We are given the relation:
$\texttt{Loan}(\texttt{loan_number}, \texttt{branch_name}, \texttt{amount})$
with the following instance:
\[
\begin{array}{|c|c|c|}
\hline
\texttt{loan_number} & \texttt{branch_name} & \texttt{amount} \\
\hline
\texttt{L11} & \texttt{Banjara Hills} & 90000 \\
\texttt{L14} & \texttt{Kondapur} & 50000 \\
\texttt{L15} & \texttt{SR Nagar} & 40000 \\
\texttt{L22} & \texttt{SR Nagar} & 25000 \\
\texttt{L23} & \texttt{Balanagar} & 80000 \\
\texttt{L25} & \texttt{Kondapur} & 70000 \\
\texttt{L19} & \texttt{SR Nagar} & 65000 \\
\hline
\end{array}
\]
The SQL query to evaluate is:
SELECT L1.loan_number
FROM Loan L1
WHERE L1.amount > (
SELECT MAX(L2.amount)
FROM Loan L2
WHERE L2.branch_name = 'SR Nagar'
);
Step 1: Evaluate the subquery
The subquery is:
SELECT MAX(L2.amount)
FROM Loan L2
WHERE L2.branch_name = 'SR Nagar';
First, filter the $\texttt{Loan}$ relation for rows where $\texttt{branch\_name} = \texttt{'SR Nagar'}$:
\[
\begin{array}{|c|c|c|}
\hline
\texttt{loan_number} & \texttt{branch_name} & \texttt{amount} \\
\hline
\texttt{L15} & \texttt{SR Nagar} & 40000 \\
\texttt{L22} & \texttt{SR Nagar} & 25000 \\
\texttt{L19} & \texttt{SR Nagar} & 65000 \\
\hline
\end{array}
\]
Now compute the maximum of the $\texttt{amount}$ column in this filtered set:
\[
\max(40000,\ 25000,\ 65000) = 65000
\]
Thus, the subquery returns the scalar value 65000.
Step 2: Evaluate the outer query
The outer query becomes:
SELECT L1.loan_number
FROM Loan L1
WHERE L1.amount > 65000;
We now scan the full $\texttt{Loan}$ instance and select all tuples with $\texttt{amount} > 65000$:
\[
\begin{array}{|c|c|c|}
\hline
\texttt{loan_number} & \texttt{branch_name} & \texttt{amount} \\
\hline
\texttt{L11} & \texttt{Banjara Hills} & 90000 \\
\texttt{L23} & \texttt{Balanagar} & 80000 \\
\texttt{L25} & \texttt{Kondapur} & 70000 \\
\hline
\end{array}
\]
These three rows satisfy the condition. The query projects only the $\texttt{loan_number}$ attribute, yielding:
- $\texttt{L11}$
- $\texttt{L23}$
- $\texttt{L25}$
Hence, the query returns 3 rows.
$\boxed{\text{Final Answer: 3}}$