GRE Sample Math-Test Questions: Comparing Quantities

By Ron Woldoff, Joseph Kraynak

About one-third of the GRE math questions are Quantitative Comparisons (QC), with plenty of traps to trip you. A QC question shows two quantities, intuitively labeled Quantity A and Quantity B. The quantities can be numbers, variables, equations, words, figures, and so on. Your job is to compare the quantities and determine whether one is greater, they’re equal, or the relationship can’t be determined from the information provided.

Sample questions

For the following questions, choose from these answer choices:

(A) Quantity A is greater.

(B) Quantity B is greater.

(C) The two quantities are equal.

(D) The relationship cannot be determined from the information given.

  1. Given the equation,

    image0.png

    what is the relationship between quantity x and quantity y?

    image1.png

    Questions 2 and 3 are based on the following information:

    Square ABCD is in the xy-coordinate plane, and each side of the square is parallel to either the x-axis or the y-axis. Points A and C have coordinates (–2, –1) and (3, 4), respectively.

  2. image2.png

  3. image3.png

  4. n > 0

    image4.png

Answers and explanations

  1. D.

    If you chose Choice (B), then you fell for the trap. Just because

    image5.png

    doesn’t mean that x = 2 or y = 3. They could be 20 and 30, for example. Or x and y could also be negative, such as –2 and –3.

  2. A.

    Draw the xy-coordinate plane and place the points A and C as directed. These are two points of the square, and you know they’re the opposite corners because the question tells you the sides of the square are parallel to the axes. Measure the width and height and multiply for an area of 25. (Or to save time, you can measure the width or the height and then square that value to find the answer, because the width and height of a square are equal.)

  3. C.

    Drawing a line from point A to point C splits the square into two 45-45-90 triangles. The side ratio of this triangle is

    image6.png

    so if two of the sides are 5, then the hypotenuse is

    image7.png

  4. D.

    If n equals 2, then Quantity A is greater; if n equals

    image8.png

    then Quantity B is greater. All you know is that n is positive, not whether it’s an integer or a fraction that’s less than 1.