# GMAT Quantitative Problem Solving: Practice with Geometry

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. *

- If
*PQ*= 16 and*QR*= 12, what is the length of arc*PQR*?*The figure shown is a rhombus in which the measure of angle A is 120 degrees.*

- What is the ratio of the length of line
*AC*to the length of line*DB*?

## Answers and explanations

- 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 isThus, 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 - The correct answer is D.
Consecutive interior angles of a rhombus are supplementary, so the measure of

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.*Thus, triangle

*AED*is aright triangle, with hypotenuse

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 ratioTherefore, the ratio of the length of line

*AC*to line*DB*equals the ratio of the length of line*AE*to line*DE*equalswhich is

in simplified form.