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by Brent@GMATPrepNow » Fri Jan 09, 2015 1:26 pm
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) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100
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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by GMATGuruNY » Fri Jan 09, 2015 2:34 pm
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) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100
An alternate approach is to PLUG IN THE ANSWERS, which represent the minimum possible population of the least populated district.

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.

Answer choice D: Least populated district = 11,000.
Maximum value of each of the other 10 districts = 11,000 + .1(11,000) = 12,100.
Sum of the 11 districts = 11,000 + 10(12,100) = 132,000.
Success!

The correct answer is D.
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