1. Given that $m$ and $n$ are two consecutive positive integers, $m<n$, and $a=m n$, let $x=\sqrt{a+n}+\sqrt{a-m}$, $y=\sqrt{a+n}-\sqrt{a-m}$. Which of the following statements is correct? ( ).
(A) $x$ is odd, $y$ is even
(B) $x$ is even, $y$ is odd
(C) Both $x$ and $y$ are odd
(D) Both $x$ and $y$ are even
-、1.G.
From the problem, we know that $a=m(m+1)=n(n-1)$. Then,
$$
\begin{array}{l}
\sqrt{a+n}=\sqrt{n(n-1)+n}=n, \\
\sqrt{a-m}=\sqrt{m(m+1)-m}=m .
\end{array}
$$

Therefore, $x=n+m=m+m+1=2 m+1$, $y=n-m=1$.
Thus, both $x$ and $y$ are odd numbers.