GMAT OFFICIAL GUIDE DS

Solution:

We begin by sketching the diagram.

In the figure above, if the area of the smaller square region is 1/2

We are given that the area of triangular region D is 4, and we must determine the length of the side of square A. We must remember that the side of square A is also equal to the length of the hypotenuse of triangle D.

Statement One Alone:

The area of square region B is 9.

Using the information in statement one, we can determine the side of square B is 3, which is also equal to the height of triangle D. We also know that the area of triangle region D is 4. Thus, we can use the area formula for a triangle to determine the base of triangle D.

area = (base x height)/2

4 = (b x 3)/2

8 = 3b

b = 8/3

Since we know the base and height of right triangle D, we can use the Pythagorean Theorem to determine the length of the hypotenuse. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The area of square region C is 64/9.

The area of a square is:

Area = s^2

64/9 = s^2

+/-√(64/9) = √s^2

s = 8/3 or -8/3

Since the side of a square can’t be negative, we will use the positive answer of 8/3 to determine that the side of square C is 8/3, which is also equal to the base of triangle D. We also know that the area of the triangular region D is 4. Thus, we can use the area formula for a triangle to determine the height of triangle D.

area = (base x height)/2

4 = (8/3 x h)/2

8 = (8/3)h

24 = 8h

h = 3

Since we know the base and height of right triangle D, we can use the Pythagorean Theorem to determine the length of the hypotenuse. Statement two is sufficient to answer the question.

Answer: D

About The Author

Scott Woodbury-Stewart is the founder & CEO of Target Test Prep. A passionate teacher who is deeply invested in the success of his students, Scott began his career teaching physics, chemistry, math, and biology. Since then, he has spent more than a decade helping students gain entry into the world’s top business schools, logging 10,000+ hours of GMAT, EA, GRE and SAT instruction. Scott also served as lead content developer and curriculum architect for the revolutionary courses Target Test Prep GMAT, Target Test Prep EA, Target Test Prep GRE and Target Test Prep SAT Quant.