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. A rectangular field is 40 yards long. Find the area of the field. I. A fence around the outside of the field is 140 yards long. II. The distance from one corner of the field to the opposite corner is 50 yards.

### Concept & Rectangle Area To find the area of a rectangular field, we need both its length ($L$) and breadth ($B$). $$ \text{Area} = L \times B $$ ### Step-by-Step Solution 1. **Given:** The length of the rectangular field is given in the question stem as $40 \text{ yards}$ ($L = 40$). 2. **Analyze Statement I:** A fence around the outside indicates the perimeter is $140 \text{ yards}$. The formula is $2(L + B) = 140$. Since we know $L = 40$, we can solve for $B$ ($40 + B = 70 \Rightarrow B = 30$). With both $L$ and $B$ known, we can find the area. Statement I alone is sufficient. 3. **Analyze Statement II:** The distance from one corner to the opposite corner is the diagonal, given as $50 \text{ yards}$. By the Pythagorean theorem, $L^2 + B^2 = 50^2$. Substituting $L = 40$, we can solve for $B$ ($1600 + B^2 = 2500 \Rightarrow B^2 = 900 \Rightarrow B = 30$). With $B$ known, we can calculate the area. Statement II alone is sufficient. ### Exam Strategy & Shortcut Since the length is already provided in the primary question stem, any statement that provides a second, independent relational metric involving the breadth (such as perimeter or diagonal) will automatically be sufficient to determine the area. ### Common Pitfall A frequent error is forgetting to incorporate the crucial information already given in the main question stem (length = $40$) before evaluating the numbered statements individually. ### 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;**.