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In a particular aircraft, there must be 9 seats across, and

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In a particular aircraft, there must be 9 seats across, and [#permalink]

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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.

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Re: Airplane seats. [#permalink]

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New post 05 Feb 2012, 18:47
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Hi, there. I'm happy to help with this.

Answer A: 1-7-1

Well, the two on the far ends, and the two at the ends of the seven are all on the aisle, no one between them and the aisle.

0, 0, _, _, _, _, _, 0, 0

Next person in on each side of that row of seven has one person between her and the aisle.

0, 0, 1, _, _, _, 1, 0, 0

Next person in on each side has two people between him and the aisle:

0, 0, 1, 2, _, 2, 1, 0, 0

Person in the center has three people between her and the aisle on either side.

0, 0, 1, 2, 3, 2, 1, 0, 0 ---> SUM = 9

(since we would divide by nine in each case, we can just find the sum --- lowest sum will be the lowest average).

Answer B: 2-5-2

Similar logic:

1, 0, 0, 1, 2, 1, 0, 0, 1 ---> SUM = 6

Answer C: 3-3-3

2, 1, 0, 0, 1, 0, 0, 1, 2 ---> SUM = 7

Answer D: 4-1-4

3, 2, 1, 0, 0, 0, 1, 2, 3 ---> SUM 12

So, they don't all have the same average. (b) has the lowest sum, so it has the lowest average.

Does that make sense? Please let me know if you have any questions on this.

Mike :)
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Re: In a particular aircraft, there must be 9 seats across, and [#permalink]

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New post 20 Apr 2015, 13:05
Please explain the question , I cannot understand or visualize it
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Re: In a particular aircraft, there must be 9 seats across, and [#permalink]

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New post 20 Apr 2015, 18:34
Hi veerdonjuan,

The answer choices give us 4 possible 'arrangements' of seats and aisles in one row of an airplane (the dashes represent where the aisles would be). From any given seat, there are a certain number of seats between that seat and the nearest aisle. We're asked to figure out which arrangement would give us the SMALLEST AVERAGE number of seats between a seat and the closest aisle.

Mike's approach was to "map out" the possibilities, which is essentially what you have to do to get to the correct answer.

Here's how the calculation is set up for each answer:

I'm going to use "S" to represent a seat and "a" to represent an aisle. In Answer A, we have.....

S a S S S S S S S a S

Working from left-to-right....
The 1st S has 0 seats between it and the nearest aisle
The 2nd S has 0 seats between it and the nearest aisle
The 3rd S has 1 seat between it and the nearest aisle
The 4th S has 2 seats between it and the nearest aisle
The 5th S has 3 seats between it and the nearest aisle
The 6th S has 2 seats between it and the nearest aisle
The 7th S has 1 seats between it and the nearest aisle
The 8th S has 0 seats between it and the nearest aisle
The 9th S has 0 seats between it and the nearest aisle

Total = 0+0+1+2+3+2+1+0+0 = 9

So the AVERAGE number of seats between any seat and the closest aisle in this arrangement is = 9/9 = 1

Since we're asked to find the SMALLEST AVERAGE, we need the smallest SUM. Working through the other 3 options will get you the answer.

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Re: In a particular aircraft, there must be 9 seats across, and [#permalink]

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New post 08 Oct 2015, 07:13
mikemcgarry wrote:
Hi, there. I'm happy to help with this.

Answer A: 1-7-1

Well, the two on the far ends, and the two at the ends of the seven are all on the aisle, no one between them and the aisle.

0, 0, _, _, _, _, _, 0, 0

Next person in on each side of that row of seven has one person between her and the aisle.

0, 0, 1, _, _, _, 1, 0, 0

Next person in on each side has two people between him and the aisle:

0, 0, 1, 2, _, 2, 1, 0, 0

Person in the center has three people between her and the aisle on either side.

0, 0, 1, 2, 3, 2, 1, 0, 0 ---> SUM = 9

(since we would divide by nine in each case, we can just find the sum --- lowest sum will be the lowest average).

Answer B: 2-5-2

Similar logic:

1, 0, 0, 1, 2, 1, 0, 0, 1 ---> SUM = 6

Answer C: 3-3-3

2, 1, 0, 0, 1, 0, 0, 1, 2 ---> SUM = 7

Answer D: 4-1-4

3, 2, 1, 0, 0, 0, 1, 2, 3 ---> SUM 12

So, they don't all have the same average. (b) has the lowest sum, so it has the lowest average.

Does that make sense? Please let me know if you have any questions on this.

Mike :)

i can not understan how you have put numbers at the two ends and you made this arrange ment. please elaborate how you made this arrange ment
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Re: In a particular aircraft, there must be 9 seats across, and [#permalink]

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New post 08 Oct 2015, 10:10
anik19890 wrote:
i can not understan how you have put numbers at the two ends and you made this arrange ment. please elaborate how you made this arrange ment

Dear anik19890,
I'm happy to respond. :-) First and foremost, this is a visual question. If you are not visualizing the five different arrangements of seats, then none of the numbers are going to make any sense. I would say that the first step for you is to get out pencil and paper and physically, on paper, draw out the five arrangements of seats. It's important to draw it out with your hands, so you can engage the tactile as well as visual components of your brain. Once you have diagrams for the five arrangements of seats, then you start by putting a zero in any seat next to the aisle, because such a seat is zero seats from the aisle. Once you have all these diagram drawn out and have labeled your zeros, come back to this page and read through my solution again.
Does this make sense?
Mike :-)
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In a particular aircraft, there must be 9 seats across, and two aisles [#permalink]

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New post 11 Nov 2016, 11:51
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
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Re: In a particular aircraft, there must be 9 seats across, and [#permalink]

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New post 15 Nov 2016, 19:13
Given the calculation intensive nature of the question, is it representative of the questions asked on the GMAT
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Re: In a particular aircraft, there must be 9 seats across, and [#permalink]

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Re: In a particular aircraft, there must be 9 seats across, and   [#permalink] 13 May 2018, 03:59
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