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GRE Math Tips: The Reasonable Test-Maker

When it comes to tackling GRE math questions, one of the most important tips I can offer is this:

The GRE test-makers are reasonable people who have little interest in your computational skills.

Granted, this tip doesn’t sound very mathematical, but it can help you determine the best approach to a lot of questions. To see how this tip works, consider the following:

If 5x – 8y = 11, and 4x – 9y = 4, what is the value of x + y?

(A)       3

(B)       4

(C)       5

(D)       6

(E)        7

Upon seeing this question, it would be perfectly natural for you to immediately begin applying one of the techniques you learned in high school for solving systems of linear equations. After all, this is a system of linear equation, and you probably solved dozens of similar systems in your life. So, with great gusto and confidence, you begin solving the system.

If you happen to like the substitution method, you might take the first equation and solve it for x to get x = 8y/5 + 11/5.  Then, you take the second equation and replace x with 8y/5 + 11/5 to get the not-so-pleasant equation 4(8y/5 + 11/5) – 9y = 4.

At this point, the original question is not testing your expertise with systems of equations – it’s testing whether or not you’re one of those people who latches onto a certain approach, and refuses to consider alternative approaches. If you happen to be one of those people, you may continue with these calculations and needlessly waste a lot of time in the process.

So, what should you do instead?

You should remember our tip and ask yourself, “Are the test-makers really interested in whether or not I can solve the equation 4(8y/5 + 11/5) – 9y = 4”?

The answer to this is a resounding NO. The test-makers have very little interest in this. In fact, they’ve given you an onscreen calculator to show how little they care about your computational skills.

So, if you truly believe (and embrace) the idea that the test-makers have little interest in your computational skills, you can be certain that there MUST be another approach to this question that does not involve extremely messy equations.

Now, what is that approach?

Well, the trick here is to recognize that the question does not ask you to find the value of x and/or the value of y. Instead, you are asked to find the sum of x and y. This is an important clue, since it tells us that we do not need to find the individual values of each variable.

From here, if we recognize that the x-coefficients (5 and 4) differ by 1, and the y-coefficients differ by 1, we might see that something convenient happens when we subtract the second equation from the first equation.

      5x – 8y = 11

   4x – 9y = 4

      x  +  y  = 7

When we do this, we get x + y = 7. So, the answer is E.

Now, this is a tricky question, so you may not have spotted that particular shortcut. If that were the case, you would be forced to tediously solve the system of equations. So, just knowing that the test-makers are reasonable people with little interest in your computational skills does not necessarily mean that you’ll be able to spot shortcuts. However, by accepting the fact that the test-makers are reasonable people, you will be better able to assess the practicality of certain approaches, and you will be able to identify instances where an easier approach must exist.

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