GWD逻辑 急求解释

jackba8888

In Patton City, days are categorized as having 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 years was 20 percent higher in 1990 than in 1910 .

If the statement above are true, then it is also possible that in P 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 1910 was more than twice what it had been in 1910
e. the average amount of rainfall per mouth was lower in 19910 than in 1910.


牛牛们看下为什么答案是A 呢。。

jackba8888

自己顶， 亲们帮忙解释解释。

sdcar2010

A is correct

There are only two likely possibilities for 1990 to have more total rainfalls than 1910:

1) Total rainfalls from heavy rainfalls is bigger in 1990 than in 1910.  This could be done either by very heavy rains in a few days in 1990 or with more heavy rainfalls days in 1990
2) Total rainfalls from moderate/light rainfalls is bigger in 1990 than in 1910.  This possibility sounds counterintuitive but is mathmatically possible.  Keep in mind the definition of moderate/light rainfalls is based on a range. It is conceivable that a moderate rainfalls day could have either 1.9 inch or 1.1 inch of rain.  So if all the moderate rainfall days in 1990 had 1.9 inch while all the moderate rainfall days in 1910 had only 1.1 inch, the total rainfall in 1990 could be bigger than in 1910.

Answer A points out the first possibility and is the right answer.

crazysalad

My personal view on this. Hope it can be helpful.
If the statements above are true, then it is also possible that in Patton City      D/A 其实这道题比较tricky，说了moderate和light的rainfall，就是没有说heavy rainfall。
A.    the number of days with heavy rainfall was lower in 1990 than in 1910 只要某天量大，下得天数少也可以的。
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   这两个因素都可以比，都可能正确，但是唯独缺少大雨因素，所以都有可能被推翻。
这道题这么假设，已经moderate的定义是1-2之间，设90的天数是a，平均降雨量为x，10年天数为y，平均降雨量为y，因此得到total number of inches of rain that fell on days with moderate rainfall each is 90年ax，10年by。
已经知道a<b,  1<x<2, 1<y<2, 所以， a<ax<2a，同理, b<by<2b, 2b<2by<4b，拿ax最大的可能值为2a来跟10年最小的比为,2b, 2a<2b 所以90年最大的可能值都小于10年最小的可能值，怎么可能ax>2by
E.    the average amount of rainfall per month was lower in 1990 than in 1910
B和C，题目中都说了no more than 2 inches 的rainfall的信息了，所以应该排除。E和题目中的信息相反。