GMAT OFFICIAL GUIDE DS

Solution:

Let’s start by sketching square ABCD inscribed in circle O.

Square ABCD is inscribed in circle O. What is the area of...

We must also remember that the diagonal of the square is equal to the diameter of the circle. That is, the diameter is equal to .

Square ABCD

We must determine the area of square ABCD. Since the diagonal of the inscribed square is the diameter of the circle, if we can determine the diameter of the circle we can then determine the area of the square.

Statement One Alone:

The area of circle O is 64л.

Since we have the area of circle O, we can use the formula for the area of a circle, A = лr^2, to determine its radius. Additionally, the diameter of a circle is twice the radius. Thus, we can determine the diameter of the circle, which is also the diagonal of the square. Knowing the length of the diagonal of the square, we can then determine the area of square ABCD. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The circumference of circle O is 16л.

Since we have the circumference of circle O, we can use the formula for the circumference of the circle, C = 2лr, to determine its radius. As in statement one, knowing the radius will allow us to determine the area of square ABCD. Statement two alone is sufficient to answer the question.

Answer: D

About The Author

Jeffrey Miller is the head GMAT instructor for Target Test Prep. Jeff has more than fourteen years of experience in the business of helping students with low GMAT scores hurdle the seemingly impossible and achieve the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GMAT instruction, and will be a pivotal resource for many more to follow.