If 38 percent of the departments in a certain research organization have 14 or fewer members each, what is the median number of members per department in this organization?(1) 58 percent of the departments have 15 or fewer members each

题目

If 38 percent of the departments in a certain research organization have 14 or fewer members each, what is the median number of members per department in this organization?

(1) 58 percent of the departments have 15 or fewer members each.

(2) 42 percent of the departments have 16 or more members each.

选项

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

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

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

EACH statement ALONE is sufficient.

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

解析

如果某研究机构中38%的部门每个部门有14名或更少成员，那么该机构每个部门成员数的中位数是多少？ **分析条件(1)** 已知38%的部门有14或更少成员，又因为58%的部门有15或更少成员。所以，58% - 38% = 20%的部门有15个成员。由此可知，中位数必然是15，因为按成员数量从小到大排序后，处于中间位置的数是15，所以条件(1)充分。 **分析条件(2)** 已知38%的部门有14或更少成员，且42%的部门有16或更多成员。那么，100% - 38% - 42% =20%的部门有15个成员。同样，按成员数量排序后，中位数是15，所以条件(2)也充分。综上，每个陈述单独都能确定中位数为15，答案是D。

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