GMAT Critical Reasoning: Necessary vs. Sufficient

Written by Kelly Granson. Posted in GMAT Study Guide

GMAT critical reasoning necessary_sufficientMany of the Critical Reasoning arguments deal with conditional statements that will require you to distinguish between necessary and sufficient conditions. Discriminating between these two basic logical concepts will sometimes help you pick the right answer when making an inference, identifying an assumption, finding a flaw in reasoning, or weakening an argument. In this article, we will look at two mistakes to avoid when necessary or sufficient conditions are presented on the GMAT.

Mistake #1. Confusing what is sufficient with what is necessary.

Some CR arguments appear to suggest that because something is sufficient, it is also necessary. Let's look at an example of such a statement in its most basic form:

If Mark misses his bus, he will be late.

Suppose the argument also states that Mark has missed his bus. In this case, you can safely infer that he will be late; knowing that Mark didn't catch his bus is sufficient to conclude that he will fail to arrive on time. Now, is it necessary for Mark to miss his bus in order to run late? The answer is NO, because he could be late for a variety of other reasons. The first premise does not exclude the possibility that Mark did catch his bus, but then was held up by traffic, got stuck in the elevator, or met other circumstances that delayed him. Thus, missing the bus is NOT a necessary condition for being late. If you understand this, you will see immediately that the following arguments are wrong:

If Mark misses his bus, he will be late. Mark is late. Therefore, he has missed his bus.

If Mark misses his bus, he will be late. Mark has not missed his bus. Therefore, he will not be late.

Mistake #2. Confusing what is necessary with what is sufficient.

Other Critical Reasoning arguments set their trap by making the opposite mistake: taking what is necessary for what is sufficient. Consider the following example:

To be eligible for a scholarship, one must have an outstanding academic record. Mark has been the top student in his class for five years in a row.

Can you infer that Mark will be eligible for the scholarship? The answer is NO. Let's see why. You know that Mark is the best student in his class, and therefore, that he fulfills the requirement of having an outstanding academic record. You know that it is necessary for an applicant to excel academically, but is it sufficient? NO, it is not. Perhaps this scholarship has an age requirement or requires evidence of community involvement. How do you know whether these or other additional requirements exist and whether Mark fulfills them? Since you don't know, saying that Mark is or must be eligible for a scholarship would be wrong. The most likely valid inferences in this case would be:

Without an outstanding academic record, one cannot be granted the scholarship.

Mark may be eligible for this scholarship.

Recognizing the difference between necessary and sufficient conditions may seem tricky at first, but it becomes clearer with experience. Try to develop your ability by examining the possible inferences from any conditional statement you encounter. Enjoy your GMAT practice!

 

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