The skills involved in tackling logic and reasoning problems include drawing well-supported conclusions, identifying and applying principles and definitions, determining if a scenario satisfies a set of characteristics, and making common-sense inferences from a set of facts.
A
portion of your police examination will assess your ability to process
information logically, to formulate an easily understood synopsis of a
situation, to correctly apply the formal
definition of a crime to different scenarios, and to
reason inductively and draw a plausible conclusion from a set of facts. The questions are based on short excerpts
from various sources, including case studies, newspapers, and informal
discourse.
Reasoning is the
process of using existing knowledge to construct viable explanations or
arguments, draw plausible conclusions, and make predictions. Logic can be viewed as the science of
reasoning. We review some essential
basics of logic, out of context, in this short section, and then dissect some of
the common types of problems you will encounter on the exam in the short
sections that follow.
The act of drawing conclusions from premises—information, facts, criteria, etc.—is called inference. For example, you see a large amount of water on the floor in the kitchen of a house and infer that either a pipe must have burst or the dishwasher malfunctioned.
The reasoning process starts with premises and produces an output, or conclusion. The main concern of logic is determining if the conclusion based on the input is correct. An argument is a sequence of statements, the last one of which is the conclusion: the beginning words of a conclusion are often therefore, thus, or hence. The input statements contributing to the formation of an argument should justify the conclusion.
Consider the following nonsensical, yet logical, argument:
All guinea pigs are birds.
All birds are
Plutonians.
Therefore, all guinea
pigs are Plutonians.
Though the statements themselves are not factually true, the argument is perfectly logical. The structure of the argument is: “All p are q. And all q are s. Therefore, all p are s.”
The following is another valid argument, this time based on factual information:
All geckos are reptiles.
No reptiles are
warm-blooded.
Thus, no geckos are warm-blooded.
A twist that many people find unintuitive is that an argument formed using factual information can still be invalid. For example, consider the following argument:
Some birds are pets.
Some pets are cats.
Thus, some birds are
cats.
The two premises are true. However, the final statement is not a logical conclusion that follows from these two statements, right?
Let us consider a more realistic scenario that involves making a logical conclusion:
Condominiums on the upper west side portion of the island cost less than condominiums on the east side of the island. Condominiums on the beach cost more than condominiums on the east side of the island. Of the three condominium locations, the beach condominiums cost the most.
This argument is valid and follows from the same logic used in our first example, but in a slightly different form. Precisely, “If p < q and q < s, then p < s.”
You are unlikely to encounter arguments like this on the exam. However, you will need to be able to ferret out logical reasoning from illogical reasoning, especially when on the job, taking reports from victims, assailants, burglars, witnesses, etc. We consider the main different types of questions you can expect on the exam in the next few sections. The underlying approach to solving these problems is rooted in these logic basics.
Inductive reasoning requires you to use pieces of information to draw a likely conclusion. These problems can take on different forms. We'll consider various sample questions below.
During a seminar on traffic stop procedures, officers are urged to follow these guidelines when confronting a driver about a traffic violation:
Based on this information, it would be most accurate for recruits to conclude that the main reason behind these guidelines is
Common sense suggests that Choice (B) is the most sensible choice here. Choice (A) would be self-serving for the department hosting the seminar. Choice (C) is not a likely consequence of following these guidelines. Choice (D) suggests a defensive action not characteristic of official department policy, and therefore would not be suitable for a seminar.
You might be asked to consider a situation presented graphically using bar graphs, pie graphs, or line graphs. Typically, you will be asked to provide a likely characterization of a scenario based on this information. For example, consider the following question:
Researchers have tracked the nature of violent crime in City X for 40 years. The categories of interest are: murder, rape, robbery, and assault. The data they have gathered is summarized in the graph below:
During which four-year time period does it appear that the rates of all forms of crime are slowing down?
The
correct time period will have all four graphs decreasing, or falling, from left
to right. Choice (A) has the two main
categories—robbery and assault—decreasing, but has rape on the rise. Choice (B) shows at least three of the four
categories having an increasing
rate. Choice (D) shows the rate at which
assault and rape were both occurring as increasing. Finally, Choice (C) shows all four
graphs decreasing from left to right, and is therefore the correct answer.
A social scientist is interested in the types of bullying that occur for males and females, and if there is a marked difference. The results of the surveys she sent out are compiled in the following bar graph:
For which of the following categories is the percent difference between the number of males and number of females experiencing that form of bullying the most distinct?
Be careful here! You are asked for the largest percent difference. So, you must determine the difference in the lengths of the bars, and divide that by the length of the smaller bar, as follows:
Social
media:
, or 18 percent
Physical: 
, or about 90 percent
Rumor spreading: 
, or about 29 percent
Race-related:
, or about 100 percent
So, the correct answer is Choice (D). About twice as many males are bullied because of their race.