Word Problem

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Mjkourtis: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Tue Feb 07, 2012 3:31 am

by Mjkourtis » Thu Oct 18, 2012 7:00 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 of 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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Source: Beat The GMAT — Problem Solving | Thu Oct 18, 2012 7:00 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Oct 18, 2012 7:01 pm

Mjkourtis 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 of 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

Algebraic Approach:

Let us assume that the minimum possible population = x
Then the maximum population = x + 10% of x = 1.1x
For x to be minimum, only one district should have minimum possible population, while the other 10 districts should have the same population, which is equal to 1.1x
So, x + 1.1*10x = 132000
12x = 132000
x = 11,000

The correct answer is D.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Oct 18, 2012 7:31 pm

Mjkourtis 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 of 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

We can also solve it like this:

Population of each district = 132000/11 = 12000
Let the least populated district have a population of 10,000.
Then, 10% greater than 10,000 = (0.10 * 10,000) + 10,000 = 1,000 + 10,000 = 11,000
With one district with 10,000 and other districts greater than 10,000, there has to be at least one district greater than 11,000.

Now 10,000 as the least populated district is not possible.
So, 11,000 as the least populated district satisfies the condition.

The correct answer is D.

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