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 (atleast 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
OA is
A IMO its D
PLease explain...
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krisraam
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Answer is A.
Explanation
A. The number of days with heavy rainfall was lower in 1990 than in 1910.
The number of days with heavy rainfall may be lower in 1900 than 1910. But the total no of inches of rain in each category ( light, moderate, heavy) may be more in 1900 than 1910 leading to 20% higher in 1900
B. the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910
ie. The no of days with light and moderate rainfall is more in 1910 than 1900. Not possible.
C. the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910
ie. The no of days with light and moderate rainfall is more in 1910 than 1900. 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
The total of number of days of rain in 1900 fewer than 1910. Lets say 20 days in 1910 and 19 days in 1900. Moderate rain has to be between 1 and 2 inches. So no. of inches in 1910 between 20<x<40. No. of inches in 1900 19<y<38. Twice the minimum value for 1900 ie 20 * 2 = 40 is less than the max value of 1910. So Not possible
E. the average amount of rainfall per month was lower in 1990 than in 1910
Explanation
A. The number of days with heavy rainfall was lower in 1990 than in 1910.
The number of days with heavy rainfall may be lower in 1900 than 1910. But the total no of inches of rain in each category ( light, moderate, heavy) may be more in 1900 than 1910 leading to 20% higher in 1900
B. the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910
ie. The no of days with light and moderate rainfall is more in 1910 than 1900. Not possible.
C. the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910
ie. The no of days with light and moderate rainfall is more in 1910 than 1900. 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
The total of number of days of rain in 1900 fewer than 1910. Lets say 20 days in 1910 and 19 days in 1900. Moderate rain has to be between 1 and 2 inches. So no. of inches in 1910 between 20<x<40. No. of inches in 1900 19<y<38. Twice the minimum value for 1900 ie 20 * 2 = 40 is less than the max value of 1910. So Not possible
E. the average amount of rainfall per month was lower in 1990 than in 1910
