# GMAT Quantitative Data Sufficiency: Practice with Geometry

The GMAT Quantitative section will contain problems that test your geometry skills, and some of these problems may appear as Data Sufficiency questions. You should be able to tackle lines, angles, two-dimensional shapes, three-dimensional solids, perimeter, area, surface area, volume, the Pythagorean theorem, and coordinate geometry.

Each Data Sufficiency problem poses a question, followed by two statements. Your task is to evaluate the statements to determine at what point there is or is not sufficient information to answer the question.

Unlike the Problem Solving questions, you do not actually have to answer the question posed. Instead, you select one of five fixed answer choices that offer different options about the sufficiency of the information provided in the two statements.

## Practice questions

- In the figure shown here, what is the value of
*z?*(1)

*m*=*n*(2)

*y*= 88**A.**Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.**B.**Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.**C.**Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient to answer the question asked.**D.**Each statement ALONE is sufficient to answer the question asked.**E.**Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked. - The circumference of circle X is 1/2 the circumference of circle Y. What is the area of circle X?
**A.**Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.**B.**Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.**C.**Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient to answer the question asked.**D.**Each statement ALONE is sufficient to answer the question asked.**E.**Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked.

## Answers and explanations

- The correct answer is B.
From (1),

*m*=*n*implies*x*=*z*(because base angles of an isosceles triangle are congruent). However, without additional information, you cannot determine the value of*x*or*z.*Thus, (1) is not sufficient.From (2), because the measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles, 88 = 54 +

*z*, which you can solve for*z*. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient. - The correct answer is D.
Recall that a circle with radius

*r*has circumference equal to 2*πr*and area equal to*πr*^{2}. From (1), in circle Y,so

*r*, the radius of circle Y, is 10 feet. Then given that the circumference of circle X equals 1/2 the circumference of circle Y, the circumference of circle X iswhich implies the radius of circle X is 5 feet and its area is

Thus, (1) is sufficient.

From (2), you know from (1) that if the circumference of circle Y is known, you can proceed as in (1) to determine circle X’s area. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.