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GRE Math Tips – Getting Rid of Your x’s and y’s

The GRE Math section is full of problem solving questions, which test exactly the way you do that—solve problems. The key is that you solve the problem in the shortest amount of time possible. Unfortunately, many students have difficulty either finding a solution for a problem, or, if they do, finding that solution quickly.

Part of the reason is that many students persist in thinking in terms of x and y; that is, they continue to think in terms of algebra. Algebra—that cauldron of variables that bubbles up in their mind whenever they see a difficult word problem—is often times the enemy. When solving a difficult word problem, the sooner you can let go of the x’s and ys, the better.

Let’s have a look at the following problem:

The product of two integers is 40. Which of the following CANNOT be the sum of these two integers?

(A) -41

(B) 3

(C) 13

(D) 14

(E) -14


Many students would proceed as follows:

xy= 40, x + y = ??

At that point, students freeze. Sometimes for seconds, sometimes for minutes. Some may try to plug the answers into the above equation. For instance, starting with (C) 13, they try to set up the equation and solve via substitution:

xy = 40, x + y =13.

After a few tedious steps, they may get:  y^2-13y+40.

You could factor this equation and find that the sum of the roots is 13. But just getting to this point is very difficult and time-consuming. And, until you get the correct answer, you would have to solve for each of the answer choices in this fashion (definitely not a good use of your 45 minutes). So, instead, let’s dispense with the x and y and break down the problem as follows, using a tip that I call “Getting Rid of Your x’s and y’s”:

What are the factors of 40?

8, 5

10, 4

20, 2

40, 1


Each of these pairs could also be negative (remember a negative * negative is a positive).

-8, -5

-10, -4

-20, -2

-40, -1


Now we just need to find the sum of each pair, and see which one is not represented above.

8 + 5 = 13

10 + 4 = 14

20 + 2 = 22

40 + 1 = 41

-8 + -5 = -13

-10 + -4 = -14

-20 + -2 = -22

-40 + -1 = -41

The only number not represented is (B) 3.


Again, the GRE Math section is testing the way you think. It wants logical thinkers who are able to see the quickest way to the solution, so use this tip to your advantage. Not that algebra is unhelpful, but, for the most part, the quickest way to the solution starts with getting rid of your x’s and y’s!


What other GRE Math tips would you like to see? Let us know. 🙂

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10 Responses to GRE Math Tips – Getting Rid of Your x’s and y’s

  1. Yogesh Kurade October 21, 2017 at 5:07 am #

    Thanks a lot, Chris. Helps me understand whenever it requires a lengthy calculation or step, there is always another elegant and simple way that leads to the answer.

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert October 21, 2017 at 1:27 pm #

      So glad this was helpful 🙂

  2. Bowen Chen July 20, 2016 at 12:34 pm #

    wow. No further explanations needed! Beautiful

  3. Neha April 24, 2016 at 8:16 pm #

    I always felt comfortable solving using X and Y. However, couldn’t solve this problem.
    Thank you for sharing this easy method.

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert April 25, 2016 at 11:27 am #

      You’re welcome! Glad to hear you liked the method 🙂

      Happy studying!

  4. Saadmaan November 14, 2015 at 1:02 am #

    Hi. I have a question regarding factors. Is 15, a factor of 15? In other words, is a particular integer considered to be the factor or divisor of itself?

    • Shrikant September 16, 2017 at 9:34 am #

      Yes, 15 is a factor of 15.

  5. Lokesh October 7, 2013 at 12:04 pm #

    After reading the question i also made the same mistake of making the Algebric expressions and then i went blank as it was taking a lot of time . Then i checked out this method it’s really simple and saves a lot of time. Thank you for such a quick solution.

  6. kikis July 24, 2013 at 8:17 am #

    The number in this question is 40 so this method was fast to solve. What if there is a huge number will this approach work fast then as well..

    • Chris Lele
      Chris Lele July 24, 2013 at 10:16 am #

      Hi Kikis,

      The GRE wouldn’t ask this type of question using a large number, say 364, because there are too many factors and too many possibilities for sums. I think the takeaway from a problem like this is to avoid trying to set up an equation (it won’t get you anywhere), but to experiment with numbers the way the question does.

      Hope that helps!

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