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.
Kaplan Teacher in Toronto
