In Patton City, days are categorized as having heavy rainfall (more th

I will go with A.


(A) the number of days with heavy rainfall was lower in 1990 than in 1910
>>>> The author says lower light and moderate rainfall, YET only 20% more rainfall in 1990. This means there was some other factor that led to lower total rainfall. Above argument solves this !

(B) the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910
>>> There is no such rainfall listed in the question. So rejected.

(C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910
>>> There is no such rainfall listed.

(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
>>> If 1910 received 1.5inch of rainfall, then 1990 would have received 3inch rainfall. But 2+ inch means heavy rainfall. So this is incorrect too.

(E) the average amount of rainfall per month was lower in 1990 than in 1910
>> This will mean that 1990 had less rainfall than 1910.

First I chose D, then after reviewing I see how A is the correct answer.

From the first statement we know

1990 has
fewer light rainfall days
fewer moderate rainfall days
20% more total rainfall

I think the question's design is for you to search for an explanation for the difference. We all know the questions:

"Which one of the following would best explain the seeming contradiction" or some wording similar......So this is the way we approach this question, that leads us to find D as a possible explanation.

But they questions is which could possibly be true.

You could read choice A as follows:

It is possible that in Patton City the number of days with heavy rainfall was lower in 1990 than in 1910.

Yes it is possible, why not. For example....

In 1990 we could have 10 days with heavy rainfall, and in 1910 we could have 11 days with heavy rainfall.

This example reminds us that when we see which could be true.....we should keep a very open mind.

I tried out some sample data for D.
1910 --> 100 moderate days x 1.0000000000000000000000000000000001 inches each day = c. 100 inches on moderate days
1990 --> 99 moderate days x 2 inches each day = 198 inches

198 inches is not greater than double 100 inches

Thats how I figured out A -

Firstly, why it can not be C,D

C - the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910. This contradicts with the stem that in 1990 we have had fewer days of moderate and light rainfall. So ruled out..

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. Lets assume in 1910 we have had three days of moderate rainfall and in 1990 the best scenario we could have two. Assume, worst case scenario we received 1 Unit of rainfall in all days in 1900 thus total 3 units and in 1990 we received 2 units (the max we could recieve for moderate) each day. Thus, it comes to total of 4 Units. But , 4<3*2. This contradicts the statement and this is the most favourable case that we could assume for 1990.

Why its A:
A) the number of days with heavy rainfall was lower in 1990 than in 1910
The number can be lower (assume just a difference of one day) , but the intensityof rainfall received 1990 could be substantially greater than in 1990 to offset this difference.

Hope it helps..


Thanks,
Aakash

Fun question

Here is why (A) the number of days with heavy rainfall was lower in 1990 than in 1910 is the answer:

On first glance this answer seems the opposite of what we are going for. Surely, Patton City had more days with heavy rain in 1990 than in 1910, otherwise how could one possibly account for the 20% increase in rain from 1910 to 1990. But here is the thing: even if Patton City had fewer days with 2+ inches of rain in 1990 than in 1910, if those days were marked by heavily deluges, then 1990 would have more inches of rain than 1910. Let me illustrate: Let's say that in 1990 Patton City had five days with 2+ inches of rain (Day 1: 4 inches, Day 2: 5 inches, Day 3: 6 inches, Day 4: 5 inches, Day 5: 3 inches). In 1910 Patton City had six rainy days with 2+ inches or rain (Day 1 : 2.5 inches, Day 2: 2.3 inches, Day 3, 2.4 inches...etc.). You can see that, despite fewer 2+ inches days, 1990 has far more inches of rainfall from 2+ inches days than 1910 does.

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.

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 actually think this is a great question. It highlights the logic that the GMAT is looking for, and of course the trickery they're known for. They also often put verbal understanding in quant questions and math understanding in verbal questions. This is such a question. If the total rainfall was higher in 1990 than 1910, you figure there were more rainiy days in 1990, but that doesn't have to be true. All the rain could have fallen on one day (at the logical extreme) and then had 364 days of clear skies. If you understand that this is possible, then you realize that A is possible. There were 5 days of 10+ inch torrential rain in 1990, and 15 days of 2 inch downpour in 1910. More days in 1910, but more rain in 1990.

The other answer choices can be eliminated by the question stem (B, C and E) or by basic math (D). Days with moderate rainfall are between 1 and 2 inches, so at a minimum value 1.00. If they double, they will no longer count as moderate rainfall days and instead move up to heavy. The biggest difference you can have was 1.00 in 1910 and 1.99 in 1990. This will never get to double the rainfall. A is the only possibility, although it is counter-intuitive. This type of reasoning is helpful in math as well, particularly in stats when you realize that average is the most misleading characteristic of them all.

Hope this helps!
-Ron

I really hope no one believes the GMAT would ever give you a question that isn't logically correct. I guess it is possible to see a question on these forums that isn't a valid GMAT question, but this one is perfectly logical, although it probably isn't intuitive.

Let's do a simple example using one week in 1910 and one in 1990:

Rainfall Week 1 1910
M T W R F S S
0 10 0 0 15 0 10

Average rainfall: 35/7 = 5
Number of heavy days: 3

Rainfall week 1 1990
M T W R F S S
20 0 0 0 22 0 0

Average rainfall: 42/7 = 6
Number of heavy days: 2

Answer A makes perfect sense in this situation. More rain in 1990, but less heavy days. I.E. Each heavy day was really heavy. No other choice works logically.

Thanks!
-Ron

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.

I think you need to reconsider again - focus on two things: Days of rainfall & Amount of rainfall

When they say 20% more rainfall, they mean AMOUNT of rainfall is 20% more. It is not directly related to the 'DAYS of rainfall'. Keep this in mind and then check out the explanation above.

Fewer days of moderate and light rainfall doesn't have any direct implications for the amount of rainfall received on moderate and light rainfall days.

Given: In 1990 there were fewer days of moderate rainfall than in 1910

1 < Moderate rainfall <= 2 inches
Say,
1910 - 20 days
1990 - 19 days

Can this be correct
(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
Is it possible that inches of rain on these 19 days of 1990 was more than twice of the inches of rain on these 20 days of 1920?
Let's look at the most favorable case - 20 days of 1910 had as little as possible rain on these moderate rain days and 19 days of 1990 had as much as possible.

1910 - 20 days - each day, rainfall was slightly more than 1 inch so total rainfall is slightly more than 20 inches
1990 - 19 days - each day, rainfall was 2 inches (max possible) and so total rainfall is 38 inches

If 1990 had fewer days of moderate rainfall, it cannot have more than twice the rainfall of 1910.
For each day of 1990, you will need to have more than twice the rainfall of each day of 1910 but that is not possible because min rainfall on a moderate day is more than 1 and max is 2 (which is less than twice of 'more than 1')

If in the first week it rains for one day and in the second week it rains for two days, can you conclude that it rained more in the second week? What if the one day of the first week was a full day of heavy downpour and the two days of the second week just saw light 5 minute showers each? Number of days is just one aspect. The amount of rainfall that fell on each day is another.

I chose [A] the number of days with heavy rainfall was lower in 1990 than in 1910

Explanation and elimination of other choices:

We are only given ranges for rainfall on a described day. Therefore a single day of heavy rain in 1990 (characterized as H > 2 inches) could have more total inches that a larger number of heavy rainfall days in 1910. If, for example, 1910 had 10 days of 2.1 inches per day then it could be possible for 1990 to have 1 day of 30 inches. This could satisfy the evidence provided. Therefore I could not eliminate A.

B. "Some rainfall" but no more than 2 inches would mean that "light" and "moderate days" fit into this definition. We are given that the number of days of moderate rainfall and light rainfall in 1990 are lower than in 1910, so this seems to contractdict the evidence provided. If both ranges were less than 1910 then how could it be possible that the totals are the same? Eliminated.

C. Same logic applied to B but now we are told that 1990 could be greater than 1910. Again, I elimiated as this doesn't fit with the evidence provided.

D. Total number of inches that fell on moderate days in 1990 was more than twice what it had been in 1910. We are given that there were fewere days with moderate rainfall in 1990 than 1910. So, the only way that twice the number of inches to fall on those fewer days would be if the allowable range (to be considered a moderate rainfall day) was higher than the range we were given. We were given that a moderate day was "more than one inch, but no more than 2", which I believe is repsented by Moderate is greater than one but less than or equal to two. That range is less than one inch by definition. Therefore, it wouldn't it be impossible to have fewer days of rain but twice the number of inches if, to be considered a "moderate" day it MUST fall with that range? This didn't seem right so I eliminated this as well.

Example: If there were 5 days of moderate rain in 1910 and 4 days of moderate rain in 1990 (satisfying the evidence given), and if each day in 1910 only rained just over 1 inche per day (lower part of range), or a little more than 5 inches,...then even if it rained exactly 2 inches per day during the 4 moderate days in 1990 we would still only have 8 inches. You cannot satisfy this choice with the evidence given.

E. Average amount of rainfall per month was lower in 1990 than in 1910. I assume that average monthly rainfall could be simply calculated as Total Rainfall/12 months. We are given that the 1990 total rainfall was 20% higher in 1990 than 1910, and since both have the same denominator (12 months), wouldn't it be impossible to have a higher total but lower average amount of rainfall per month? I eliminated this also.

Final answer: A

Not sure if my logic is correct. Took me 4 minutes to solve.

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).

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.

days are categorized as

drh +(a-1)rm+(b-1)rl>crh +(a)rm+(b)rl

since medium and light are not of much rainfall they can be neglected.
so dr>cr
no of days of heavy rain in 1990 can be more than that of 1910 with an average rainfall of >2"
or no of days can be less and rainfall in 1990 can be much more of some 10" than those of 1910

and still total rainfall of 1990 can be more than 1910

(A) the number of days with heavy rainfall was lower in 1990 than in 1910(Possible)

(B) the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910
(less than 2"=moderate or light rainfall and corresponding no of days in 1990 were given less than that of 1910.
This info negates the premise.)

(C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910
(same as of B. less than 2"=moderate or light rainfall and corresponding no of days in 1990 were given less than that of 1910.
This info negates the premise.)

(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
(it can be less than 2 and more than zero but not more than 2. wrong info)

(E) the average amount of rainfall per month was lower in 1990 than in 1910
(negates the premise-total is more then avg per month is also more)

tough pb indeed.

The argument:
HR > 2
1 < MR < 2
0 < LR < 1
NR
# days LR of 1990 < # days LR of 1910
#days MR of 1990 < # days MR of 1910
Total # R of 1990 (#LR + #MR + #HR) > Total #R of 1910 (#LR + #MR + #HR)
(A) possible. suppose in 1990 there were only 5 days with heavy rainfall but rain was 100 inches a day and in 1910 there were 6 days but rain was only 3 inches a day. Thus total in 1990 can be greater than total in 1910
(B) impossible
(C) impossible
(D) (X) days of MR in 1990 < (Y) those in 1910
=> (X) x from 1 to 2 cannot double (Y) x (from 1 to 2)
(E) impossible because total rainfall in 1990 = 120% total in 1910

C. the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910

The days with some rainfall, but no more than two inches are LR days and MR days. So (C) says
LR Days + MR Days (1990) > LR Days + MR Days (1910)

But from our analysis of the argument, we already know that
LR Days + MR Days (1990) < LR Days + MR Days (1910)

Hence (C) is not possible.

As for (A), it is based on the logic that more days of rainfall does not mean more rainfall (inches). The intensity of rainfall can be higher over fewer days and hence fewer days could result in more rainfall.

I choose D because:-

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.

Say in 1990 the no.of days with light rainfall was 10
In 1910 it were 20.

Say in 1990 no.of days of moderate rainfall was 15.
and in 1910 it was 20

Total rainfall in 1910=100cm
Total rainfall in 1990=120cm

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.

No.of days of heavy rainfall can or cannot be greater in 1910.
because in one day in 1990 a heavy rainfall can give 20cm or 2.1 cm of rain.

B. the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910.
This is also not necessary

C. the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910.
It is given that it was fewer in 1990

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.
After applying POE i am left with this option.
This some what makes sense to me.That even if der was no heavy rainfall then too rainfall would have been greater in 1990

E. the average amount of rainfall per month was lower in 1990 than in 1910.
we cannot determine this.But i think that it is given that it was higher in 1990.

Please explain where i am wrong.........