You are Here: Home >< Maths

# Interview question - logic/thought

Announcements Posted on
Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
1. The question asks about how many planes are in the sky at this moment?

I just want to look at how you approach to this question. It is looking at the way of thinking.

My try would be to say there is about 15 planes on average in each country and multiply it by number of countries x.

I know this is not the right way of thinking, but that was my first try.
2. What a dumb question.
Bet oxford ask it.

Posted from TSR Mobile
3. Yeh, I'd say ur about right. Just try looking instead at the product of several more fractions to incorporate more detail ie treat it like a fermi problem
4. Personally, I'd consider the time of year and day and weather before I come up with an answer, then I'd make some sort of guesstimate and a ratio :-)
5. Key approach:

- identify what you know
- be very careful with units, they are crucial
- at each step, identify what you need to do next, and what type of quantity you need to estimate
- estimate using averages, or by splitting into sub-groups
Spoiler:
Show

For example, let's say a flight takes off or lands at an airport every ~90 seconds during the daytime. So that's a takeoff every 3 minutes, or 20 an hour. Let's assume flights go from 7am to 10pm at that rate, and then stop afterwards. That's 15 hours, so 15*20 = 300 takeoffs per runway per day. So let's say 300 flights per runway per day, since each flight involves one takeoff.

We don't really want flights, though, we want flight times, i.e. number of hours spent in the sky by planes each day. We can compare that figure with the total number of hours in which there are flights (15 hours) to get an average number of flights in the air at any moment. For example, if there are 300 flight-hours per day, then that means at any one time there is 300/15 = 20 planes in the sky at any moment. So let's calculate that: flight-hours per day = flights per day * average duration of flight. (note this is much easier when you keep control of your units!)

How long is the average flight? I'd say there's a pretty skewed distribution, with many flights of ~1-3 hours to European destinations, and then quite a few more to the US & Asia. But we only need the average, so let's estimate an average duration of 3 hours. If there are 300 flights (per runway) per day, that estimate means we have 3*300 = 900 flight-hours per runway per day.

Now we divide by the number of daytime hours in which flights are running (15), and we find that there are 900/15 = 60 planes in the sky at any one time per runway.

To get the total number of planes in the sky, we just need to figure out how many (highly-active) runways there are in the world. Let's say 50 in the USA, 75 in Europe, 75 in Asia (hub), 25 in Australasia, 25 in South America/Africa, so 250 in total. That means 60*250 = 15,000 planes in the sky at any moment, during daytime hours.

Seems like a lot, doesn't matter. The most important fact is the model. Inputs (estimates) can be tweaked as more information is gathered.
6. (Original post by mik1a)
Key approach:

- identify what you know
- be very careful with units, they are crucial
- at each step, identify what you need to do next, and what type of quantity you need to estimate
- estimate using averages, or by splitting into sub-groups
Spoiler:
Show

For example, let's say a flight takes off or lands at an airport every ~90 seconds during the daytime. So that's a takeoff every 3 minutes, or 20 an hour. Let's assume flights go from 7am to 10pm at that rate, and then stop afterwards. That's 15 hours, so 15*20 = 300 takeoffs per runway per day. So let's say 300 flights per runway per day, since each flight involves one takeoff.

We don't really want flights, though, we want flight times, i.e. number of hours spent in the sky by planes each day. We can compare that figure with the total number of hours in which there are flights (15 hours) to get an average number of flights in the air at any moment. For example, if there are 300 flight-hours per day, then that means at any one time there is 300/15 = 20 planes in the sky at any moment. So let's calculate that: flight-hours per day = flights per day * average duration of flight. (note this is much easier when you keep control of your units!)

How long is the average flight? I'd say there's a pretty skewed distribution, with many flights of ~1-3 hours to European destinations, and then quite a few more to the US & Asia. But we only need the average, so let's estimate an average duration of 3 hours. If there are 300 flights (per runway) per day, that estimate means we have 3*300 = 900 flight-hours per runway per day.

Now we divide by the number of daytime hours in which flights are running (15), and we find that there are 900/15 = 60 planes in the sky at any one time per runway.

To get the total number of planes in the sky, we just need to figure out how many (highly-active) runways there are in the world. Let's say 50 in the USA, 75 in Europe, 75 in Asia (hub), 25 in Australasia, 25 in South America/Africa, so 250 in total. That means 60*250 = 15,000 planes in the sky at any moment, during daytime hours.

Seems like a lot, doesn't matter. The most important fact is the model. Inputs (estimates) can be tweaked as more information is gathered.
Thank you so much. That's so helpful and I appreciate that.

I see the idea, but will need to read it again.
7. (Original post by physicsmaths)
What a dumb question.
Bet oxford ask it.

Posted from TSR Mobile
agree, and yes it is.
8. (Original post by DeuteriumPie)
Yeh, I'd say ur about right. Just try looking instead at the product of several more fractions to incorporate more detail ie treat it like a fermi problem
(Original post by typicalvirgo)
Personally, I'd consider the time of year and day and weather before I come up with an answer, then I'd make some sort of guesstimate and a ratio :-)
Thank you
9. I'd just tell them to sod off.
10. (Original post by mik1a)
Key approach:

- identify what you know
- be very careful with units, they are crucial
- at each step, identify what you need to do next, and what type of quantity you need to estimate
- estimate using averages, or by splitting into sub-groups
Spoiler:
Show

For example, let's say a flight takes off or lands at an airport every ~90 seconds during the daytime. So that's a takeoff every 3 minutes, or 20 an hour. Let's assume flights go from 7am to 10pm at that rate, and then stop afterwards. That's 15 hours, so 15*20 = 300 takeoffs per runway per day. So let's say 300 flights per runway per day, since each flight involves one takeoff.

We don't really want flights, though, we want flight times, i.e. number of hours spent in the sky by planes each day. We can compare that figure with the total number of hours in which there are flights (15 hours) to get an average number of flights in the air at any moment. For example, if there are 300 flight-hours per day, then that means at any one time there is 300/15 = 20 planes in the sky at any moment. So let's calculate that: flight-hours per day = flights per day * average duration of flight. (note this is much easier when you keep control of your units!)

How long is the average flight? I'd say there's a pretty skewed distribution, with many flights of ~1-3 hours to European destinations, and then quite a few more to the US & Asia. But we only need the average, so let's estimate an average duration of 3 hours. If there are 300 flights (per runway) per day, that estimate means we have 3*300 = 900 flight-hours per runway per day.

Now we divide by the number of daytime hours in which flights are running (15), and we find that there are 900/15 = 60 planes in the sky at any one time per runway.

To get the total number of planes in the sky, we just need to figure out how many (highly-active) runways there are in the world. Let's say 50 in the USA, 75 in Europe, 75 in Asia (hub), 25 in Australasia, 25 in South America/Africa, so 250 in total. That means 60*250 = 15,000 planes in the sky at any moment, during daytime hours.

Seems like a lot, doesn't matter. The most important fact is the model. Inputs (estimates) can be tweaked as more information is gathered.
Good try, but this model allows only to estimate a VERY inacurrate number of cruise aircrafts, and moreover it ignores small aircrafts and military aircrafts, however as you say, it would still work with proper inputs, taking all aircrafts into account.
Anyway an estimation without any factual data input is next to worthless.
11. (Original post by PTMalewski)
Good try, but this model allows only to estimate a VERY inacurrate number of cruise aircrafts, and moreover it ignores small aircrafts and military aircrafts, however as you say, it would still work with proper inputs, taking all aircrafts into account.
Anyway an estimation without any factual data input is next to worthless.
I think you are missing the point of the exercise.
12. (Original post by mik1a)
I think you are missing the point of the exercise.
The point is to find out, is a candidate clever enough to figure out some method that may be useful to some extend, isn't it?
Still, the method can be improved.

I might add: I haven't seen the whole test, but the question alone is a little bit disturbing for someone who lives in a country, where a conspiracy theory about one particular aircraft, does a lot of damage to political life of the state.
Major part of misunderstandings come from a fact that some not the most clever people try to judge real events, using such rough estimations as basis for their deductions.
13. Even trying to come up with a half decent number for this question is almost impossible. You can try and suggest any model but in the end the answer is going to be completely bs. It is just about sounding fancy and trying to look like you actually know what you are talking about when in reality, it is all wrong
14. (Original post by scientific222)
Even trying to come up with a half decent number for this question is almost impossible. You can try and suggest any model but in the end the answer is going to be completely bs. It is just about sounding fancy and trying to look like you actually know what you are talking about when in reality, it is all wrong
No, it is about basing your estimate on logic rather than pulling a number out of thin air. When you make a guess, your brain has some kind of process. It is better for everyone concerned when that process is transparent.

If you just said "I think 5,000", then nobody would take you seriously.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
your full birthday is required
1. Oops, you need to agree to our Ts&Cs to register

Updated: September 17, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### Who is getting a uni offer this half term?

Find out which unis are hot off the mark here

Poll
Useful resources

## Make your revision easier

Can you help? Study help unanswered threadsStudy Help rules and posting guidelinesLaTex guide for writing equations on TSR

## Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.