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# m05 Q30

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02 Aug 2011, 05:48
AriBenCanaan wrote:
Pepe wrote:
ZMAT is right, the minimum solution isn't 232 but 288. Because the "average is a multiple of 12".

232/24 = 9,6667 (average) isn't a multiple of 12. So we have to search for a number, which is greater than 232 and the average of this number is a multiple of 12.

12 * 24 = 288.

But I have another question. If the "The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12". In my opinion you didn't need neither the stat 1 nor the stat 2 to solve this question. Because the minimum solution is 288 flights because of the statement in the question.

I have the same question, can anyone help answer this? I thought S1 & S2 were redundant....

The answer is A. The question states the average number of total flights for the day is a multiple of 12. Not the average of each hour. So the minimum flights for the day is 24. 1 per hour being a multiple of 12.
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02 Aug 2011, 09:56
according to the question, average is not per hour, it is the average no of flight for whole saturday.
May be its calculated averaging over a month or over a year for each Saturday.
T/24 gives you average number of flights per hour.
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03 Aug 2011, 21:59
24 is even so the median must be an average of the 12th and 13th term:

so 12th and 13th is 17

1th-11th terms must be 1 flight (lower value possible)

14th-24th terms must be 17 (lower value possible)

now: 11*1+17+17 (bothe terms creating the median)+ 17*11=232

the minimum flights are 240 since it has to be a multiple of 12 so its above 180
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06 Aug 2012, 05:38
On any given Saturday, flights arrive at XYZ airport every hour, for 24 hours. The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12. Is the total number of flights that arrived on a Saturday > 180?

1. On the same Saturday, the median number of flight arrivals every hour is 17.
2. On the same Saturday, the highest number of flight arrivals in an hour was 30.

----------------------------------

1.
(1) Since the median is 17, the average of 12th and 13th value (when lined up in increasing order) is 17, be it (17,17), (16,18), (15,19) etc.
(2) The minimum value of sum(14th~24th) is 17x11=187. To make the sum minimum, 13th value needs to be 17 (by default, 12th value is also 17).
(3) To me, the statement "The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12" didn't really matter (not sure if it was even necessary for determining statement 1), since the total number of flights is already >180.
(4) Therefore, 1 is sufficient.

2. was easy, insufficient.

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06 Aug 2012, 06:22
Followed the worst case scenario approach while estimating the median. Considered a few more cases when calculating the total value.

(i). The median is 17 i.e. (12th+13th)/2=17.

Case 1 : both 12th and 13th are 17. Hence terms 1 to 11 can be 1. and the remaining 13 terms are all 17. 17*13>180 hence the entire value is >180.

Case 2 : the 12th terms is 16 and the 13th terms is 18. Hence terms 1 to 11 can be 1. The terms from 13th onwards have to be atleast. Terms 13th to 24 are 18 or greater than 18. Hence 12*18>180 thus total is also greater than 180.

Thus concluded that (i) is sufficient.

(ii). It only gives the highest number of flights in an hour. The other 23 hours could have had 1 flight each in which case worst case value is 53 (60 since total is divisible by 12). Alternatively the other 23 could sum up for greater than 180 with say 29 for the remaining 23 hours. Hence (ii) is insufficient.

This problem could have been much harder with a tough condition. Solving the statement (i) itself took me close to 2 mins.
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06 Aug 2012, 08:04
In st 1: upto the 11 hr can we take flight arrived each hour as '0' Zero. I know it will not harm this prob, but may be tricky for other median problem.
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06 Aug 2012, 11:41
I solved it like this. Is my thinking correct?

Median for an even set of numbers is (x+y)/2 = median

In this case it is (x+y)/2 = 17, so x+y = 34. The statement says the total number of flights is a multiple of 12. If you factor 12 to its primes it is 2, 2, 3. Now, if we factor 34 to its primes, it is 2, 17.

Now for 34 to be a multiple of 12, it needs to have at a minimum all the factors of 12. However, it is missing a 2 and 3. So, you multiply 6*34 and you get 204 which is greater than 180.
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06 Aug 2012, 16:33
SOURH7WK wrote:
In st 1: upto the 11 hr can we take flight arrived each hour as '0' Zero. I know it will not harm this prob, but may be tricky for other median problem.

Hi,

The problem statement states that there is one flight every hour. So you will need to take the least value as 1. Hope this helps.
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06 Aug 2012, 16:36
bteller wrote:
I solved it like this. Is my thinking correct?

Median for an even set of numbers is (x+y)/2 = median

In this case it is (x+y)/2 = 17, so x+y = 34. The statement says the total number of flights is a multiple of 12. If you factor 12 to its primes it is 2, 2, 3. Now, if we factor 34 to its primes, it is 2, 17.

Now for 34 to be a multiple of 12, it needs to have at a minimum all the factors of 12. However, it is missing a 2 and 3. So, you multiply 6*34 and you get 204 which is greater than 180.

Not sure about the logic that you are using here.

If it was given that the average was multiple then I guess your reasoning is sound. However the statement given is that the total number of flights is a multiple of 12. It is not necessary for the median value to be a factor of 12.
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06 Aug 2012, 23:41
Correct me please, if I am wrong since I am a rookie here...

But I think the answer would be (D) - Either statement alone, because of following:

Average=Total/24, let it be Total = 24*A (average)
But we know that A/12 = is an integer, let it be B, thus we get: A=12*B
From here Total = 24*A=24*12*B=288*B, from here we see that the Total>180

We don't need any additional statements? Where is the trick?
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08 Aug 2012, 06:57
Javoni wrote:
Correct me please, if I am wrong since I am a rookie here...

But I think the answer would be (D) - Either statement alone, because of following:

Average=Total/24, let it be Total = 24*A (average)
But we know that A/12 = is an integer, let it be B, thus we get: A=12*B
From here Total = 24*A=24*12*B=288*B, from here we see that the Total>180

We don't need any additional statements? Where is the trick?

I believe the issues lies with the wording of the statement,
"The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12"

Some people have interpreted this meaning the average number of planes per hour is a multiple 12. (including yourself, thus the solution you provided is correct). However, others have interpreted it meaning the total numbers of planes on any given Saturday, meaning the average of all Saturdays the daily total is a multiple of 12.
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22 Jul 2014, 05:04
Quote:
On any given Saturday, flights arrive at XYZ airport every hour, for 24 hours. The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12. Is the total number of flights that arrived on a Saturday > 180?

The question stem states that flights arrive every hour for 24 hours and that the average of the total number of flights arriving on any Saturday is a multiple of 12. It doesn't say that 12 flights arrive every hour. So, it could be anything which is a multiple of 12, e.g. 12, 24, 36, and so on.

Now in stmt 1, its given that the median is 17. This means that the first half of the day sees fewer than 17 flights per hour and the second half gets more than 17 flights per hour (do not confuse 'median' with 'average'). So, even if we keep it to the very minimum, i,e. 1 flight per hour for the first half of the day and 17 flights per hour for the second half of the day, we still get a figure(232) > 180.

Hope all the queries could be satisfied here.

Please correct me if I'm wrong anywhere.
m05 Q30   [#permalink] 22 Jul 2014, 05:04

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