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# m05 Q30

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08 Mar 2009, 02:46
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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, Highest number of flight arrivals in an hour was 30.

[Reveal] Spoiler: OA
A

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Sol:
We don't really need the average number of flights.

We can immediately eliminate statement 2 as it is insufficient by itself as it only tells us about maximium arrivals. It is possible that there were 30 in one hour and then only 23 in the other 23.

Statement 1 tells us that median is 17; let's assume worst case scenario: out of 24 hours, in 11 hours only 11 planes arrived. Then 17 afterwards for each of the remaining 13 hours. equals more than 200. Statement 1 is sufficient.

Can sumon this worst case scenario? I cldnt understand how they tuk those values.
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08 Mar 2009, 10:15
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ritula wrote:
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, Highest number of flight arrivals in an hour was 30.

Sol: We don't really need the average number of flights.

We can immediately eliminate statement 2 as it is insufficient by itself as it only tells us about maximium arrivals. It is possible that there were 30 in one hour and then only 23 in the other 23.

Statement 1 tells us that median is 17; let's assume worst case scenario: out of 24 hours, in 11 hours only 11 planes arrived. Then 17 afterwards for each of the remaining 13 hours. equals more than 200. Statement 1 is sufficient.

Can sumon this worst case scenario? I cldnt understand how they tuk those values.

1: The wrost case possibility is that each of first 11 hours has flight of 1 (I guess 0 is not possible), and each of rest hours has 17.
So, Total flights = (11 x 1) + (13x17) = 11 + 221 = 232.

2: Highest is 30 doesnot say much. The flight could vary from 52 (1x22 + 30x1) to 720.
Not suff...

This is how 1 is suff.
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08 Mar 2009, 18:42
BUt I disnt understand how in worst case senario they tuk value 11?
GMAT TIGER wrote:
ritula wrote:
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, Highest number of flight arrivals in an hour was 30.

Sol: We don't really need the average number of flights.

We can immediately eliminate statement 2 as it is insufficient by itself as it only tells us about maximium arrivals. It is possible that there were 30 in one hour and then only 23 in the other 23.

Statement 1 tells us that median is 17; let's assume worst case scenario: out of 24 hours, in 11 hours only 11 planes arrived. Then 17 afterwards for each of the remaining 13 hours. equals more than 200. Statement 1 is sufficient.

Can sumon this worst case scenario? I cldnt understand how they tuk those values.

1: The wrost case possibility is that each of first 11 hours has flight of 1 (I guess 0 is not possible), and each of rest hours has 17.
So, Total flights = (11 x 1) + (13x17) = 11 + 221 = 232.

2: Highest is 30 doesnot say much. The flight could vary from 52 (1x22 + 30x1) to 720.
Not suff...

This is how 1 is suff.
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09 Mar 2009, 15:55
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ritula wrote:
BUt I disnt understand how in worst case senario they tuk value 11?
GMAT TIGER wrote:
ritula wrote:
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, Highest number of flight arrivals in an hour was 30.

Sol: We don't really need the average number of flights.

We can immediately eliminate statement 2 as it is insufficient by itself as it only tells us about maximium arrivals. It is possible that there were 30 in one hour and then only 23 in the other 23.

Statement 1 tells us that median is 17; let's assume worst case scenario: out of 24 hours, in 11 hours only 11 planes arrived. Then 17 afterwards for each of the remaining 13 hours. equals more than 200. Statement 1 is sufficient.

Can sumon this worst case scenario? I cldnt understand how they tuk those values.

1: The wrost case possibility is that each of first 11 hours has flight of 1 (I guess 0 is not possible), and each of rest hours has 17.
So, Total flights = (11 x 1) + (13x17) = 11 + 221 = 232.

2: Highest is 30 doesnot say much. The flight could vary from 52 (1x22 + 30x1) to 720.
Not suff...

This is how 1 is suff.

for st 1: the following the distribution of flights for each of 24 hours.

Hour 1: 1 plane
Hour 2: 1 plane
Hour 3: 1 plane
Hour 4: 1 plane
Hour 5: 1 plane
Hour 6: 1 plane
Hour 7: 1 plane
Hour 8: 1 plane
Hour 9: 1 plane
Hour 10: 1 plane
Hour 11: 1 plane
Hour 12: 17 planes
Hour 13: 17 planes
Hour 14: 17 planes
Hour 15: 17 planes
Hour 16: 17 planes
Hour 17: 17 planes
Hour 18: 17 planes
Hour 19: 17 planes
Hour 20: 17 planes
Hour 21: 17 planes
Hour 22: 17 planes
Hour 23: 17 planes
Hour 24: 17 planes

you assign the minimum possible flight for each of first 11 hours and do not assign more than 17 flights for each of rest hours (13 hours).

hth..
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01 Apr 2009, 22:18
Statement (1) says that median number of flight arrivals every hour is 17, which means that the 12th hour must have 17 plains arriving. (see the definition of median)
Now in order to make it "worst case scenario" you try to keep the numbers at the very minimum.
Since "flights arrive to XYZ airport every hour for 24 hours" you must have at least one flight up until 12th hour.
Then 17 flights on the 12th hour. Then the very minimum you must have for the following hours cannot fall behind the median which is 17.
This is how you get the 11 and the distribution mentioned above.
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05 Apr 2009, 01:18
Median is 17 which means...we need to consider 12th and 13th hour..
12th and 13th hour can have (17,17) or (16,18) or (15,19).....and so on....so worst case we take...(17,17) so that all the flights after 13th hour are minimum i.e. 17...so in this case all flights before 12th hour can be 1.
hence it becomes 1*11 + 13*17 = 232.
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30 Jul 2010, 05:42
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Does this graphic help?
Attachment:
File comment: Excel table and histogram

flights.JPG [ 78.46 KiB | Viewed 7906 times ]
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30 Jul 2010, 09:06
Statement 2 is directly ruled out because it does not give any info about the remaining hrs.

Coming back to statement 1, when the median of a set of 24 numbers is 17, the two middle nos have to be 16 and 18 (since even no. of things have two middle nos when arranged in order). To complete the series of 24 nos, we have to add 11 nos to the left of 16 and 11 to the right of 17. This gives the 1st number as 5 and the last number as 29. The sum of the series works out to 435(which is greater than 180)
Even if both the middle nos are considered to be equal(i.e. 17 & 17) then all the nos before 17 must be smaller than 17 and all the numbers after it should be greater than 17. The statement holds true even if we work this way.

therefore statement 1 alone is sufficient to answer the qn.
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30 Jul 2010, 10:39
"The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12." What does this mean?
I saw above discussing like from stat 1 the flights are 232. 232 is not divisible by 24?
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30 Jul 2010, 10:42
Thanks for the good question.
I went for A from my gut :D

Why can't we have more than 17 for the last 13 hours (incremented by 1) ?
e.g. 18, 19, 20 .....
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30 Jul 2010, 17:22
lordspace wrote:
Thanks for the good question.
I went for A from my gut :D

Why can't we have more than 17 for the last 13 hours (incremented by 1) ?
e.g. 18, 19, 20 .....

We can have more than 17, but that doesn't change the answer to the original question
ritula wrote:
Is the total number of flights that arrived on a Saturday > 180?

So let's say in hour 20 we have 18 planes. The end result is now 233 flights, still more than 180.

The way I approached this was to minimize the total flights (meaning there were no more than the median flights in any hour) even in the minimal case we have more than 180 flights.
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31 Jul 2010, 17:48
I had a follow up question. The median flights being 17 indicates that there are 17 flights for the 12th and 13th hour. Why cannot we have 1 flight each hours from 14th the 24th hour as well? Why does the solution say that 12th hour onwards there are 17 flights each hour? Am I missing something?
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31 Jul 2010, 19:03
suhasrao wrote:
I had a follow up question. The median flights being 17 indicates that there are 17 flights for the 12th and 13th hour. Why cannot we have 1 flight each hours from 14th the 24th hour as well? Why does the solution say that 12th hour onwards there are 17 flights each hour? Am I missing something?

The sentence in red is incorrect.

The median flights being 17 means that if we took all the flights per hour and put them in order from least to greatest the flights in the middle would average 17.

What you have described above would yield a median of 1.

In this set.....

Attachment:

flights2.JPG [ 50.81 KiB | Viewed 7498 times ]

The median is 1.
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31 Jul 2010, 20:45
Thanks TallJTinChina. I now see what you mean.
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02 Aug 2010, 10:55
Option A looks good.
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07 Aug 2010, 23:50
Can someone answer ZMAT's question, because I have the same problem...many thx!
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12 Aug 2010, 22:53
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.
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12 Oct 2010, 07:59
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.
The avg no. of flights is multiple of 12. Hence the minimum number of flights is anyway greater than 180.
Why do we need stmt 1 or 2 ?

Please correct me if i am wrong here.
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24 Jun 2011, 19:55
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....
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02 Aug 2011, 04:48
Same question as above - the question already states that number of flight is more than 180. There is something wrong in the question stem.
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