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## Question from Gmat Prep- Help please! 3

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bobdylan Rising GMAT Star
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Question from Gmat Prep- Help please! 3 Fri Apr 13, 2012 2:21 pm
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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 population that the least populated district could have?
a)10,700
b)10,800
C) 10,900
d) 11,000
e) 11,100

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Bill@VeritasPrep GMAT Instructor
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Fri Apr 13, 2012 3:31 pm
If the population is distributed equally, then each district has 132,000/11 = 12,000 residents. Let's define x as the district with the lowest population. Since no other district can exceed x by more than 10%, we can set up the following equation:

x + 1.1(10x) = 132,000
12x = 132,000
x = 11,000

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iwillsurvive101 Rising GMAT Star
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Fri Apr 13, 2012 5:57 pm
Bill

x + 1.1(10x) = 132,000

How did you get 1.1(10x) ?

I reasoned as follows:

- Apart from x, there are 10 other districts. Each of those districts can have 10% more population than x. So 10% x X 10 (10 percent of x times 10). I know this is not right.

Thanks

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Anurag@Gurome GMAT Instructor
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Fri Apr 13, 2012 6:24 pm
bobdylan 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 population that the least populated district could have?
a)10,700
b)10,800
C) 10,900
d) 11,000
e) 11,100
Let us assume that the minimum possible population of the least populated district be P.

It is given that "no district is to have a population that is more than 10% greater than the population of any other district."

Then the population of 11 districts should be between P and (P + 10% of P) = 1.1P
Now we have minimize P. For this we should make only one district to have minimum possible population and the remaining 10 districts should have maximum possible population.
So, P + (10 * 1.1P) = 132,000
12P = 132,000
P = 11,000

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GMATGuruNY GMAT Instructor
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Fri Apr 13, 2012 7:00 pm
Quote:
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 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
An alternate approach is to plug in the answer choices, which represent the minimum possible population.

To MINIMIZE the smallest population, we need to MAXIMIZE the other 10 populations.
Thus, each of the other 10 districts must have the maximum allowed population: 10% greater than the smallest population.
Since the total population of the city is 132,000 -- a multiple of 1,000 -- the correct answer choice is almost certainly a multiple of 1,000.

Each of the other 10 districts = (132,000 - 11,000)/10 = 12,100.
Difference between the populations = 12,100 - 11,000 = 1100, which is 10% of the smallest population.
Success!

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