A certain city with a population of 132,000 is to be

[RonPurewal]

In summary, for both, the max # of attempts is two, but you have more chances to solve in 1 guess, if you try B or D.

Regards!!

that's correct, but it's too advanced a consideration for anyone who is just becoming familiar with the concept of starting in the middle.

the advantage of starting with (b)/(d), versus starting with (c), is minuscule -- in the long run, it will save you only a couple of seconds per attempt -- and so isn't worth the confusion for most newbies.

[nghiaac2002]

Hi Ron,
Could you please explain the idea behind this for me please?

NOV1907 said that, "For x to be he lowest value it can be, every other town has to be equal to the maximum population value. (Hope that makes sense, think about a set of numbers where you know the total and the maximum value. The minimum value will be at its least possible when every other number in the set is equal to the max value.)."

I don't understand why every other town has to be equal to the maximum population value. Why can't I just take 1000 from answer (d) for example and put it over to another district to make it 13,000? I know this approach is wrong but I don't understand why the above approach is the correct one.

Please help. Thank you very much !

[RonPurewal]

I don't understand why every other town has to be equal to the maximum population value.

Because that's how you get a minimum -- you maximize other things. Similarly, to get a maximum, you minimize other things.

E.g., let's say you have $100 to spend on food, taxi fare, and admission to a club. If you want to have as much as possible left for the club, that means you have to spend as little as possible on BOTH food and taxi fare.

Why can't I just take 1000 from answer (d) for example and put it over to another district to make it 13,000?

"No district is to have a population that is more than 10% greater than the population of any other district." If two districts have populations 11,000 and 13,000, this criterion is violated.

[FranzD]

I had a different approach here, but it worked for me and made the problem quite clear:
If you consider the different values to be on a number line, the maximum value (district with the greatest number of inhabitants) is linked to the minimum value (district with the smallest number of inhabitants) by the 10% constraint. So in order to minimize the minimum value, you also have to minimize the maximum value. With this in mind you know that you have to distribute the people which you take away from the smallest district to all remaining 10 districts.
The rest is simple algebra as explained already.
10*1.1N+N=132000
12N=132000
N=11.000

[RonPurewal]

in order to minimize the minimum value, you also have to minimize the maximum value.

Interesting, but ultimately incorrect.

The first step of the problem is to maximize the high population value (as is customary when you want to minimize something else).
I.e., by going with the idea that the highest population will be exactly 10% more than the lowest one, you're maximizing the high one. (At the same time, you're also minimizing the low one. In other words, you're placing them as far apart as possible.)

Once you've done that, there's no more maximizing or minimizing of anything at all. Once the 1:1.1 ratio is in place, there's a unique solution.

[RonPurewal]

If you did want to "minimize the maximum value", then you'd just give every district the same population as every other one, yielding eleven districts with 12,000 people each.


--

In any case, there's exactly one thing that's important here, and that is for you to know what you're doing.

It's clear that you know exactly what you're doing"”so it really doesn't matter that your terminology is imperfect. Doesn't matter at all. You solved the problem. Well done.

[AceTheGM@]

After reading this forum several times, I understand the solution for this particular problem, but I think I'm missing the big picture here. What type of question is this?

I am making the mistake of thinking of my inability to solve this correctly as "oh, this must be a one-off weird question"-- what is the larger theme here, and how do I apply it to future questions?

[AceTheGM@]

What's the bigger theme of this question? What is the question type?

I understand the logic and mechanics of this specific question, but fear that I couldn't apply the logic/solution to a different quesiton. I keep thinking of my error on questions like this as "oh, this is a tricky, unique question with a solution that isn't really used elsewhere."

[RonPurewal]

What's the bigger theme of this question? What is the question type?

I understand the logic and mechanics of this specific question, but fear that I couldn't apply the logic/solution to a different quesiton. I keep thinking of my error on questions like this as "oh, this is a tricky, unique question with a solution that isn't really used elsewhere."

This problem is far from unique. It's a problem about maximizing and/or minimizing. There are plenty of such problems on the test.

Basically, here's the key principle behind these problems:
* If you want to minimize something, you should maximize everything else.
* If you want to maximize something, you should minimize everything else.

[RonPurewal]

Basically, here's the key principle behind these problems:
* If you want to minimize something, you should maximize everything else.
* If you want to maximize something, you should minimize everything else.

Like lots of other "word problem" principles, these ^^ are things you already know. (If you owned a baseball team with a salary cap, and you wanted to pay a superstar as much as you could, you know exactly what you'd do"”you'd try to pay everyone else the league minimum.)
The problem is that, as soon as people think that this is an "academic" problem, there's a feeling of helplessness"”one that rarely manifests anywhere outside classrooms"”that sets in. "OMG I've never seen this before I don't know what to do! HELP!"

You have to fight this feeling. If you see an "unusual problem type" on the GMAT, it will almost always be something you can solve with ordinary common-sense thinking"”e.g., scheduling, maximizing, minimizing, planning routes, times of day/days of the week, etc.

The classroom stuff is, of course, important too. (Common sense is not going to solve algebraic equations anytime soon.) But, when you see "unusual" problems, you shouldn't be afraid; you should just think, "ok, I can do this without any special preparation at all." Because you can. Just don't call it "academic".