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A certain city with population of 132,000 is to be divided into 11

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 14 Jul 2015, 07:43
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Hi honchos,

If you read the other posts in this thread, you'll learn the EXACT situation described by the prompt: If 10 of the districts have the SAME population, then the 11th could be the one with the 10% difference in population.

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 18 Oct 2015, 09:17
Bunuel wrote:
ddp123 wrote:
i approached the answer like this, 132000/11= 12000, hence the max population that each city can have is 12000. Let min. population be x. Therefore, x+10x/100=12000, which gives x as 12000/1.1 and x=10909.9. is this method right plz help


Your approach is not correct. Please check here: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html#p831969

Hope it helps.


Hi Bunuel,

Can you please explain me why have you used 12x instead of 11? There are 11 cities mentioned in the question.

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 18 Oct 2015, 09:21
excelingmat wrote:
Bunuel wrote:
ddp123 wrote:
i approached the answer like this, 132000/11= 12000, hence the max population that each city can have is 12000. Let min. population be x. Therefore, x+10x/100=12000, which gives x as 12000/1.1 and x=10909.9. is this method right plz help


Your approach is not correct. Please check here: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html#p831969

Hope it helps.


Hi Bunuel,

Can you please explain me why have you used 12x instead of 11? There are 11 cities mentioned in the question.


You missed the point there.

\(x+10*1.1x=132\) (so 1 times x plus 10 times 1.1x) gives \(12x=132\).
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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 09 Feb 2016, 17:51
Dear Bunuel Had the question asked that no two districts can have the same population, how the question could have been solved?

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 09 Feb 2016, 19:06
HI ankushbagwale,

The reason why this question 'works' the way it does (and can be approached in the way described) is because it was 'designed' that way. Every prompt on the GMAT comes with specific information/facts/restrictions that you're supposed to use to answer the question. If the populations were all different, then the question would have to be completely rewritten (with different facts and restrictions in place).

You could certainly see a question that tells you the average population of 12 districts, then compares the 'largest' to the 'smallest' (in some mathematical way), tells you that all 12 numbers are different and then asks you for either the largest or smallest. That is NOT this question though.

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 18 Feb 2016, 08:06
11 D = 130,000
Large <= 1,1 Small
Maximum large = 1,1 Small <=> 10L + S = 11S+S = 12S <=> S = 132,000/12 = 11,000
Answer D.

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 20 Feb 2016, 12:56
The way I thought of it is:

132/11 = 12 is the average. So all the cities can have 12,000 people fit into 11 groups.

If you bring one city down from 12 to 11 another city has to go up to 13 to keep the average the same but the difference between the smallest and biggest will be closer to 20%. Or, you could go down with one city a certain amount and spread out the difference among all the other numbers.

X = smallest city
1.1 = the greatest difference allowed
10 = the rest of the cities.
x+10(1.1x) = 132
x = 11

Or if you wanted to find the number that you needed to subtract from the average, the equation would look like this:
(12-x) +10(1.1(12-x)) = 132
X=1
so X is one less than the average

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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Flexxice wrote:
A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 % greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A) 10700

B) 10800

C) 10900

D) 11000

E) 11100


Let x = the population of the district with the LOWEST population.
To MINIMIZE the population in the smallest district, we must MAXIMIZE the population of the other 10 districts.

IMPORTANT: No other district can exceed x by more than 10%.
So 1.1x = the MAXIMUM population of each of the other 10 districts.

The TOTAL population is 132,000, so we can write:
(population of smallest district) + (population of other 10 districts) = 132,000
Rewrite as: x + [(10)(1.1x)] = 132,000
Simplify: 12x = 132,000
x = 11,000

Answer: D

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 24 Jul 2016, 13:15
Absolutely tricky and have missed this question several times. The hard part is the setup.

For some reason, I had it setup as 10x + 1.1 x = 132,000. and actually did it in reverse. Now in hindsight, it makes sense to have the equation
(10* 1.1 x) + x = 132,000 makes sense as (10 * 1.1 x) equals to 10 that are much higher and x is for the smallest group. 12 x = 132,000 is much more easier to solve too!

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 17 Oct 2016, 12:50
We have 11 different districts, and the sum of their population is 132,000.
Moreover, the gap between two district populations is no more than 10%.

Thus, to MINIMIZE the least possible value:
- we want the maximum number of districts at the highest possible value : 10 districts = 10*b
- we want only one district at the least possible value : 1 district = a

If you have 10 high population values, then it remains few people in the last district.

Plus, we know that b=1,1*a // b=a+10%a

So,
10*b+a=132,000
10*1,1a+a=132,000
11*a+a=132,000
12*a=132,000
a=11,000, answer choice D

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 17 Dec 2016, 11:37
avrgmat wrote:
I got this problem on my recent GMATPrep mock. This was the 8th question and I ended up getting this one wrong. This was my first mistake on the test in the quant section. I ended up getting 49Q with a total of 10 incorrect.

Coming to the problem, at the test time, I started with the below logic --:

let city 1 =x

Now city2 can have a max of 10% greater of city1 i.e., city2 = 1.1x

At this point, I guess I missed the trick and I am still trying to digest the solutions provided above.

For city3 = 10% of city2 i.e. 1.1(city2) = 1.1*1.1x = 1.21x

I lost the problem at this stage and could not proceed further. I guessed the answer choice as 10,900.

Going over the mentioned solutions, I think it makes sense to say that the sum of the other 10 would have been approximately 10*1.1x only since the value is going to increase only on the decimal side.

Thus, the equation would have indeed been x + 10(1.1x) = 132

Sometimes it is the easily worded problems which cause the most difficulty in understanding.


Funny, this was also the 8th question on my GMAT Prep mock.

The problem with your approach is that it contradicts the question.

If city 1 = x and city 3 = 1,21x than you contradict the restriction "no district is to have a population that is more than 10 percent greater than the population of any other district".

However in your approach the population of city 3 is 21% greater than the population of city 1.


Hope it's clear!

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 17 Dec 2016, 11:48
mojorising666 wrote:
If we take the max polulation to be x


then

10x + 0.9x=132000
10.9x=132000
x= 12110.09

0.9 x = 121110* .9
=10899.08

Whats the error. Pls tell


If you want to do it this way, you shold consider the following:

As stated by you:

max. population = x

min. population = X/1,1

Therefore:

10x + (x/1,1) = 132.000

120x/11 = 132.000

x= 12.100

Since we are looking for the minium 12.100/1,1 = 11.000

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 18 Dec 2016, 14:09
One of the Best Official Questions.

Here is my solution to this one =>

Let the population in districts be
w1
w2
w3
w4
w5
w6
w7
w8
w9
w10
w11


Now w1 =>Least value.
To minimise w1,we must maximise all other values -> w2,w3...w11

Now it is given that no population can be 10 percent greater than any other.
Hence all w2,w3,...w11 => w1[1+10/100]=11w1/10

Hence w1+10*11w1/10=132000
=> 12w1=132000
Hence w1 = 11000

Hence D

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 30 Dec 2016, 06:18
ugimba wrote:
A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A. 10,700
B. 10,800
C. 10,900
D. 11,000
E. 11,100


To minimise one population we have to max all other , restriction on max value of all other is that each is max 1.1 times of any other .

let the min value = x , all other = 132-x , to max value of all other , 132-x/10 = 1.1x thus 132 = 12x thus x = 11,000

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 05 May 2017, 11:27
This is the fist GMAT question that in my opinion is completely illogical. If I have a district with 11,000, that means that I can have a 13,000 population district.... WHICH is more than 10% greater than the least district.

It is totally ambiguous, specifically because the question states that Any OTHER District. For me this question goes totally against the GMAC standard.

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 08 May 2017, 12:24
highest value-lowest value<= 0.10*lowest value
lowest:highest=10:11
now
10x+11x*10=132000
x=1100
lowest value=1100*10=11000(ans)

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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 06 Jun 2017, 15:46
ugimba wrote:
A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A. 10,700
B. 10,800
C. 10,900
D. 11,000
E. 11,100


Anytime we are presented with a “minimum value” problem, we must “maximize” all components except for one of them, thus leaving the last component as the “minimized” component of our set.

Let’s use an easy example to test this idea. For instance, we can say that Bob and Frank have a total of 100 apples between them. What is the minimum number of apples that Frank can have? We must “maximize” the number of apples that Bob has; this number is 99. Thus, the minimum number of apples that Frank can have is 1 apple.

Similarly, in this problem we are given 11 voting districts and we must minimize the population of one of those districts. This means that we want to maximize the population of the 10 other districts. We are also given that no district is to have a population that is more than 10% greater than the population of any other district.

Thus, if we label the population of the least populous district as x, we can then say that the maximum population in any other district must be: x + 0.1x = 1.1x. This satisfies the condition that no district has a population that is more than 10% greater than that of any other district.

Because we need to maximize the population of 10 of the 11 districts, all of these 10 districts must have populations of the maximum allowed number, which is 1.1x, and thus, the total population of these 10 districts is (1.1x)(10) = 11x.

We know that the total population of all the districts is 132,000, so we can say:

10 most populous districts + 1 least populous district = 132,000

11x + x = 132,000

12x = 132,000

x = 11,000

Answer: D
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Re: A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 04 Sep 2017, 02:15
Guys, Bunuel,

am i right, that if the question asked "...and no district is to have a population that is less than 10 percent than the population of any other district. What is the maximum possible population that the most populated district could have?

then the equation would be:

X+0.9X*10=132

So difference between 'X+0.9X*10=132' and '1.1X+X*10=132' is whether a question asks "less than" or "greater than"? right?

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A certain city with population of 132,000 is to be divided into 11 [#permalink]

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New post 27 Nov 2017, 18:13
Same question @Brunuel,

I set up the equations as \(10x + 0.9x = 132,000\), and ended up rounding up by 1 to \(10,900 (answer C)\). I'm pretty upset as this is the second time I make that same mistake on a Min/Max question, writing down the equation with a variable reduced by 10% as opposed to a variable increased by 10%. I want to fix this once and for all.

Thanks!

Galiya wrote:
Guys, Bunuel,

am i right, that if the question asked "...and no district is to have a population that is less than 10 percent than the population of any other district. What is the maximum possible population that the most populated district could have?

then the equation would be:

X+0.9X*10=132

So difference between 'X+0.9X*10=132' and '1.1X+X*10=132' is whether a question asks "less than" or "greater than"? right?

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