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How to Use Formal Logic on the GMAT Critical Reasoning Section

Posted in Test Prep on December 1, 2010 by



GMAT Critical Reasoning questions test your ability to use logic. In most cases this means making inferences, identifying details, and understanding arguments. Occasionally, however, you will have to apply formal logic to understand what a CR paragraph implies.

Formal, or, classical logic, has its own set of rules, and questions that make use of it will try to trip you up with wrong answer choices that contradict those rules.

Consider the example below:

Studies have shown that a large percentage of car accidents are caused by aggressive driving. To help reduce the number of accidents and to promote traffic safety in general, insurance companies have begun to issue discounts to drivers who take defensive driving courses. Research shows that people who practice defensive driving are considerably less likely to get into a car accident. Therefore, the insurance company’s plan should help reduce the number of accidents.

Assuming the statements above are true, which of the following can be inferred from them?

A. The majority of accidents are caused by drivers who possess insurance.
B. People who manage to consistently avoid car accidents are likely practicing defensive driving.
C. Young males and other demographics known for disproportionately being involved in car accidents are less likely to practice defensive driving than other demographics.
D. An individual who does not practice defensive driving is always more likely to get into a car accident than an individual who does practice defensive driving.
E. Discounts are the most effective way for insurance companies to promote defensive driving.

Which of the answer choices logically follows from the paragraph above? To answer this, we need to know some basic rules about classical logic. What we have in this question is a conditional, also known as an “if… then” statement. It can be written as follows: “If people practice defensive driving, then they will have a lower chance of being in an accident.” In classical logic, conditional statements follow certain rules if we negate or change the order of their clauses.

Consider a simpler conditional: If it is cold, I will wear a sweater.

The inverse of this statement is the negation of both clauses: If it is not cold, I will not wear a sweater.

The converse reverses the order of the clauses: If I wear a sweater, it is cold.

The contrapositive both negates and reverses: If I will not wear a sweater, it is not cold.

Under the rules of classical logic, if a statement is true, its contrapositive must also be true. The statement’s negation and converse, however, are NOT necessarily true. For the sweater example, this means the following:

Statement: If it is cold, I will wear a sweater. TRUE

Inverse: If it is not cold, I will not wear a sweater. TRUE OR FALSE –  I may wear a sweater even if it is not cold.

Converse: If I will wear a sweater, it is cold. TRUE OR FALSE. I may wear a sweater even if it is warm.

Contrapositive: If I will not wear a sweater, it is not cold. TRUE. If it were cold, I would wear a sweater. Since I won’t wear a sweater, it must not be cold.

In real English conversation these rules are not quite so absolute. However, on the GMAT, you can avoid trap answer choices on Critical Reasoning questions by knowing these rules. Remember the basic conditional here: “If people practice defensive driving, then they will have a lower chance of being in an accident.”  Now take another look at the answer choices.

Choices A and E can be eliminated first because neither follow from the stimulus; both are just assumptions that may or may not be true.

Choice B is the converse of the original statement. While it may be tempting as an answer choice — since it at least seems plausible — the rules of formal logic show that it cannot be inferred.

Choice D also sounds plausible, but it cannot be inferred since it is the inverse of the conditional statement in the argument and is too extreme as it is written. It is possible for a person who does not practice defensive driving to have the same probability of getting into an accident as someone who DOES practice defensive driving.

Choice C is the contrapositive of the original statement. If defensive driving leads to fewer accidents, people who get into more accidents are less likely to be defensive drivers than people who rarely get into accidents. Using our knowledge of formal logic, we can conclude that choice C is correct.

While formal logic is not the most common type of Critical Reasoning question, it is still useful to know if you find yourself stuck on an inference question. Try to keep it in mind on test day.

Here at Knewton, we even have a term for people who make fundamental reasoning errors: