Yesterday between 9:00 a.m. and 6:00 p.m. at Airport X, all flights to

Here is a simple explanation.

Given :
- Flights depart between 9:00 a.m to 6:00 p.m
- A flight to Atlanta and a flight to New York City both departed from Airport X at 1:00 p.m yesterday.
- Flights depart at regular intervals to their respective places.

To find: Was there any simultaneous departure between 1:00 p.m. and 3:00 p.m. yesterday ?

Data needed :
- At what time the flights start their first departure.
- What are the respective flight time intervals.

Statement(1) Yesterday at Airport X, a flight to Atlanta and a flight to New York City both departed at 10:00 a.m.
We have no information about the minimum data that we need. The time intervals could be anything.
Case 1: If atlanta flight departed at 10am and the next one at 1pm (from given) then time interval could be 3 hrs for the atlanta flight. And might not even be any atlanta flight between 1pm and 3pm.
Case 2: If atlanta has 1 hr time intervals then there will be another flight between 1pm and 3pm but we have no idea about the New york flight intervals. Maybe it has 4 hrs intervals or less even.

Statement(2) Yesterday at airport X, Flights to New york departed every 15 minutes between 9am and 6pm.
Okay so now we have time intervals for new york flights but still no idea about atlanta flight or its time interval. Maybe there is just one flight every hour or maybe there are four every hour.


Now both statements together :
Combining all the data we have -
- Flights depart between 9:00 a.m to 6:00 p.m
- A flight to Atlanta and a flight to New York City both departed from Airport X at 1:00 p.m yesterday.
- Flights depart at regular intervals to their respective places.
- A flight to Atlanta and a flight to New York City both departed at 10:00 a.m.
- Flights to New york departed every 15 minutes between 9am and 6pm.
We still do not know the first or starting departure time and the time interval of the Atlanta Flight.

Case 1 - Again Assume Atlanta first flight departed at 10am with 3 hrs intervals which satisfies all the conditions above. And New york flight every 15 minutes between 9am to 6pm. This means there was never another atlanta flight between 1pm and 3pm.
Case 2 - Assume atlanta flight departs every 1 hr starting at 10am. Again all above conditions are satisfied and here we have a more than one chance of the two flights departing simultaneously between 1pm and 3pm.

Since we can have two different cases here. Option E



Hope it helps

Gap between flights to Atlanta= x
Gap between flights to NY= y

Statement 1- LCM(x,y) is a factor of 180.
We can't say whether it's less than or greater than 120

Insufficient

Statement 2- y=15. we have no idea about x
Insufficient

Combining both equation.
Can't say any thing about x.
Insufficient

E

Given departure timeline:- 9:00 a.m.- 6:00 p.m
Simultaneous departure:- 1.00 p.m.
Flight departure restriction:- At equal intervals

Question stem:- Is there any simultaneous departure between 1:00 p.m. and 3:00 p.m. yesterday ?

Missing information:- 1)1st departure time of flights(both type) at Airport X. (because this is the key parameter to ascertain the successive departure time of flights) 2) Magnitude of equal interval for each type of flight(To NYC & To Atlanta).

St1:- Yesterday at Airport X, a flight to Atlanta and a flight to New York City both departed at 10:00 a.m.

Case-I (say 1st departure at 9:30 a.m. to both the air stations at an equal interval of 30 min)
Flight to Atlanta--------------------------------Flight to NYC
9:30 a.m.------------------------------------------9:30a.m.
10:00 a.m.----------------------------------------10:00 am
.
.
1:00 p.m.----------------------------------------1.00 p.m.
1:30 p.m.----------------------------------------2:00 p.m.
so on till 6p.m.
There were simultaneous departures between 1:00 p.m. and 3:00 p.m.

Case-II (say 1st departure at 9:30 a.m. to Atlanta at an interval of 30 min and 1st departure at 10 a.m. to NYC at an equal interval of 3hr)
Flight to Atlanta--------------------------------Flight to NYC
9:30 a.m.------------------------------------------10:00a.m.
10:00 a.m.----------------------------------------1:00 p.m.
.
.
1:00 p.m.----------------------------------------4.00 p.m.
1:30 p.m.
so on till 6p.m.
There were no simultaneous departures between 1:00 p.m. and 3:00 p.m.

Case-III (say 1st departure at 10:00 a.m. to both the air stations at an equal interval of 3 hours)
Flight to Atlanta--------------------------------Flight to NYC
10:00 a.m.------------------------------------------10:00 a.m.
1:00 p.m.----------------------------------------1:00 p.m.
4:00 p.m.----------------------------------------4:00 p.m.
There were no simultaneous departures between 1:00 p.m. and 3:00 p.m.
Therefore, insufficient.

St2:- Yesterday at Airport X, flights to New York City departed every 15 minutes between 9:00 a.m. and 6:00 p.m
Case-I (say 1st departure at 9:15 a.m. to both the air stations at an equal interval of 15 min)
Flight to Atlanta--------------------------------Flight to NYC
9:15 a.m.------------------------------------------9:15a.m.
.
.
1:00 p.m.----------------------------------------1.00 p.m.
1:15 p.m.----------------------------------------1:15 p.m.
1:30 p.m.----------------------------------------1:30 p.m.
1:30 p.m.----------------------------------------2:00 p.m.
so on till 6p.m.
There were simultaneous departures between 1:00 p.m. and 3:00 p.m.

Case-II (say 1st departure at 10 a.m. to Atlanta at an interval of 3hours and 1st departure @9:15 a.m. to NYC at an equal interval of 15 min)
Flight to Atlanta--------------------------------Flight to NYC
10:00 a.m.------------------------------------------9:15 a.m.
1:00 p.m.-----------------------------------9:30 a.m.
.
.
4:00pm-----------------------------------------------1:00 p.m

There were no simultaneous departures between 1:00 p.m. and 3:00 p.m.

Insufficient.

Combining, we have the same situation as depicted in st1 and st2. We are still searching for the missing info.

Therefore, insufficient.

(E)
_________________

Can this not mean that if the flight left at 10 am, and given that the interval begins at 9am, there is already an interval period which is shorter than 9 - 10, since that time period exists for it to be a consistent interval ?

I think this DS requires analogy such as CR required.

(1) We can't infer what is the space gap period for either city after 10 am. Insufficient.

(2) But we don't have information about flights from X to Atlanta. Insufficient.

Considering Both:
Though there was coincide of flights departure time at 1 pm still we can't infer that was there any other coincide in between 1 to 3 pm. Though the options give us information about another coincide at 10 am and gave flights departure interval from X to Altlanta but we don't have information to deduce any further coincide. Insufficient.

The answer is E.

Elite097

That's not how I read it. In fact, the crux of the question is when aside from the stated times there might or might not be coinciding flights. If there is one between 1pm and 3pm, then the interval between coinciding times would be less than two hours, which would mean there would also be another coinciding time between 11am and 1pm.

From the stem, we have that there were coinciding flights at 1pm.

Looking at statement 1 alone, we know that there were coinciding flights at 10am. So we know that our interval for coinciding flights is at least every 3 hours. There might be coinciding flights every minute, maybe only once every three hours, or maybe some other interval between. Do we have enough information to know whether there will be another coinciding time between 1pm and 3pm? Nope. BCE.

Looking at statement 2 alone, we know that there are a bunch of NY flights throughout the day...every 15 minutes. Okay, if Atlanta flights are every minute, we will have a lot of coinciding times. It the 1pm is the only Atlanta flight, 1pm will be the only coinciding time. Do we have enough information to know whether there will be another coinciding time between 1pm and 3pm? Nope. CE.

Looking at both statements together, we could have coinciding times at 1:15pm, 1:30pm, 1:45pm, etc... or maybe that 1pm is the only Atlanta flight and there are no other coinciding times between 1pm and 3pm. Do we have enough information to know whether there will be another coinciding time between 1pm and 3pm? Nope. E.

Answer choice E.

Flights to Atlanta and flights to New York depart at equally spaced time. That means, Flights can depart after a fixed period of time interval. It can be 10 minutes, 1 hour or 5 hours etc.
Statement 1 : As per it, the interval is of 3 hours. Our given interval is of 2 hours (1 pm-3 pm). Even if New york's flight interval was of 2 hours, we cannot have any information about the Atlanta flight. Again, any number (starting from 0) of flights can depart in the meantime. Not suficient.
Statement 2: Information about only one flight. Not sufficient.
Together: Only information about NY flight, so not sufficient.

Highlighted part is incorrect. Time interval between NY flights can never be 2 hours; It must be a factor of 3hrs or 180 minutes.

Yesterday between 9:00 a.m. and 6:00 p.m. at Airport X, all flights to Atlanta departed at equally spaced times and all flights to New York City departed at equally spaced times. A flight to Atlanta and a flight to New York City both departed from Airport X at 1:00 p.m. yesterday. Between 1:00 p.m. and 3:00 p.m. yesterday, did another pair of flights to these 2 cities depart from Airport X at the same time?

(1) Yesterday at Airport X, a flight to Atlanta and a flight to New York City both departed at 10:00 a.m.
To Atlanta: 13h
Option 1: 10h --> 13:00--> 16:00 (must be)
We do not know if there any flight between 13:00 and 15:00

(2) Yesterday at Airport X, flights to New York City departed every 15 minutes between 9:00 a.m. and 6:00 p.m.
To New York: 13h
Every 15 mins --> 13:15, 13:30, 13:45, 14:00...

---> E

avigutman ThatDudeKnows does this question by any chance imply that there could be no other coinciding timings for both flights between 10 am and 1 pm? Just asking to be sure I understand the phrasing clearly

Bunuel

Curious how you would solve this one

(1) Yesterday at Airport X, a flight to Atlanta and a flight to New York City both departed at 10:00 a.m.
There are flights to Atlanta at 10 a.m. but we don't know if the first flight departs at 9 a.m., so we can only be certain that after every three hours there is a flight (10 a.m. to 1 p.m.). Similar logic for New York.
Hence not sufficient

(2) Yesterday at Airport X, flights to New York City departed every 15 minutes between 9:00 a.m. and 6:00 p.m.
There are flights to New york every 15 minutes and there was a flight at 1 p.m. so there must be a New york flight at 3 p.m. but no information related to Atlanta flight.
Hence not sufficient

Combining both statements
New york we are certain departs at 3 p.m. Even on combining there is no relevant information for flights departing from Atlanta.

Hence not sufficient Option (E)

I initially thought the same thing, but the error here I believe is that we are assuming the cycle begins at 9am while that may not be the case. And the first flight scheduled itself is at 10am from where the cycle begins. Making statement 1 insufficient.