).

2) The number of separate numbers is equal to the number of elements “receiving” the allocated set.

• Let’s break it down: Basically, how many numbers you have in your distribution is equal to the number specified in the receiving variable set. (ex. 2-2-1-1 is 4 numbers; 4 floors in the receiving set).

Question 17

The set of variables being _____________ amongst another set is oftentimes ____________ than the _______________ set.

Answer 17

allocated; greater; receiving

Question 18

Fixed vs. Unfixed Distributions

Answer 18

Unfixed Distribution: When the variables can move around freely in the distribution; when the receiving set is not assigned specifically to the variables from the allocated variables set.

Ex. Six reviewers will review four restaurants. Each reviewer reviews exactly one restaurant, and each restaurant is reviewed by at least one of the six reviewers.
RA RB RC RD
__ __ __ __ =
1 1 1 1 4
3 1 1 1 6
2 2 1 1 6
(The variables can move around anywhere in the distribution)

Fixed Distribution: when the variables CANNOT move around freely in the distribution; the receiving set is assigned to one of the variables from the allocated variable set.

Ex. Six reviewers will review four restaurants. Each reviewer reviews exactly one restaurant, and each restaurant is reviewed by at least one of the six reviewers.

Now let’s add a rule: “Restaurant A must be reviewed by exactly twice as many reviewers as B.”
- This rule FIXES the distribution such that whatever numerical amount represents B’s allocated variable cannot move.

RA RB RC RD
__ __ __ __ =
1 1 1 1 4
3 1 1 1 6
2 2 1 1 6

The distribution here would HAVE TO BE: 1-2-2-1, or 1-2-1-2
2 remaining reviewers

Question 19

3 Steps to Creating Distributions Systematically:

Answer 19

1) Fulfill minimum requirements for receiving set.
2) Examine the remaining extra variables, figure out how many configurations can be made.
3) Show the other distributions that can be made using the minimum requirements.

Question 20

Try an example problem:

“Seven shrubs are planted at three buildings – a school, a town hall, and a post office. At least one shrub must be planted at each building, and the post office receives exactly twice as many shrubs as the school.”

• Identify what type of Distribution it is; fixed or unfixed
• Identify your receiving set
• Identify your allocated set
• Create all possible distributions

Answer 20

Distribution Type: Fixed (last sentence)

Receiving Set: S T P

Allocated Set: Seven Shrubs

1) Fulfill Minimum Requirements: (2:1 relationship has been created between P and S)
S T P
__ __ __ =
1 1 2 4
2) Identify Extra Variables: 3 remaining variables; there are 2 possible configurations left.
1 4 2 7
2 1 4 7

3) Show the possible distributions using the minimum requirements.

     S  T  P
    \_\_ \_\_ \_\_ = 
     1  1  2    4 ---------------------------
     1  4  2    7
     2  1  4    7

Question 21

Try an example problem:

Game #1: October 2001 Questions 6-12

A showroom contains exactly six new cars–T, V, W, X, Y, Z–each equipped with at least one of the following three options: power windows, leather interior, and sunroof. No car has any other options. The following conditions must apply:

V has power windows and a sunroof.
W has power windows and a leather interior.
W and Y have no options in common.
X has smore options than W.
V and Z have exactly one option in common.
T has fewer options than Z.

Identify what type of distribution it is; fixed or unfixed
Identify your receiving variable set / base
Identify your allocated variable set.
Create your distributions

Answer 21

Distribution Type: Unfixed

Base: T, V, W, X, Y, Z

Allocated Variable set: P, L, S

T V W X Y Z
__ __ __ __ __ __ =
1 1 1 1 1 1 6

                        S
     S        L       L              L (PLS) P        P      P       S    S/P \_\_     \_\_      \_\_\_    \_\_\_   \_\_\_   \_\_\_ T       V       W       X      Y     Z (1)                                 b
                                  l
                                 o
                                 c
                                 k
                                 e
                                 d

Question 22

Limited Solution Set Games

Answer 22

Games in which the possibilities are limited / restricted by the rules to only a few limited solutions.

Question 23

How to Identify a Limited Solution Set Game:

In Limited Solution Set games there will be a controlling _________ or a set of _________ that affects certain areas of the game in such a way as to suggest that only a _______ options are presented.

This can either come in the form of a…
1) Limiting principle (e.g. like a numerical _____________ that is _________ where “x has exactly 2 more shrubs than y.”)

OR

2) Odd block rule, that is so odd that it configures the variables in the diagram in a very _____________ way, such that one variable may not be able to be placed anywhere else.

Answer 23

rule; rules; few; distribution; fixed; limiting

Question 24

2 Different Ways to Attack Limited Solution Set Games

Answer 24

1) Identify the Templates
2) Identify the Possibilities

Question 25

Identify the Templates

Answer 25

Way of solving Limited Solution Set games where a major component of the game is limited by the rules, restricting them to 2 or 3 options.

In this case you would diagram those 2 or 3 possibilities separately on different templates, showcasing the major possibilities BUT NOT THE EXACT POSSIBILITIES.

Question 26

Identify the Template should only be used in games with ___ or fewer major directions.

Answer 26

4

Question 27

Identify the Possibilities

Answer 27

Extension of Identify the Templates where instead of diagram the major possibilities, it goes a step further and diagrams the exact possibilities (which is considerably more time consuming).

This is more time consuming because here, full, exact determinations are being made unlike the Identify Templates attack, where only the major direction of the game is diagrammed.

Question 28

Identify the Possibilities techniques should only be applied to games with _______ or fewer possibilities.

Answer 28

8