GRE Algebra - Plug and Test

Another great way to solve difficult GRE algebra questions is to use the plug and test method. Assuming that you have eliminated those choices that you know are not correct, you can use the remaining answer choices and plug them back into the original equation. For example, consider the following sample GRE algebra question:

For what values of x and y is 3x2 + 2y = 14?

a. x = 0, y = 0
b. x = 1, y = 3
c. x = 1, y = 5
d. x = 2, y = 1
e. x = 2, y = 2

When you look at this question, you can rearrange the equation to be 3x2 = 14 - 2y, but that doesn't make it much easier. In fact, there are two variables in this equation, and only one equation, so there is no way to solve for the variables exactly. But notice that the choices are all simple numbers. So just plug them into the equation and then it:

  • When x = 0 and y = 0, then the equation is 3(0) + 2(0) = 14, which is NOT true
  • When x = 1 and y = 3, then the equation is 3(1) + 2(3) = 14, which is NOT true
  • When x = 1 and y = 5, then the equation is 3(1) + 2(5) = 14, which is NOT true
  • When x = 2 and y = 1, then the equation is 3(4) + 2(1) = 14, which IS true
  • When x = 2 and y = 2, then the equation is 3(4) + 2(2) = 14, which is NOT true
So, using the plug and test method, you see that ONLY when x = 2 and y = 1, then does the equation evaluate to true.

Test Tip The plug and test technique is a great way to arrive at the answer to an GRE algebra equation question if you are stuck or if you have been able to narrow down the choices to two or three candidate answers. However, use the plug and test method only when you can use quick, easy calculations for the evaluation part, otherwise it will take too long and, in fact, it will be a waste of time.