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In Patton City, days are categorized as having heavy [#permalink]

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18 Dec 2012, 02:52

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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

I cant seem to understand why the answer is what it is.. i have the reasoning available with me will post this soon..

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

I cant seem to understand why the answer is what it is.. i have the reasoning available with me will post this soon..

Coming to choice A, Can the number of days of heavy rainfall be lower in 1990 than in 1910? It is possible because even if the number of days of heavy rainfall was lower, the rainfall could have been lot more heavier on those days making the total rainfall for the year more. Let us keep this choice.

Choice B and C are not possible because they directly contradict the information given that there are fewer number of days of both light and moderate rainfall in 1990 than in 1910.

Choice D contradicts the definition of moderate rainfall as moderate rainfall on any two days by definition has to vary by less than twice.

Choice E is also not possible because if total rainfall for a year was higher than that of another year, then the average rainfall per month for that year also has to be higher than that of the other year.

So Choice A should be the answer.
_________________

Re: In Patton City, days are categorized as having [#permalink]

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15 May 2015, 03:37

Why not option D?? It says that the no of inches of rainfall was twice of the number of inches in 1991, this also might be a reason as to why the rainfall in 1990 was 20% more as compared to the rain in 1991.

B and C are impossible, because we know that in 1910 there were more days with light rainfall than in 1990, and in 1910 there were more days with moderate rainfall than in 1990. So light+moderate in 1910 must be greater than light+moderate in 1990.

For D, suppose we had k days in 1910 with moderate rainfall, and z days in 1990 with moderate rainfall. The question tells us that k > z. The most rainfall you can have per moderate day is 2 inches, so in 1990, the most rainfall you could have in total on moderate days is 2z inches. The least rain you could have on a moderate day is 1 inch, so in 1910, the least total rainfall you could have on all moderate days is k inches.

We've made the moderate rain in 1990 as big as possible, and the moderate rain in 1910 as small as possible, so if it is possible for D to be be true, it will certainly be true in this case. But if it's true that 2z more than twice as big as k, then it would be true that 2z > 2k, or that z > k, and we know that is false. So D is impossible.

For E, if the total annual rainfall in 1910 was T, the question tells us the total was 1.2T (20% greater) in 1990. So the average monthly rainfall in 1910 was T/12, and the average in 1990 was 1.2T/12, which is larger than T/12. So E is impossible.

A, however, can easily be true. I'll ignore the 20% part of the question, because it's not important - the question is whether we could have more rain in 1990 even if there are fewer days with heavy rain, with moderate rain, and with light rain than in 1910. And suppose in 1990 there were 364 days with no rain, 0 days with light rain, 0 days with moderate rain, and just 1 day with heavy rain, but on that 1 day there was 500,000,000,000 inches of rain. And suppose in 1910 you had 65 days with no rain, 100 days with 0.5 inches, 100 days with 1.5 inches, and 100 days with 2.5 inches. Then we have far more rain overall in 1990, even though we have fewer days with heavy, moderate and light rainfall - fewer days in every category. Answer A can still be true as long as the heavy rainfall days in 1990 were much heavier than in 1910 (there are other ways it can be true, but this is probably the easiest one to see).
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Re: In Patton City, days are categorized as having heavy [#permalink]

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23 May 2016, 08:13

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