Beware Shortcuts in Thinking


gmat thinkingWe’ve heard the expression Don’t reinvent the wheel. There is no need to start from scratch every time you undertake a task.  The same reasoning applies in many ways to GMAT problems.  In fact, this logic is exactly why doing practice problems is a valuable tool for improving your GMAT score.  If you have seen a similar problem before, you will probably have a jumping off point for that problem on the actual GMAT.

While focusing on efficiency is important on the GMAT, in some cases it can be problematic to rely on traditional rules of thumb.  The GMAT is good at finding and testing the exceptions to rules that apply in many cases.  For example, the adage it takes two equations to solve for two variables is not true in all cases.

One common shortcut of thinking is the assumption that to show the converse of a statement you need exactly the opposite information.
That is: If in order to prove x, I must know y and z are true then in order to prove the opposite of x I must know that y and z are false.

In many cases this logic does work.  In order to be sure x is a positive number, I could know that x * 4 was positive.  To show the opposite (x is negative), I could do so knowing x * 4 is negative.

But you want to be cautious of just reversing logic because there are exceptions to this general rule, especially related to number properties questions.

To show: the product of the integers xy is odd
I must know: that both x and y are odd.
To show: the product of the integers xy is not odd
I must know: either x or y is even
In the first case I had to know something about both x and y, while in the second I only needed to know that one integer was even.

To show: x is divisible by 15
I must know: that x is divisible by all the prime factors of 15 (3 and 5)
To show: x is not divisible by 15
I must know: that x is not divisible by either of the prime factors of 15
More broadly, to show a number is divisible, you must know about divisibility by all the prime factors while to show a number is not divisible you just must be able to exclude one prime factor.

If I know: the product abc does not equal 0.
I know: that none of the variables (a, b, or c) is equal to 0.
If I know: the product abc equals 0.
I know: that one of the variables equals 0.

This same warning on shortcuts in thinking can apply in the verbal section as well.  You have likely seen a critical reasoning question similar to the following:

All of the statements below strengthen the environmentalist’s contention EXCEPT

A common line of thinking on such a question is to rephrase it into a familiar question type, or the weaken question (e.g. Which of the answer choices weakens the environmentalist’s contention?).  Why is this rephrase not entirely accurate?  In order to not strengthen a conclusion a statement does not necessarily have to weaken it.  Any completely irrelevant statement (e.g. Puppies are cute.) could be a correct answer to the original question, but would not be a correct answer to the rephrased question.

Clearly, there is need to focus on efficiency given the time pressure inherent in the GMAT.  However, I would warn against taking shortcuts in your thinking or logic.  To excel on the GMAT, you must always be thinking critically and deeply and seeking out the exceptions rather than the rules of thumb.  Instead, save your speed shortcuts for when you move towards the execution stages of a problem (e.g. actually doing calculations) rather than when you initially evaluate the problem.

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