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Re: In Patton City, days are categorized as having heavy [#permalink]
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01 Jul 2013, 08:25
This question is ridiculous, none of the answers really support the conclusion of the passage. Answer D was the closest possibly but that mathematically fails, Moderate rain (greater than 1 inch and less than 2 inches). So double of moderate rain quantity, will be heavy rain, so this answer fails as well.



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Re: In Patton City, days are categorized as having heavy [#permalink]
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01 Jul 2013, 09:05
rgmes3 wrote: This question is ridiculous, none of the answers really support the conclusion of the passage. Answer D was the closest possibly but that mathematically fails, Moderate rain (greater than 1 inch and less than 2 inches). So double of moderate rain quantity, will be heavy rain, so this answer fails as well. Hi, this one is not ridculous rather a tricky one. the question is which one is possible and not must be true....? for example : lets say X is an integer====>question is which can be possible? 1) X is even 2)X is odd 3) X is prime 4) x=10 5) X= 2.5 in this case you will say all is possible except 5 th option....because integer cannot be a fraction. now coming to question: argument has defined HEAVY = greater than 2 inches mod rain= 12 inches light rain= 01 inches no rain= 0 also given: no.days with mod rain and no. of days with heavy rain is fewer in 1990 compared to those of 1910. moreover overall rain of 1990 is greater than rain in 1910 now as you see if we have to make 1990 overall rain more than 1910's rain.....then we can increase rain quantity only by HEAVY rain..because in other 2 categories 1990 is already behind. now suppose: in 1990 no of days with heavy rain = 10.....with 10 inches of rain(because it can be anything greater than 2 inches) in 1910 no. of days with heavy rain =20....with 2 inches of rain now if you calculate total rain in 1990 with category of heavy rain= 10*10=100 inches and total rain in 1910 with category of heavy rain= 3*20= 60 inches. now this thing clearly satisfies the argument... total rain will be more and the number of days with heavy rainfall was lower in 1990 than in 1910 hence OPTION A ...is right KUDOS if it helped you.
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Re: In Patton City, days are categorized as having heavy [#permalink]
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01 Jul 2013, 09:14
I picked D at the 2 min. but the answer is A. Remember, the question is asking for possible conclusion based on the arguments. B, C, D, E are proved as not possible based on the arguments.. D  Mathematically not possible, as you mentioned.. E  If average rain fall per month is less in 1990 than 1910, then the total rainfall for the year in 1990 can never be more than 1910 B, C  Not possible since the number of days of moderate and slight rain in 1990 is less than number of days of similar rain in 1910
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Re: CR Rainfall [#permalink]
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01 Jul 2013, 20:21
buffdaddy wrote: 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 definitely possible. Consider in 1990 one day about 1000000000 inches fell. (just kidding, but u get the point)B. the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910 can't be true because we know moderate and light says were fewer in 1990 than in 1910C. the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910 same problem as in BD. 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 not mathematically possible. We can only get twice the amount of rainfall if the number of moderate days were the same and all the moderate days in 1990 have 2 inches of rain and all the moderate rain days have 1 inch of rain in 1910E. the average amount of rainfall per month was lower in 1990 than in 1910 not possible (unless there were more months in 1990 )since we are told total in 1990 was hight really tuff one I am still confused about option D. As you said that one day it can rain 1000000000 so option A) is the answer. Likewise why can we assume that there were days in 1990 with moderate rainfall where it rained longer and hence total no. of rainfall is more. if i assume correctly the size of the rainfall (given in inches) is the diameter of rain drops . so say 99 days in 1990 and 100 days in 1910: in 1990 total rainfall =99 * 2(approx)*24(hours) in 1910 total rainfall = 100*1 *11 hours so 1990 it is more than twice.. please explain as to why above cannot be a possiblility
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Re: In Patton City, days are categorized as having heavy [#permalink]
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02 Jul 2013, 09:00
No kidding tough. 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 Everyone pretty much eliminated B,C, and E, so I won't repeat what's been said. Option D) This one looks tricky but is very simple. Moderate rainfall is defined as "more than one inch, but no more than two inches". 1.00001" x 2 = 2.00002", which would put the rainfall into the heavy category. So purely according to definition this answer is impossible. That leaves Option A as "possible". Basically anything over 2" to infinite amounts of rain per day. So you could have 5 days of 2" rain in 1910 and 4 days of 8" rain in 1990 and still have more total rainfall in 1990.
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Re: In Patton City, days are categorized as having heavy [#permalink]
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02 Jul 2013, 09:38
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 counterintuitive. 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
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Re: In Patton City, days are categorized as having heavy [#permalink]
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06 Jul 2013, 01:55
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NO option is logically correct... but, i will go with D



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Re: In Patton City, days are categorized as having heavy [#permalink]
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06 Jul 2013, 09:41
sakiii wrote: NO option is logically correct... but, i will go with D 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
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Re: In Patton City, days are categorized as having heavy [#permalink]
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21 Aug 2013, 21:18
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.
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Re: In Patton City, days are categorized as having heavy [#permalink]
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22 Aug 2013, 19:47
Hi Karishma
I understand the logic for A however there could be another meaning to the statements :
Question Steam: 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.
Question stem means that days of moderate+light rainfall for 1900 < moderate+light rainfall for 1910 however the total rainfall for 1900 > total rainfall for 1910.
This could mean that heavy rainfall for 1900 > heavy rainfall for 1910 for the total rainfall for 1900 to be greater than 1910 and this is what choice C states  (C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910. I interpreted some rainfall = heavy rainfall +moderate+light.
Request you to pl clarify.
Thx



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Re: In Patton City, days are categorized as having heavy [#permalink]
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23 Aug 2013, 00:26
sshivanis04 wrote: Hi Karishma
I understand the logic for A however there could be another meaning to the statements :
Question Steam: 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.
Question stem means that days of moderate+light rainfall for 1900 < moderate+light rainfall for 1910 however the total rainfall for 1900 > total rainfall for 1910.
This could mean that heavy rainfall for 1900 > heavy rainfall for 1910 for the total rainfall for 1900 to be greater than 1910 and this is what choice C states  (C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910. I interpreted some rainfall = heavy rainfall +moderate+light.
Request you to pl clarify.
Thx 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.
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Re: In Patton City, days are categorized as having heavy [#permalink]
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23 Aug 2013, 00:48
Thanks . I figured one more thing which i overlooked in C . I overlooked 'no more than two inches' and this means that author is clearly stating that heavy rainfall are not to be accounted . This choice is clearly negated in the question stem.
Thanks for the quick turnaround !



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Re: In Patton City, days are categorized as having heavy [#permalink]
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31 Aug 2013, 23:26
jaituteja wrote: Subject: In Patton City, days are categorized as having heavypqhai wrote: 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 Beautiful question!!! I picked D but OA is A. After review I absolutely agree with A. By using POE, answers B, C, and E are eliminated quickly. A and D are contenders. (A) the number of days with heavy rainfall was lower in 1990 than in 1910 > CORRECT. The number of days with HR was lower but what if the amount of rain on HR days in 1990 was significantly higher than that in 1910 > the total amount of rainfall in 1990 could be higher than that in 1910. (B) the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910 > OUT. Because "some rainfall" means moderate or light rainfall. The stimulus clearly says the number of days with MR and LR are fewer in 1990 than in 1910, not "the same".(C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910 > OUT. Same reason as B.
(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 > OUT. stimulus says MR is between 1 and 2 inches, it means the maximum is only two times. Why MR in 1990 could be more than twice what in 1910. > it's a shell game. (E) the average amount of rainfall per month was lower in 1990 than in 1910 > OUT. Because if the average amount of rainfall/month was lower in 1990 > total amount of rainfall in 1990 was less than that in 1910. Clearly contradict.Hi, Can you explain D.. I did not get your point. Hi Jai Because there were fewer MR (Moderate rainfall) days in 1990 than in 1910. Let analyze the " BEST" scenario for total MR in 1990: We have: (1) The number of MR days in 1990 = that in 1910 = X (2) MR day in 1990 had average 2" (the maximum MR level) ==> Total rainfall inches in 1990 = 2X (3) MR day in 1910 had ONLY average 1" (the minimum MR level) ==> Total rainfall inches in 1910 = X ==> The MAXIMUM total rainfall inches in 1990 can ONLY be TWICE that in 1910 ==> If the number of MR days in 1990 was fewer than that in 1910 as the stimulus says. ==> The MAXIMUM total rainfall inches in 1990 WOULD less than twice that in 1910 However, D says " more than twice" <== that case NEVER happens. Hope it's clear.
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Re: In Patton City, days are categorized as having heavy [#permalink]
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24 Oct 2013, 13:58
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 Looking at the answers, (B) and (C) won't be the answers for sure. Reason:These two options are contradicting the argument.In the argument it is mentioned that in 1990 there were fewer days with moderate rainfall. Down to (A), (D) and (E). Option(E) is Incorrect. Reason:If the avergae rainfall will be ow then total rainfall will also be low. Contradicts the argument. Down to (A) and (D) Looking at Option (D) It is given in the argument that the number of days with moderate rainfall was more in 1910. let us take the no of days be same as 10 rainfall in1900 >20 rainfall in 1910=10 But stated in the argument moderate rainfall is more than 1 inch and less than 2 inches . The above cannot be true if No of days of rainfall in 1900<no of days in 1910, (D) out Left with Choice (A).Rainfall is more than two inches let no of days in 1900 be 4 and 1910 be 10 but rainfall in 1900 be 20 but in 1910 be 9 inches. Total rainfall in 1900=4*20=80 total rainfall in 1910=10*9=90 let no of days in 1900 be 5 and 1910 be 10 but rainfall in 1900 be 20 but in 1910 be 9 inches. Total rainfall in 1900=5*20=100 total rainfall in 1910=10*9=90Possible.So it holds a possibility and is thus the right answer.
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Re: In Patton City, days are categorized as having heavy [#permalink]
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24 Oct 2013, 23:57
I did it by POE.
(A) the number of days with heavy rainfall was lower in 1990 than in 1910. Correct. (because of POE) haha. Also if you look at it closely, there is no upper limit given for heavy rainfall. it is possible that 1910 witnessed 30 days with 3 inches of rainfall but 1990 witnessed only 20 days but with 5 inches of rainfall. The total rainfall will still be more in 1990. (B) the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910. Incorrect as question stem directly says that it was less and not the same. (C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910. Incorrect. Same as B. (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. Incorrect. the range of moderate rainfall is more than one inch, but no more than two inches. If it was moderate rainfall it should have been 1. even if it was a little more that one say 1.0001 its double would be 2.0002 which then falls in heavy rainfall category. So the total number of inches of rain that fell on days with moderate rainfall in 1990 cannot be more than 'double' of what it had been in 1910. (E) the average amount of rainfall per month was lower in 1990 than in 1910. Incorrect. Question stem says rainfall was 20% higher.



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Re: In Patton City, days are categorized as having heavy [#permalink]
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06 Nov 2013, 15:37
the argument states
1990  1910 Light days (L) < Light days Moderate days (M) < Moderate days
Total rain (T) > total rain
Total Rain 20% more than in 1910 Rl=amount of rain in light day Ml=amount of rain in moderate day Hl=amount of rain in heavy day we should focus on the addition L(Rl)+M(Ml)+H(Hl)= Total Rain
If we have more heavy rainfall days or we have more lower days but more rain we can reach 20% more than in 1910 so that A answer this requirement



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Re: In Patton City, days are categorized as having heavy [#permalink]
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25 Nov 2013, 00:10
got it down to A and D. Marked D.
Only then I realized it to be A.
Question is how to identify such things during actual GMAT?



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Re: In Patton City, days are categorized as having heavy [#permalink]
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28 Nov 2013, 00:01
kulkarnios wrote: got it down to A and D. Marked D.
Only then I realized it to be A.
Question is how to identify such things during actual GMAT? (D) is incorrect. The exam expects you to identify such things and think logically on all questions. I have discussed why (D) is incorrect here: inpattoncitydaysarecategorizedashavingheavy6546960.html#p1259286One needs to practice enough and sharpen his/her reasoning skills to perform well in this exam.
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Re: In Patton City, days are categorized as having heavy [#permalink]
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11 Dec 2013, 18:16
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 Can someone explain with more clarity. Even after reading the explanations I fail to understand why is D not the correct answer



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Re: In Patton City, days are categorized as having heavy [#permalink]
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11 Dec 2013, 20:44
A4G wrote: 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 Can someone explain with more clarity. Even after reading the explanations I fail to understand why is D not the correct answer 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')
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