Problem from the MBA.com practice test 1

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pranavc: Master | Next Rank: 500 Posts; Posts: 167; Joined: Tue Feb 26, 2008 4:37 am; Thanked: 5 times; Followed by:1 members

Problem from the MBA.com practice test 1

by pranavc » Thu Jul 03, 2008 7:55 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 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

(A) 10,7000
(B) 10,800
(C) 10,900
(D) 11,000
(E) 11,100

Any input on this will be highly appreciated. Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Thu Jul 03, 2008 7:55 pm

wawatan: Master | Next Rank: 500 Posts; Posts: 171; Joined: Sat May 03, 2008 3:51 pm; Thanked: 8 times

by wawatan » Thu Jul 03, 2008 8:50 pm

total population = 132,000
11 voting districts named D1, D2, D3, ..., D11

we know that D1 + D2 + D3 + ... + D11 = 132,000 (a)
and that the maximum gap between all districts is 110% in terms of population count, i.e. Di <= 1.1 Dj (b)

the minimum possible population for a given district is the one for which all the others districts have the same population (thus maximizing the gap)

hence if D1 is the least populated district, D2 = D3 = ... = D11
(a) can then be written as D1 + 10 D2 = 132,000
and when the gap is maximum, (b) translates into D2 = 1.1 D1

combining the two gives us D1 + 11 D1 = 132,000
and D1 = 11,000

You can verify that equations (a) and (b) above are respected