Directions: Each of the questions given below consists of a sta tement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (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; Give answer (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; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the area of the circle ? I. Perimeter of the circle is 88 cm. II. Diameter of the circle is equal to the side of the square having area 784 sq. cm.

### Concept & Area of a Circle The area of a circle can be perfectly calculated if its radius $r$ is known. $$ \text{Area} = \pi r^2 $$ ### Step-by-Step Solution 1. **Analyze Statement I:** The perimeter (circumference) is $88 \text{ cm}$. The formula for circumference is $2\pi r$. Setting $2\pi r = 88$ allows us to uniquely solve for $r$, and consequently, the area. Statement I alone is sufficient. 2. **Analyze Statement II:** The diameter ($2r$) equals the side of a square with an area of $784 \text{ sq. cm}$. The side of this square is $\sqrt{784} = 28 \text{ cm}$. Thus, the diameter is $28$, meaning $r = 14 \text{ cm}$. With $r$ known, we can calculate the area. Statement II alone is sufficient. 3. Since both statements independently provide a way to deduce the radius, either statement alone is sufficient. ### Exam Strategy & Shortcut Any statement that provides a single linear measure of a circle (such as circumference, diameter, or a direct geometric equivalent) is independently sufficient to find the circle's area. No calculation is needed to deduce this. ### Common Pitfall A common mistake is wasting time computing the actual final area. In data sufficiency, establishing that you *can* find the definitive answer is all that is required. ### Final Answer Therefore, the correct answer is **if the data either in Statement I or in Statement II alone are sufficient to answer the question;**.