Consider the following question and decide which of the statements is sufficient to answer the question.
Question:
Find the value of `p^(2)-4`,
Statements:
1) `(p)/(2)=(5)/(7)`
2) `p^(2)-q^(2)` = 729

Options

A. Only 1 is sufficient
B. Either 1 or 2 is sufficient
C. Neither 1 nor 2 is sufficient
D. Only 2 is sufficient

Answer

To solve the question, we need to find the value of \( p^2 - 4 \) based on the given statements.

### Step-by-Step Solution:

1. **Analyze Statement 1:**
- The first statement is \( \frac{p}{2} = \frac{5}{7} \).
- To find \( p \), we can cross-multiply:
\[ p = 2 \cdot \frac{5}{7} = \frac{10}{7} \]

2. **Calculate \( p^2 \):**
- Now that we have \( p = \frac{10}{7} \), we can calculate \( p^2 \):
\[ p^2 = \left(\frac{10}{7}\right)^2 = \frac{100}{49} \]

3. **Find \( p^2 - 4 \):**
- We need to express 4 in terms of a fraction with a denominator of 49:
\[ 4 = \frac{4 \cdot 49}{49} = \frac{196}{49} \]
- Now we can find \( p^2 - 4 \):
\[ p^2 - 4 = \frac{100}{49} - \frac{196}{49} = \frac{100 - 196}{49} = \frac{-96}{49} \]

4. **Conclusion:**
- The value of \( p^2 - 4 \) is \( \frac{-96}{49} \).

5. **Analyze Statement 2:**
- The second statement is \( p^2 - q^2 = 729 \).
- However, this statement introduces an additional variable \( q \) which is not relevant to finding \( p^2 - 4 \). Therefore, it does not provide sufficient information to answer the question.

### Final Answer:
- The first statement is sufficient to find the value of \( p^2 - 4 \), while the second statement is not.