Data Sufficiency

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.

I am not comfortable with this question

We know the average is a multiple of 12, 12k

Total Flights/24 = 12 k

Total flights = 24x12xk = 288K So the total flights number is multiples of 288 ?

Is the total number of flights that arrived on a Saturday > 180?

Well YEAH

logitech wrote:I am not comfortable with this question

We know the average is a multiple of 12, 12k

Total Flights/24 = 12 k

Total flights = 24x12xk = 288K So the total flights number is multiples of 288 ?

Is the total number of flights that arrived on a Saturday > 180?

Well YEAH

The average total flights is a multiple of 12, not the average total per hour!

The OA is A
I am not comfortable with this Q either.
The language seemed to throw me off
The source is gmatclub

Stuart Kovinsky wrote:

logitech wrote:I am not comfortable with this question

We know the average is a multiple of 12, 12k

Total Flights/24 = 12 k

Total flights = 24x12xk = 288K So the total flights number is multiples of 288 ?

Is the total number of flights that arrived on a Saturday > 180?

Well YEAH

The average total flights is a multiple of 12, not the average total per hour!

:roll: Thanks Stuart!!

So the question is asking whether the average number of lights is greater than 15. (180/12)


1. On the same Saturday, the median number of flight arrivals every hour is 17

24 is even number, so the median is the average of 12th and 13th term.

So there are at least 12 terms equal or greater than 17

12x17 = 204 . which is greater than 180 SUF


2. On the same Saturday, Highest number of flight arrivals in an hour was 30.

SO

Choose A

vittalgmat 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.

This question seems poorly worded to me.

"The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12" does NOT mean that the number of flights arriving on ANY given Saturday is a multiple of 12. So, this piece of information is completely irrelevant to this question. I'm not sure I've ever seen a DS question that contained 100% irrelevant information.

Q: is the number of flights on a Saturday > 180?

(1) Median per hour is 17. So, there are an equal number of flights/hour below 17 as above. Let's look at the extreme cases:

Maximizing # of flights: well, we could have 11 hours with 16 flights, 2 hours with 17 flights and 11 hours with a billion flights. Clearly the # of flights could be greater than 180.

Minimizing # of flights: well, we could have 11 hours with 1 flight, 2 hours with 17 flights and 11 hours with 18 flights, giving us:

11 + 34 + 198 which is > 180. So, if the median is 17, there MUST be more than 180 flights: sufficient.

(2) Highest flights/hour is 30.

Well, we could have 24 hours of 30 flights each to get a "yes" answer.
However, we could also have 1 hour of 30 flights and 23 hours of 1 flight each, giving us a total of 53 to get a "no" answer: insufficient.

(1) is sufficient alone, (2) isn't: choose (A).

Stuart,

Is there any flaw in my reasoning ?

So there are at least 12 terms equal or greater than 17

12x17 = 204 . which is greater than 180 SUF

logitech wrote:Stuart,

Is there any flaw in my reasoning ?

So there are at least 12 terms equal or greater than 17

12x17 = 204 . which is greater than 180 SUF

Nope, all good!

Hello-
I am new here- I am bit confused about your logic. Please correct me, if I am wrong. If there is a possibility of the flights to be either over or less then 180. Wouldnt that make A insufficient? Furthermore, I am trying to grasp how did you end up coming with those numbers in the case of minimizing? I solved the answer the same way logitech did, where I simply took the averages. Although both would have yielded the same answer of A. I am trying to understand the actual logic and yours seems to be done in an entirely different way. Thanks for any explanation.

Stuart Kovinsky wrote:

vittalgmat 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.

This question seems poorly worded to me.

"The average number of flights arriving at XYZ airport on any Saturday is a multiple of 12" does NOT mean that the number of flights arriving on ANY given Saturday is a multiple of 12. So, this piece of information is completely irrelevant to this question. I'm not sure I've ever seen a DS question that contained 100% irrelevant information.

Q: is the number of flights on a Saturday > 180?

(1) Median per hour is 17. So, there are an equal number of flights/hour below 17 as above. Let's look at the extreme cases:

Maximizing # of flights: well, we could have 11 hours with 16 flights, 2 hours with 17 flights and 11 hours with a billion flights. Clearly the # of flights could be greater than 180.

Minimizing # of flights: well, we could have 11 hours with 1 flight, 2 hours with 17 flights and 11 hours with 18 flights, giving us:

11 + 34 + 198 which is > 180. So, if the median is 17, there MUST be more than 180 flights: sufficient.

(2) Highest flights/hour is 30.

Well, we could have 24 hours of 30 flights each to get a "yes" answer.
However, we could also have 1 hour of 30 flights and 23 hours of 1 flight each, giving us a total of 53 to get a "no" answer: insufficient.

(1) is sufficient alone, (2) isn't: choose (A).

res123 wrote:Hello-
I am new here- I am bit confused about your logic. Please correct me, if I am wrong. If there is a possibility of the flights to be either over or less then 180. Wouldnt that make A insufficient? Furthermore, I am trying to grasp how did you end up coming with those numbers in the case of minimizing? I solved the answer the same way logitech did, where I simply took the averages. Although both would have yielded the same answer of A. I am trying to understand the actual logic and yours seems to be done in an entirely different way. Thanks for any explanation.

The logic is almost identical, it's just a slightly different way of looking at it.

From statement (1), the only possibility is more than 180 flights. I'm not sure where I suggested otherwise.

For minimizing, I tried to pick numbers to give us the smallest possible number of flights. The median is the middle number in the set or, in the case of an even number of terms as we have here, the average of the two middle terms.

With a median of 17, the two middle terms add up to 34. Letting them both be 17 simplifies things.

So, the 12th and 13th terms are 17. If we want to minimize, the first 11 terms should be as small as possible. I selected 1, but I suppose we could also have selected 0 to get an even smaller result.

However, that turns out to be irrelevant, since the last 11 terms all must be greater than or equal to 17 (I chose 18, but we should have used 17 instead, to give us an even small possible result). 11*17 is itself greater than 180, so we know that no matter what, there will be more than 180 flights.