Min/Max Problems, Statistics And Sets Problems

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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 \(10\) 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. \(11,100\)

The OA is D

Source: GMAT Prep

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swerve wrote:
Sun Jul 31, 2022 8:47 am
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. \(11,100\)

The OA is D

Source: GMAT Prep
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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