1. Given $A=(2-x)-\sqrt{2}(\sqrt{2} x-5)$. The natural number $x$ that makes $A$ positive has ( ).
(A) 1
(B) 2
(C) more than 2 but a finite number
(D) an infinite number
$-1 . C$.
Let $A=(2-x)-(\sqrt{2} x-5) \sqrt{2}>0$.
Solving, we get $x<\frac{2+5 \sqrt{2}}{3}$.
Also, $3<\frac{2+5 \sqrt{2}}{3}<4$, so the natural numbers $x=0,1,2,3$ satisfy the condition, for a total of 4.