Question

The area of a square is equal to the area of a circle. What is the circumference of the circle?
Statement I. The diagonal of the square is X inches.
Statement II. The side of the square is Y inches.

• A. If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
• B. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
• C. If the data either in statement I alone or in statement II alone are sufficient to answer the question.
• D. If the data even in both statements I and II together are not sufficient to answer the question.

Hint:

The area of a square is equal to \(s^2\) where \(s\) is the side length. For the circle, use \(A = \pi r^2\) to relate the areas.

Answer 1

The Correct Option is C

- Statement I: The diagonal of the square is X inches.
- The area of the square can be found from the diagonal using the formula \(A = \frac{1}{2} \times d^2\), where \(d\) is the diagonal. This can give us the area, which is equal to the area of the circle. From this, we can find the radius of the circle, and then calculate the circumference.
- Statement II: The side of the square is Y inches.
- The area of the square can also be found from the side using \(A = s^2\), where \(s\) is the side length. This can give us the area, which is equal to the area of the circle. Again, we can find the radius of the circle and calculate the circumference.
Thus, the correct answer is (C).