quantum wrote:
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
really tuff one
Responding to a pm:
I think Ron has explained it really well above. I would suggest you to read his explanation. As requested, I am putting down the explanation in my words too.
The first and only thing to note here is that "fewer days of rain" does not mean "less rainfall". Say, last year it rained for 10 days. This year it rained for 5 days. Still it is possible that it rained much more this year than last year. Perhaps in those 5 days, the rain received was very very heavy and it more than made up for the 5 day shortfall.
It is possible that 1990 had fewer days in each category but overall had more rainfall. Think of a case which looks like this:
1910
Light rainfall - 10 days - A trace on each of the 10 days
Moderate rainfall - 10 days - 1.1 inch on each of the 10 days
Heavy rainfall - 10 days - 2.1 inch on each of the 10 days
1990
Light rainfall - 8 days - 1 inch on each of the 10 days
Moderate rainfall - 8 days - 2 inch on each of the 10 days
Heavy rainfall - 8 days - 4 inch on each of the 10 days
Would you agree that 1990 had more rainfall than 1910 even though the number of days of rainfall in each category is lower?
So (A) is certainly possible and is the correct answer.
(B) the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910
The no of days of light/moderate rainfall in 1990 is less, not equal hence this is not possible.
(C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910
The no of days of light/moderate rainfall in 1990 is less, not higher in 1990 hence this is not possible.
(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
Moderate rainfall is more than 1 inch but less than or equal to 2 inches. The least rainfall you can get on a moderate rainfall day is 1.00001 inch (i.e. a little more than 1 inch). The maximum you can get is 2 inches. So on any given moderate rainfall day, you cannot have twice the rainfall of any other given moderate rainfall day. Since 1990 had fewer days of moderate rainfall, it cannot have more than twice the rainfall obtained in 1910 on moderate rainfall days.
(E) the average amount of rainfall per month was lower in 1990 than in 1910
If the average rainfall is lower in 1990, the total rainfall will also be lower in 1990 (since both years had 12 months!). This is not possible since we know that total rainfall in 1990 is higher.