DSE 2021 Question 27: Welfare economics and social choice

In an exchange economy there are two goods $X$ and $Y$ and two agents A and B. A owns 10 units of good $Y$ while B owns 10 units of good $X$. A has lexicographic preferences with good $X$ coming before good $Y$ (she chooses the bundle with the most $X$; only in a tie on $X$ does she compare $Y$). B has lexicographic preferences with good $Y$ before good $X$. Statement I: an allocation where A gets 10 units of good $X$ and B gets 10 units of good $Y$ is Pareto optimal. Statement II: an allocation where A gets 10 units of $X$ and 5 units of $Y$ while B gets 5 units of $Y$ is Pareto optimal. Choose the correct answer.