## Min/Max Problems, Statistics And Sets Problems

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### Min/Max Problems, Statistics And Sets Problems

by swerve » Sun Jul 31, 2022 8:47 am

00:00

A

B

C

D

E

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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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### Re: Min/Max Problems, Statistics And Sets Problems

by [email protected] » Mon Aug 01, 2022 6:58 am
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