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by arjunshn » Wed Apr 27, 2011 4:25 am
A certain city with population 132000 is to be divided into 11 districts and no district is to have a population that is more than 10% greater than the population of any district.What is the minimum possible population that the least populated district could have?

a-10700
b-10800
c-10900
d-11000
e-11100

ans-d
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by Anurag@Gurome » Wed Apr 27, 2011 4:32 am
arjunshn wrote:A certain city with population 132000 is to be divided into 11 districts and no district is to have a population that is more than 10% greater than the population of any district.What is the minimum possible population that the least populated district could have?

a-10700
b-10800
c-10900
d-11000
e-11100

ans-d
Let the 11 voting districts have populations d1, d2, d3, d4,….d11 respectively.
Let d1 be the least population.
So, d1+d2+d3+…+d11 = 132,000.
Now, according to question d2 <= 1.1*d1, d3 <= 1.1*d1,….d11<=1.1*d1.
Adding all inequality, we get that (d2+d3+d4…d11) <= 10*1.1*d1.
Or (d2+d3+d4…d11) <= 11d1.
Or (d1+d2+…+d11) <= 12d1.
Or 132,000 <= 12d1.
Or d1 => 11,000.
So, the minimum possible population of least populated district is 11,000.

The correct answer is D.
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by sanju09 » Wed Apr 27, 2011 4:39 am
arjunshn wrote:A certain city with population 132000 is to be divided into 11 districts and no district is to have a population that is more than 10% greater than the population of any district.What is the minimum possible population that the least populated district could have?

a-10700
b-10800
c-10900
d-11000
e-11100

ans-d


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by Ashish8 » Wed Apr 27, 2011 7:56 pm
I did it using some back substitution. In order to minimize one, we need to maximize the others.

If they were all the same population, then each would be 132000/11 = 12,000.

I started with C (10900).

10900 means adding 1100 to the other 10 districts to keep the same population. 10% of 10900 = 1090. 1090 < 1100, aka more then a 10% difference.

Next, D (11000)

this time we need to add 1000 to the other 10 districts. 10% of 11000 = 1100. 1100 > 1000, aka within the 10% threshold.
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