Given:
- Property tax is $p %$ of the home value.
- For a $\(\$ 55,000\)$ home, property tax $\(=\$ 5,500\)$.

Step 1: Find the tax rate $p$
Property tax $=p % \times$ home value
Given:

$$
\(5500=\frac{p}{100} \times 55000\)
$$


Solve for $p$ :

$$
\(\begin{gathered}
5500=55000 \times \frac{p}{100} \\
\frac{5500}{55000}=\frac{p}{100} \\
0.1=\frac{p}{100} \\
p=10
\end{gathered}\)
$$


So, the property tax rate is $10 %$.

Step 2: Calculate property tax on a $\(\$ 65,000\)$ home


\(Tax=10\) % \(\times 65000=\frac{10}{100} \times 65000=6500\)


Compare Quantity A and Quantity B:
- Quantity $\(A=\$ 6,500\)$
- Quantity \(B = \$6,600\)

Answer:
- Quantity $\(B(\$ 6,600)\)$ is greater than Quantity $\(A(\$ 6,500)\)$.

Final conclusion:
Quantity B is greater.