题目

A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?


(1)


(2)

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

一个学区的组织方式是,每个部门领导(D)都有恰好T名教师向其汇报,且每名教师都有恰好S名学生。这个学区的学生与部门领导的比例是多少? - **条件(1)**:\(\frac{T}{D}=\frac{2}{1}\) - **条件(2)**:\(\frac{S}{T}=\frac{4}{1}\) - 已知每个部门领导对应\(T\)名教师,每名教师对应\(S\)名学生,那么学生与部门领导的比例为\(\frac{S\times T}{D}\)。 - **对于条件(1)**:\(\frac{T}{D}=\frac{2}{1}\),即\(T = 2D\),但是我们不知道\(S\)的值,所以无法确定\(\frac{S\times T}{D}\)的值,条件(1)单独不充分。 - **对于条件(2)**:\(\frac{S}{T}=\frac{4}{1}\),即\(S=4T\),但是仅根据此条件我们不知道\(D\)与\(T\)之间完整的关联(缺少\(D\)与\(T\)的直接比例关系中\(D\)的信息),所以无法确定\(\frac{S\times T}{D}\)的值,条件(2)单独不充分。 - **综合两个条件**:将\(T = 2D\)和\(S = 4T\)联立,可得\(S=8D\),那么学生与部门领导的比例\(\frac{S\times T}{D}=\frac{8D\times2D}{D}=16D\),由于\(D\)的值不确定,所以综合两个条件也不能确定学生与部门领导的比例,即两个条件联合起来也不充分。 综上,答案是E 。
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