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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.

By the way, students who use Magoosh GRE improve their scores by an average of 8 points on the new scale (150 points on the old scale.) Click here to learn more.

6 Responses to GRE Math Tips: The Reasonable Test-Maker

  1. Brent
    Brent February 27, 2012 at 11:12 am #

    Hi Nikhil,

    Sorry for the delay.

    The great thing about almost all GRE questions is that they can be solved using at least 2 different approaches. One of those approaches will typically allow you to solve the question in very little time, and the other(s) will eat up a lot of time.

    So, our goal for all math questions is to not just find a solution, but to find the best (fastest) solution.

    Now, how do we find the fastest solution? Well, that’s the million-dollar question.

    To find the fastest solution, we need to first recognize that a fast solution probably exists for any question. So, when you encounter a math question, you must ask yourself the right question.

    Many students ask, “How do I solve this?” This is not the right question, since it doesn’t recognize that there are several possible approaches. These students recognize one approach and begin solving the question without considering any other (possibly faster) approaches.

    The question you should ask is, “What are my options here?” Try to identify at least 2 approaches, and THEN begin working on the fastest approach.

    Now, of course, all of this is hard to do when the clock is ticking. However, when you’re practicing at home, be sure to take a moment and look for multiple approaches before you begin working on one approach. Doing so now will help you embark on the best approach on test day.

    Also, it’s important to have a very large “mathematical tool kit” consisting of a wide range of strategies and techniques.

    I hope that helps.


  2. Nikhil Gupta February 23, 2012 at 8:07 pm #

    hi Brent,
    I need to ask that there are many lengthy question in GRE quant that requires more than half min to read, 15 sec approx to understand and then another 1 min to solve.
    these are very time consuming questions and cause of them, i tend to miss other simple questions.
    please suggest any approach to deal with such questions.

  3. Meenu November 27, 2011 at 3:18 pm #

    This tip will help me too. Thanks Brent.

  4. Najwat September 6, 2011 at 7:37 am #

    Hi Brent,

    Thanks for this helpful tip. I have an issue with GRE quant and I hope you could help me with that.

    I immediately recognized the clue in this problem, before reading your explanation, and I had my answer in a few seconds. However, the answer I got was 5! Yes, I subtracted 4 from 11 and wrote down 5 on my sheet of paper!

    I am quite prone to ridiculous errors like this. Any tips on avoiding such errors on the actual test?


    • Brent
      Brent September 6, 2011 at 6:35 pm #

      Hi Najwat,

      Your dilemma is not uncommon. For people who often make careless mistakes, I suggest that you:
      1. carefully read the question
      2. solve the problem
      3. reread the question
      4. reread your solution
      5. submit your answer


      • Najwat September 17, 2011 at 8:01 am #

        Thanks a lot Brent! 🙂

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