Example 1: Let condition A: real numbers $x, y$ satisfy $\left\{\begin{array}{l}2<x+y<4, \\ 0<x y<3 ;\end{array}\right.$ Condition B: real numbers $x, y$ satisfy $\left\{\begin{array}{l}0<x<1, \\ 2<y<3 .\end{array}\right.$ Then A is B's ( ).
(A) Sufficient but not necessary condition
(B) Necessary but not sufficient condition
(C) Sufficient and necessary condition
(D) Neither sufficient nor necessary condition
Solution: Clearly, when $x=\frac{3}{2}, y=1$, $x+y=\frac{5}{2} \in(2,4), x y=\frac{3}{2} \in(0,3)$ satisfies condition A, but $x=\frac{3}{2} \notin(0,1)$ does not satisfy condition B, i.e., A $\nrightarrow$ B, so condition A is not sufficient;

Conversely, if $\left\{\begin{array}{l}0<x<1, \\ 2<y<3,\end{array}\right.$ by the properties of adding and multiplying inequalities in the same direction, we have $2<x+y<4$ and $0<x y<3$, i.e., A $\leftarrow$, so condition A is necessary.
Therefore, A is a necessary but not sufficient condition for B. Choose B.
Guidance for solving: When determining what kind of condition a premise is for a conclusion, first clearly identify what the premise and conclusion are; then try to deduce the conclusion from the premise, and then try to deduce the premise from the conclusion. The reasoning methods can be direct proof, indirect proof (i.e., proof by contradiction), or providing counterexamples to show that it does not hold; finally, indicate what kind of condition the premise is for the conclusion. Generally, when making judgments, both sufficiency and necessity should be evaluated.