Problem Solving

If you have two minutes to solve this question, what's the best / fastest method?

In a particular aircraft, there must be 9 seats across, and two aisles. If the dash symbols represent aisles, which of the following arrangements provides the lowest average number of seats between passengers and the closest aisle?

a) 1-7-1

b) 2-5-2

c) 3-3-3

d) 4-1-4

e) all of the above arrangements produce the same average distance from the closest aisle.

IMO the correct arrangement should be 3-3-3 as this will be the one with the least distance.

There will be 4 people sitting next to the aisle and 3 people sitting in the middle will have only one person in between and the 2 people on the extremities will have 2 people in between hence a total of 7 amongst the 9 people seated.

If you have two minutes to solve this question, what's the best / fastest method?

First, take your time figuring out exactly what the question is asking; this will be time well spent. Study the language of the question, and think about the real-life situation. The question wants us to minimize the average number of seats between passengers and the closest aisle. The goal is to make it so that passengers don't have to go by a whole bunch of seats in order to make it to an aisle. For many average problems, we should think in sums. Here, we want to minimize the sum of the number of seats that is in the way of each passenger getting to the closest aisle. Use your scratchpad to diagram each answer choice.

Use a slot to represent each SEAT (the passengers sit in the seats). For each seat count how many other other seats separate that seat from the closest aisle. Put this number in underneath each slot. (In my diagram below, I used "S" instead of a slot because whenever I tried using slots, I wasn't able to; it didn't show up correctly in the post):

Let's look at the choices:

A: 1-7-1

S.....SSSSSSS.....S
0.....0123210.....0

So the sum of other seats that separate passengers from the closest aisle is: 1+2+3+2+1 = 9

B: 2-5-2

SS....SSSSS....SS
10....01210....01

So the sum is: 1+1+2+1+1 = 6. Eliminate A.

C: 3-3-3

SSS....SSS....SSS
210....010....012

So the sum is 7. Eliminate C.

You can just begin visualizing choice D, and you will see that it is too big.

Choice B yields the smallest sum so it will represnt the arrangement that minimizes the average number of seats between passengers and seats. (And that average woud be 6/9 = 0.6666. That is, on average, 2/3 of a seat separates each passenger from the closest aisle).

Choose B.

Thanks, Testluv. Great explanation as usual.

I was able to solve the question, but it took me a little longer than 2 minutes to come up with the answer.

Not understanding what the question is asking is by far the biggest reason why I get questions wrong.

Anyway, thanks for the tips!

I used following rules:

1. folks in the middle col have two sides to get out from, whereas folks inside columns can only get out from one side - so common sense said that I should reduce people from side columns)
2. there would always be 4 people (on either side of aisles) that have 1 degree of separation from aisle)
3. this means that we should start from putting people closest to these "aisle" people which gives us 2-4-2 (one person next to each of the aisle guys
4. So now one person is left. put him in the middle and we get 2-5-2

Nice question i must say...it took me a while to figure out the question itself....

Answer is B.

A very good question
Can anyone comment on the source
My answer is also B...
I was able to out think but how about the timing I took close to 4 minutes to do this one.......

The answer is B.

The wording of the question is little bit tricky. This is how I deciphered it:-
"lowest average number of seats between passangers and the closest aisle"
shortening it more
Average of (number of seats between passengers and the closest aisle)
which is equal to (number of seats between passengers and the closest aisle)/9

So the part to find out is -number of seats between passengers and the closest aisle

Let the seats be named ABCDEFGHI and aisle be denoted by X and Y

a) Taking first option, partition of 1-7-1
It means A X BCDEFGH Y I
Number of seats between A and closest aisle i.e. X = 0
Number of seats between B and closest aisle i.e. X = 0
Number of seats between C and closest aisle i.e. X = 1
Number of seats between D and closest aisle i.e. X = 2
Number of seats between E and closest aisle i.e. Y = 3
Number of seats between F and closest aisle i.e. Y = 2
Number of seats between G and closest aisle i.e. Y = 1
Number of seats between H and closest aisle i.e. Y = 0
Number of seats between I and closest aisle i.e. Y = 0

So the total number of seats between passenger and the closest aisle = 0+0+1+2+3+2+1+0+0 = 9
Average = 9/9 = 1

Similarly for other options

b) Average = (1+0+0+1+2+1+0+0+1)/9 = 6/9 = 2/3
c) Average = (2+1+0+0+1+0+0+1+2)/9 = 7/9 = 7/9
d) Average = (3+2+1+0+0+1+2+3)/9 = 12/9 = 4/3
e)

Hence the answer

Best Regards,
JOHN

Find out the max number of people sitting in any of the three segments A (left), B(Centre), C (Right). If any one of the three segments has higher people seated in it than the other or in other words if the layout is UNEQUAL then the average distance of those passengers from the aisle will be higher than in a EQUAL DISTRIBUTION of passengers on either side of the aisle . The reason for this is deviations from the nearest point will be greatest when your data points lie unequally on either side of the target. SIMILAR to STANDARD DEVIATION CONCEPT.

a) 1-7-1
b) 2-5-2
c) 3-3-3
d) 4-1-4
e) all of the above arrangements produce the same average distance from the closest aisle.

good explanation by Test Luv, agree answer is B

Understanding the question makes the answer obvious. Good Question, Thanks...

I could get the answer B but took more than a minute to understand what it is asking for.

D.

(4+1)/2=(1+4)/2=5/2

1-7-1: no of seats btw passengers & closest aisle: 9
2-5-2: no of seats: 6
3-3-3: 7
4-1-4: 12

Choose B