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no district is to have population

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no district is to have population

by sanju09 » Thu Apr 09, 2009 3:50 am
A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least population district could have?
A. 10700
B. 10800
C. 10900
D. 11000
E. 11100



OA D
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by bluementor » Thu Apr 09, 2009 3:59 am
highest population district = y
lowest population district = x

"no district is to have population that is more than 10 percent greater than the population of any other district"

so, y <= 1.1x

In order to have the lowest possible value for x, all other 10 districts must be equal to the highest population. Therefore:

10y + x = 132000
10(1.1x) + x = 132000
11x + x = 132000
x = 132000/12 = 11000.

Choose D.

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