题目

Let x and y be two distinct digits in the decimal x.yx, what is x?


(1) When rounded to the nearest integer, the decimal becomes y


(2) When rounded to the nearest tenth, the decimal becomes x.y

选项

A.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.


B.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.


C.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.


D.

EACH statement ALONE is sufficient.


E.

Statements (1) and (2) TOGETHER are NOT sufficient.

解析

设\(x\)和\(y\)是小数\(x.yx\)中两个不同的数字,\(x\)是多少? (1)当四舍五入到最接近的整数时,该小数变为\(y\) (2)当四舍五入到最接近的十分位时,该小数变为\(x.y\) - **对于条件(1)** 相当于是 $y \ge 5$,即 $y$ 的取值集合为 $\{5, 6, 7, 8, 9\}$; 由 $x = y - 1$,可得 $x$ 的取值集合为 $\{4, 5, 6, 7, 8\}$,对应两位小数 $x.yx$ 的结果为:$4.54$、$5.65$、$6.76$、$7.87$、$8.98$。**条件(1)不充分**。 - **对于条件(2)** 相当于是 $x < 5$,即 $x$ 的取值集合为 $\{1, 2, 3, 4\}$。**条件(2)不充分**。 - **综合条件(1)和(2)** (1) 与 (2) 联立:两个集合的交集为 $\{1, 2, 3, 4\} \cap \{4, 5, 6, 7, 8\} = \{4\}$,可唯一确定取值。**条件(1)+(2)充分**。 **答案:C**
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