GRE Sample Math-Test Questions: Geometry - dummies

GRE Sample Math-Test Questions: Geometry

By Ron Woldoff, Joseph Kraynak

Geometry questions on the GRE deal with lines, angles, triangles, rectangles, squares, circles, cubes, and more. They may take the form of comparison questions, or simple multiple choice. The following sample questions are similar to what you will find.

Sample questions

  1. The following circle has a radius of 5.

    image0.png

    Angle CAB originates at the center of the circle and measures 36 degrees.

    image1.png

    Which of the following statements is true about the two quantities?

    (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.

  2. The trapezoid shown here,

    image2.png

    has an area of

    image3.png

    The following table contains two quantities relating to the trapezoid.

    image4.png

    Which statement is true about the two quantities?

    (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.

  3. Given the following triangle,

    image5.png

    what is the area of the shaded section?

Answers and explanations

  1. C.

    If the angle CAB measures 36 degrees, minor arc BC also measures 36 degrees, making it one tenth of the circle:

    image6.png

    A circle with a radius of 5 has a circumference of

    image7.png

    Multiply this circumference by the fraction of the circle, giving you a minor arc length of

    image8.png

    Therefore, the two values are equal.

  2. C.

    You can find the area of a trapezoid with the formula

    image9.png

    where b1 represents one base, b2 represents the other base, and h represents the height. To find the height, set the formula equal to the area and simplify it:

    image10.png

  3. The area is 21.

    For the area of a triangle, multiply the base by the height and divide by 2. The base of this triangle is 7 and the height is 6, for an area of 21. The 2 in the drawing has no bearing.