6.27 Suppose a positive number $x$ exactly satisfies three of the following four conditions:
(甲) $|x-2.5|<0.5$.
(乙) $|x-3|<1$.
(丙) $|x-4|<1.5$.
(丁) $|x-2.5|>2$.
Then the condition that $x$ does not satisfy is
(A) 甲.
(B) 乙.
(C) 丙.
(D) 丁.
(E) Cannot be determined.
(China Beijing Junior High School Mathematics Competition, 1983)
［Solution］(a) The condition is equivalent to $1<x<4$.
(b) The condition holds for any positive integer $x$.
(d) The condition is equivalent to $0<x<\sqrt{10}(x \neq 1)$.
Thus, if the positive number $x$ satisfies (c), then $x$ is a positive integer. When $x=2$ or 3, this number not only satisfies (c), but also satisfies (a), (b), and (d). This contradicts the premise that $x$ satisfies only three out of the four conditions.
Therefore, $x$ must not satisfy (c).
Hence, the answer is $(C)$.