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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 03 Mar 2018, 07:17
Is this process correct?

132,000 / 11 = 12,000

132,000/ 12,000 = 11, hence answer is "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 Nov 2018, 08:04
I still don't get it. I think the answer is C.
Lets say that indeed the population in the first distinct is 10900 then the other distincts have a population of 12110.
10900+10*12110=132000. So in this scenario, the minimum population is 10900 and not 11000. If I did something wrong, please explain.
Thanks!!
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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 Nov 2018, 20:14
Giorgos92 wrote:
I still don't get it. I think the answer is C.
Lets say that indeed the population in the first distinct is 10900 then the other distincts have a population of 12110.
10900+10*12110=132000. So in this scenario, the minimum population is 10900 and not 11000. If I did something wrong, please explain.
Thanks!!


Hi Giorgos92,

The prompt states that no district has a population that is more than 10% greater than any other district.

IF.... the smallest district has 10,900, then the largest any of the other districts could be would be 10,900 + (10% of 10,900)....

10,900 + 1,090 = 11,990

In your calculation, the other districts each have a population of 12,110, which is not permissible given what we are told.

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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 21 Nov 2018, 06:20
EMPOWERgmatRichC wrote:
Giorgos92 wrote:
I still don't get it. I think the answer is C.
Lets say that indeed the population in the first distinct is 10900 then the other distincts have a population of 12110.
10900+10*12110=132000. So in this scenario, the minimum population is 10900 and not 11000. If I did something wrong, please explain.
Thanks!!


Hi Giorgos92,

The prompt states that no district has a population that is more than 10% greater than any other district.

IF.... the smallest district has 10,900, then the largest any of the other districts could be would be 10,900 + (10% of 10,900)....

10,900 + 1,090 = 11,990

In your calculation, the other districts each have a population of 12,110, which is not permissible given what we are told.

GMAT assassins aren't born, they're made,
Rich



I found that 10900/12110>0.9 so I thought that 10900 is less than 10% but I see know where is the miscalculation.
Thank you very much!!!!
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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 21 Nov 2018, 08:52
I reverse-plugged answer choices and calculated the 1.1x (max value) and compared it to the mean + distribution of missing value.

For example (after plugging in answer [C] and finding values that did not fit), for answer [D], the correct answer:

I took value 11,000 and multiplied by 1.1 (the parameter in the question).

This left me with 12,100 as the max value the other 10 groups can be.

Comparing that to a mean of 12,000, I noticed that 100 people per remaining group must be recouped, which coincides with our max value for the 10 remaining groups.

Answer [D] will be the only answer value that fits.
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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 01 Jan 2019, 09:23
Hello guys I solved this with the following manner, I am not sure however if the approach is correct.

say x is the least amount of population and 12.000 is the greatest amount, based on stem no district is to have a population that is more than 10 percent greater than the population of any other district, thus lets say that the max increase could be 1.1x=12.000 => 10909
so the difference between the highest and lowest is 12.000-10909=1091
so , 12.000-x <= 1091 or x>=10909
Hence minimum value 11.000
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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 04 Feb 2019, 14:14
Hi,

Here are my two cents . Though not quick as Bunuel mentioned method but let me know if this makes sense.

We are told the the total population is 132000 which is to be be divided into 11 groups. So average population per group is 12000.

Now if we reduced population of any group Say Group 1 then the difference from average i.e Avergage - Grp 1 is at least added equally among remaining other 10 groups or to few groups.

here is what i mean

Say group 1 to group 11 each have population of 12000, average population is 12000 and total population is 132000.

Here no group has population more than 10% of other group.

Now if i reduced the population of group 1 by 2000 and make it 10000 then to maintain average we will have to add this population to some group of 10 .
Lets say we add equal members to each group then we will have add \(\frac{2000}{10}\)= 200 members to each of the remaing 10 groups .

Which makes the population of Group 2 to Group 10 as 12200 members each.

Now Population of Group 1 is 10,000 and any of the group can't have members more than 11000. Now this scenario is not possible since we have to divide a total 132000 and many will be left out. Atleast one of the group will have population more than or equal to 12200.

Similarly

if
(A)10700, then other groups must be atleast 12130 but other groups can't be more than 11770.
(B)10800, then other groups must be atleast 12120 but other groups can't be more than 11880.
(C)10900, then other groups must be atleast 12110 but other groups can't be more than 11990.
(D)11000, then other groups must be atleast 12100 Here other groups can't be more than 12100.
(E)10100, then other groups must be atleast 12090 but other groups must be atleast 12210

now from answer choices A through C if you reduce any of the subsequent groups members to match upto 10% more of Group 1 then the difference between them will have to add up to some group to make the total 132000,

Say Group 1 is 10700 and group 2 is 11770 then one of the groups will have members which will more than 10 % of group 1.


But in Option D we have if i reduced my group 1 members to 11000 than i can have other groups take that hit and balance out which will turn out that difference between any two groups will not be more than 10 %

In option E we have a similar scenario. But since we are asked for what is the minimum possible population clearly D is smaller than E

I am not sure if i was able to frame my understanding clearly.

Looking for hearing back from community.
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A certain city with population of 132,000 is to be divided into 11   [#permalink] 04 Feb 2019, 14:14

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