请教一道难题

shouyang12

In Patton City, days are categorized as having heavy rainfall (more than two inches), moderate rainfall (more than one inch, but no more than two inches), light rainfall (at least a trace, but no more than one inch), or no rainfall.  In 1990, there were fewer days with light rainfall than in 1910 and fewer with moderate rainfall, yet total rainfall for the year was 20 percent higher in 1990 than in 1910.

If the statements above are true, then it is also possible that in Patton City

A.the number of days with heavy rainfall was lower in 1990 than in 1910
B.the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910
C.the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910
D.the total number of inches of rain that fell on days with moderate rainfall in 1990 was more than twice what it had been in 1910
E.the average amount of rainfall per month was lower in 1990 than in 1910

顾风

应该是A，写错了

[此贴子已经被作者于2006-4-14 16:20:58编辑过]

顾风

分析如下：

B,C,E错误明显，不说了

关键是D

1<m<2, 1<n<2

设 1990是x天,m是1990平均天降雨量,1910是y天,n是该年该类型平均降雨量

x<y

根据D假设， n>m

假设 x = y，这是极限情况

则 n*x>m*y => n>m => 2>n>m>1

又因为 x < y

所以：mx 有可能 大于 ny，但绝对不可能 大于二倍 ny