问两道数学题 谢谢各位

sayyessi

1. Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150k, and the median sale price is 130k. Which of the following statements must be true?
I. At least one of the homes was sold over 165k
II. At least one of the homes was sold more than 130k and less than 150k
III. At lease one of the homes was sold less than 130k.

2. Each employee of company Z is an employee of either division X or division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for division x than for company z? D
(1) the ratio of the number of full-time employees to the umber of part-time employees is less for division Y than for company Z?
(2) More than half of the full-time employees of company Z are employees of division X, and more than half of the part-time employees of company Z are employees of Division Y.

dong870501

同问2，式子可以列出来，但是比较起来貌似很复杂~~

lovedoublej

median 130位于第八套房，前七套小于或等于130，后七套大于或等于130，平均150。即使前八套房都取130，后七套房也可把前边每套和平均值差值20补回来，故（3）错；同理也可没有房大于130小于150，故（2）错；
关键是（3）考虑到前八套房最多每套售都130，故8*（150-130）=160，假设取最大值，后7套房都为165，7*（165-150）=105，不足以弥补前8套160的差值，故肯定有房大于165

sayyessi

讲得很清楚~谢谢！

henguc

第二题
F(x): number of full-time employees in x
P(x): number of part-time employees in x
F(y): number of full-time employees in y
P(y): number of part-time employees in y
比较 F(x)/P(x) 和 F(y)/P(y) 的大小 ？
条件一：可以采用“混合不同浓度溶液”的思想——将高浓度和低浓度的溶
液混合，混合液的浓度位于两者之间。如果将 F(*)/P(*)看成浓度的话，x部
门和y部门混合后，混合液浓度位于x,y两者浓度之间。条件一给出了y的浓度
低于混合液浓度，因此x浓度必须高于混合液浓度。
条件二：由条件可知，F(x)>F(y); P(x)<P(y)。结果明显
答案：D