M05-30

Question

At XYZ airport, flights arrived every hour for 24 hours on a certain Saturday. Was the total number of flights that arrived on that day greater than 180?

(1) The median number of flight arrivals per hour on that Saturday was 17.
 
(2) The highest number of flight arrivals in a single hour on that Saturday was 30.

Bunuel · Accepted Answer

Official Solution:

At XYZ airport, flights arrived every hour for 24 hours on a certain Saturday. Was the total number of flights that arrived on that day greater than 180? 
 
(1) The median number of flight arrivals per hour on that Saturday was 17.
 
The median of a set with an even number of terms (in this case, 24) is determined by finding the average of the two middle terms, when they are arranged in ascending or descending order. Since the median is 17, this implies that 17 is the average of the 12th and 13th greatest numbers of arrivals per hour. Therefore, for at least 12 hours (from the 13th greatest to the 24th greatest), there were at least 17 flight arrivals per hour. This, in turn, means that the total number of arrivals on Saturday was at least  12*17=204 , which is greater than the threshold of 180. Hence, the statement is sufficient.
 
(2) The highest number of flight arrivals in a single hour on that Saturday was 30.
 
This statement is clearly insufficient to determine whether the total number of arrivals on Saturday was greater than 180. While the maximum number of arrivals in a single hour was 30, this information does not tell us anything about the number of arrivals in the other 23 hours. For example, it's possible that there were only 1 arrival per hour for 23 hours, and 30 arrivals in the remaining hour, resulting in a total of only  23*1+30 = 53  arrivals for the day, which is less than 180 but it's also possible that there were 30 arrivals each hour, resulting in a total of  24*30 = 720  arrivals for the day, which is more than 180. Therefore, statement (2) alone does not provide enough information to answer the question.

Answer: A

IonutCZ · Answer

I think this question is  good  and  helpful .

Celerma · Answer

It is one of the gmatclub test questions which I always get wrong. Thanks Bunuel for the beautiful explanation.

Andrewscm · Answer

I think this is a  high-quality  question and I agree with explanation.

Krishna7568 · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

barcalisa · Answer

I also think this is a high-quality question.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

Marz127 · Answer

(+) Solution:
 Concept Note  
 Median  is a measure of central tendency of a data set such that it represents a point where half of the data lies before and after it. It is the middle most observation within a dataset.
 Median Calculation for ungrouped data : (ungrouped data: there are absolute numbers only, no frequencies wrt some data classes)
(1) Arrange the data in ascending order.
(2) Count the total number of observations, denoted as “n”.
(3) - If n is odd, the median is the middle value:
Median =   term
    - If n is even, the median is the average of the two middle values:
Median =   term +   term divided by 2

Approaching the Question 
 Given: 
 flights arrive d  every hour   for  24 hours on  a  certain Satur day 
i.e. every hour (24 counts) we have some flights coming in (crazy concert lineup me thinks)
 Need to find out: 
total number of flights > 180

Method: 
 Statement 1 : If we know that  the median is 17 ,
then lets go with the worst case scenario (least possible values)
that, from the middle to the top we only have 17 in the record & every value beneath the middle point (median) is measly 1,2 etc.
then,
(least value)>>>> middle value: 17.....> max value
since we know the total count is 24, then according to the concept note of median,
(N/2 or 24/2 or) for 12 hours the number of flights should be higher or equal to 17.

going back to being a menace means considering 17 flights each must have landed for at least 11 hours straight.
this is still 187 flights in number (already!)
(ignoring 12 values before median that could be lower compared to 17, and max value that could be 17 or higher: we still, already have 187 flights within 11 hours)
thus, Statement 1 is sufficient as is.

Statement 2: Max flight is 30  counts per hour
> this will hint at the least number of flights for an hour IF we know another central tendency as well. Since we already have the 187>180 revelation with statement 1, this statement is not really required.
+ we will need to focus on knowing the  central tendency of the data set to understand how all the observations lined up.

TLDR:   Knowing the central tendency: median case, we can already take up 17*11=187 (min possible values associated for other top half) calcultation to understand the #of flights that linedup for this certain Saturday. Thus statement 1 then, is sufficient as is.
Statement 2 not being central tendency, can be kicked out bro.

MoeKo · Answer

I like the solution - it’s helpful.

deepansh5315 · Answer

I like the solution - it’s helpful.

deepansh5315 · Answer

I like the solution - it’s helpful.

3D · Answer

I like the solution - it’s helpful.

av15 · Answer

"Not correct. With 24 hourly counts, “median = 17” means the average of the 12th and 13th values is 17, not that both equal 17. They could be 16 and 18. So we can only guarantee at least 12 hours with at least 17 arrivals, giving a minimum total of 12*17 = 204. 221 is not guaranteed."

Why is that?

If median is 17 flights, that means 12th + 13th hour = 34 flights 
min possible value for 13th hour = 17 flights so all hours post 13th hour (i.e. 11 hours) will have at least 17 flights/hour
34 + 17*11 
17(2+11) 
17*13 = 221

Bunuel · Answer

Yes, you are right.

M05-30

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