GRE Sample Math-Test Questions: Algebra

By Ron Woldoff, Joseph Kraynak

Although you’ve probably already solved lots of algebra questions in your high school and college courses, you may need a refresher to prepare for the GRE. The following sample questions are similar to what you’ll see on the algebra section of the test.

Sample questions

  1. If n is a positive even integer, which of the following represents the product of n and the consecutive even integer following n?

    image0.png

    For the following question, choose all that apply.

  2. If n is an integer and

    image1.png

    is an integer, which of the following could be the value of n?

    (A) 11

    (B) 12

    (C) 18

    (D) 24

    (E) 27

    (F) 66

  3. If n is a positive integer, for which of the following would the units digit always be equal to the units digit of n? (Choose two answers.)

    image2.png

Answers and explanations

  1. C.

    Pick two consecutive even integers, such as 8 and 10, giving you a product of 80. Only one formula will return 80 if you plug in 8 for n.

  2. A, C.

    For any square root to be an integer, each factor under the radical has to be in a pair. For example,

    image3.png

    is an integer because it equals

    image4.png

    and the 2s are in a pair. For

    image5.png

    to be an integer, all the factors of 60 have to be in pairs:

    image6.png

    The 2s are in a pair, but the y has to complete the 3 pair and the 5 pair to make an integer. So y has to contain 3 and 5, making 15 one possible value. However, y could also be 15 times any other perfect square, such as 4;

    image7.png

    which is the other possible value of y in this list.

  3. A, C.

    Factor

    image8.png

    making both 0 and 4 possible answers for x.