GMAT Quantitative Problem Solving: Practice with Geometry

By Sandra Luna McCune, Shannon Reed

Some Problem Solving questions in the Quantitative section of the GMAT will involve geometry. You should know how to work with angles, lines, two-dimensional shapes, three-dimensional solids, perimeter, area, surface area, volume, the Pythagorean theorem, and coordinate geometry.

Practice questions

The figure shows a triangle inscribed in a semicircle.

gmat-triangle-semi

  1. If PQ = 16 and QR = 12, what is the length of arc PQR?

    GMAT_0901

    The figure shown is a rhombus in which the measure of angle A is 120 degrees.

    gmat-rhombus

  2. What is the ratio of the length of line AC to the length of line DB?

    GMAT_0902

Answers and explanations

  1. The correct answer is A.

    An angle inscribed in a semicircle is a right angle. Thus, triangle PQR is a right triangle with legs of lengths 16 and 12. The length, PR, of the hypotenuse is

    GMAT_0903

    Thus, the diameter of the semicircle is 20. The length of the arc PQR is half the circumference of the circle that contains the semicircle. This length is

    GMAT_0904

  2. The correct answer is D.

    Consecutive interior angles of a rhombus are supplementary, so the measure of

    GMAT_0905

    The diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus. Construct the diagonals of the rhombus. Label the intersection E.

    gmat-bisector

    Thus, triangle AED is a

    GMAT_0906

    right triangle, with hypotenuse

    GMAT_0907

    Given that the diagonals bisect each other, the length of line AC is twice the length of line AE, and the length of line DB is twice the length of line DE. Hence, the ratio of the length of line AC to the length of line DB is the same as the ratio of the length of line AE to the length of line DE. The lengths of the sides of a 30 – 60 – 90 right triangle are in the ratio

    GMAT_0908

    Therefore, the ratio of the length of line AC to line DB equals the ratio of the length of line AE to line DE equals

    GMAT_0909

    which is

    GMAT_0910

    in simplified form.