Anyone can tell you that Critical Reasoning helps to measure your logical thinking skills. What you may not know is that the formal logic required to truly becoming a master of this question type originated in part with Aristotle, and is highly mathematical in nature. This means that even when you’re working on the Verbal section of the GMAT, you are still applying mathematical concepts.
Here’s how to form a contrapositive:
Step 1: Start out with a cause/effect statement. This is best done in the “if/then” format. Here’s our example: “If you are a fish, then you live in water.” This statement is arguably true (with the exception of mudskippers, but that’s debatable!).
Step 2:Now, reverse the elements of your statement: “If you live in water, then you are a fish.” This statement is not NECESSARILY true. Many other non-fish organisms live in the water as well, like whales, seaweed, crustaceans, and plankton.
Step 3:Negate both sides of the statement: “If you don’t live in water, then you are not a fish.” This statement is equally true as the original statement. It is the CONTRAPOSITIVE!
When you have complex statements, that involve “and” or “or,” you must switch them around. For example, the contrapositive of “If you are at least 18 years old and registered, then you can vote” is “If you can’t vote, then you are not at least 18 years old OR not registered.” If one of those two elements is missing, the person cannot vote. Simple, really!
Now, let’s apply our knowledge of the contrapositive to a Critical Reasoning question, and see why it’s so useful:
The interview is an essential part of a successful hiring program because, with it, job applicants who have personalities that are unsuited to the requirements of the job will be eliminated from consideration.
The argument above logically depends on which of the following assumptions?
(A) A hiring program will be successful if it includes interviews.
(B) The interview is a more important part of a successful hiring program than is the development of a job description.
(C) Interviewers can accurately identify applicants whose personalities are unsuited to the requirement of the job.
(D) The only purpose of an interview is to evaluate whether job applicants’ personalities are suited to the requirements of the job.
(E) The fit of job applicants’ personalities to the requirements of the job was once the most important factor in making hiring decisions.
When we look at the question stem, it’s clear that we’re looking for a necessary assumption, or an assumption upon which the success of the argument “depends.” Let’s break the argument down into a formal logic statement. Our keyword here is “because” – that means we need to switch the order of the argument’s elements. Here it is:
“If job applicants with unsuitable personalities can be eliminated from consideration, then interviews are essential.”
Now, make your contrapositive.
“If interviews are NOT essential, then job applicants with unsuitable personalities CANNOT be eliminated from consideration.”
What does this mean to us? This means that if the author’s argument is in favor of interviews, and his proof is that interviews weed out unsuitable people, we must then select an answer choice that makes this argument entirely waterproof. That means that answer choice (C) is the correct answer.