Official Solution:


(1) On that Saturday, the median number of flight arrivals every hour was 17. The median of a set with even number (24) of terms is the average of two middle terms when arranged in ascending/descending. So, the median of 17 means that 17 is the average of 12th and 13th greatest numbers of arrivals. Hence, at least 12 hours of arrivals (from 13th greatest to 24th greatest) had at least 17 flights, which means that the total number of arrivals on Saturday was at least \(12*17=204 \gt 180\). Sufficient.

(2) On that Saturday, the highest number of flight arrivals in an hour was 30. Clearly insufficient: if each hour had 30 arrivals then the total number of arrivals on Saturday would be \(24*30 \gt 180\), but if 23 hours had 1 arrival and one hour had 30 arrivals then the total number of arrivals on Saturday would be \(23*1+30 \lt 180\). Not sufficient.


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

I think at least 232 flights as it was said "flights arrived to XYZ airport every hour for 24 hours" which mean there is at least one flight arrived every hour.

So, the least number is 11 * 1 flights before the median PLUS 13*17 flights from the median and after. That makes 232 flights.

I agree. In order for the median value to be 17, the number of flights for the 12th hour must also be 17; so, the number of hours that had 17 flights would be (24-12+1) = 13, which would result in 221 flights (17*13). Bunuel please clarify.

Hi all, can anyone explain, the below line in detail;
"On that Saturday, the median number of flight arrivals every hour is 17."

I actually assumed the median of arrivals per hr is 17 every hr; which would mean totally 33 arrivals per hr; easily >180 for 24 hrs.

The sets are always in ascending order if not stated.

Bunuel chetan2u PKN GMATPrepNow niks18 KarishmaB pushpitkc

Can you please explain below quote?



My understanding:
Median can be decimal or an integer for even number of elements in a sequence.
e.g. S1: {1,2,2,3}
Here, mean = (2+2)/ 2 = 2
S2: {1,2,3,4}
Mean = (2+3) / 2 = 2.5

In above quote, am I supposed to find mean of 12 and 13? How is it equal to 17?
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Hi adkikani,

Absolutely correct.



What is said in the question:-
flights arrive at XYZ airport every hour for 24 hours. It means, every hour corresponds to certain number of flights( minimum no of flights being 1).
We have 24 hours in a day. So, we have a minimum of 24*1=24 numbers of flights arriving at XYZ.
Maximum number of flights could be any number depending upon additional info provided in the question.

Question stem:- Is # of flights in 24 hrs>180 ?

St1:- On the same Saturday, the median number of flight arrivals every hour is 17.
We have total no of hours=24 ( If we consider it a set, then it has 24 data points and each data point has certain frequency(here no of flights))
Median number of flights is equal the mean number of flights at 12th and 13th hours or data point when the data points are arranged in ascending or descending fashion.
No of hours ---------------.No of flights/frequency
1st---------------------------- \(\geq1\)
2nd---------------------------- \(\geq1\)
.
.
.
11th---------------------------\(\geq1\)
12th--------------------------- \(\leq17\) & \(\geq1\)
Median-------------------------17
13th---------------------------- \(\geq17\) & \(\leq33\)
.
.
.
24th--------------------------- \(\geq17\)

We can take the above data in descending order too.

Minimum # of flights arrived in 24 hrs=11*1+17*1+17*1+11*17=11+17+17+187=232>180
Sufficient.

P.S:- You have to take the average of no of flights in 12th hour and no of flights in 13th hour. Not the average of 12 and 13. 12 and 13 represent the hour number not the no of flights in 12th and 13th hours respectively.

Hope it helps.
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PKN

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