The Reasonable Test-Maker

When it comes to tackling GMAT math questions, one of the best tips I can offer is this: The GMAT test-makers are reasonable people who have little interest in your computational skills.

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

If 4x – 7y = 9, and 3x – 8y = 4, what is the value of x + y ?

(A)        2

(B)        3

(C)        4

(D)        5

(E)        6

If you were to encounter this question on the GMAT, it would be perfectly natural to 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 equations, and you have probably solved dozens (if not hundreds) of similar systems in the past.

If you prefer the substitution method, you might take the first equation and solve it for x to get x = 7y/4 + 9/4.  Then you’d take the second equation and replace x with 7y/4 + 9/4 to get the somewhat cumbersome equation 3(7y/4 + 9/4) – 8y = 4.

At this point, the original question is not testing your ability to solve 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 other options. If you happen to be one of those people, you may continue with these calculations and waste considerable time in the process.

So, what should you do instead?

You should remember my 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 do not care whether or not you are a human calculator.

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

Now, what is that approach?

Well, the trick here is to recognize that the question does not ask us to find the individual values of x and y. Instead, we are asked to find the sum of x and y.  So, if we happen to notice that the x-coefficients (4 and 3) differ by 1, and the y-coefficients differ by 1, we might recognize that something convenient happens when we subtract the second equation from the first equation:

      4x – 7y = 9

 -   3x – 8y = 4

      x  +  y  = 5

When we do this, we get x + y = 5. So, the answer is D.

Granted, this is a tricky question. As such, you may have missed the time-saving shortcut. In that case, you would be forced to solve the system of equations. So, just knowing that the test-makers have little interest in your computational skills does not necessarily mean you’ll instantly spot shortcuts. However, by accepting the fact that the test-makers are reasonable, you’ll be better able to assess the practicality of certain approaches, and you’ll be able to identify instances where an easier approach must exist.