Directions: Each of the questions given below consists of a statement 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. Determine the perimeter of the square. I. A circle is inscribed in the square. II. The area of the circle is $36\pi$.

### Concept & Inscribed Shapes When a circle is exactly inscribed within a square, the diameter of the circle is equal to the side length of the square. The perimeter of a square is calculated as $4 \times \text{side}$. ### Step-by-Step Solution * **Analyze Statement I:** "A circle is inscribed in the square." This establishes a geometric relationship: Side of square ($a$) = Diameter of circle ($2r$). However, it provides no numerical data to calculate actual lengths. I alone is insufficient. * **Analyze Statement II:** "The area of the circle is $36\pi$." Using the area formula: $\pi r^2 = 36\pi \implies r^2 = 36 \implies r = 6$. We now have the size of the circle, but without Statement I, we do not know how this circle relates to the square mentioned in the question stem. II alone is insufficient. * **Combine I and II:** Statement II tells us the radius is 6, so the diameter is 12. Statement I tells us the side of the square equals this diameter. Thus, the side of the square $a = 12$. * We can now find the perimeter: $4 \times 12 = 48$. ### Exam Strategy & Shortcut Recognize dependent statements. Statement II gives a raw number about a shape, but Statement I is the "bridge" that connects that shape back to the target shape in the question. You always need the bridge and the number together. ### Common Pitfall Assuming "the circle" in Statement II automatically implies the inscribed circle from Statement I without actively combining them. In data sufficiency, each statement must be evaluated in total isolation first. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question**.