题目

­A certain country with a total population of 50 million is divided into six regions J, K, L, M, N and P, ranked from the most populated to the least populated, with some of the populations possibly equal. If 21 percent of the total population of the country is in region M and if the population of region P is 2 million, what is the greatest possible population of region N?


选项

A.

5 million

B.

6 million

C.

7 million

D.

8 million

E.

9 million­

解析

某个国家总人口为5000万,分为J、K、L、M、N、P六个地区(按人口从多到少排序,部分地区人口可能相等)。若该国21%的人口位于M地区,且P地区人口为200万,那么N地区的最大可能人口是多少? 已知人口关系:\( J \geq K \geq L \geq (M = 10.5) \geq N \geq (P = 2) \)(注:M地区人口为5000万×21% = 1050万) 要最大化N的人口,需最小化J、K、L的人口。它们的最小取值为10.5(与M相等)。因此有: \[ \begin{align*} (J = 10.5) &\geq (K = 10.5) \\ &\geq (L = 10.5) \geq (M = 10.5) \geq N \\ &\geq (P = 2) \end{align*} \] 根据总人口\( J + K + L + M + N + P = 50 \),代入得: \[ 4×10.5 + N + 2 = 50 \] 解得:\( N = 6 \) 答案:B
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