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A certain city with a population of 132,000 is to be divided in 11 voting districts, and no district is to have population that is more than 10% greater than the other district. What is the minimum possible population of a district?

Re: Population of a city PS GMAT prep [#permalink]

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24 Mar 2009, 16:39

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Accountant wrote:

A certain city with a population of 132,000 is to be divided in 11 voting districts, and no district is to have population that is more than 10% greater than the other district. What is the minimum possible population of a district?

A. 10,700 B. 10,800 C. 10,900 D. 11,000 E. 11,100

minimum possible = x max = 1.1 (minimum possible) = 1.1x

nx + (11 - n) (1.1x) = 132000

When is the x minimum? when n is mimimum. the minimum value of n, whcih cannot be 0, is 1. x + (11 - 1) (1.1x) = 132000 x + 1.1 (10)x = 132,000 12x = 132,000 x = 11,000 _________________

Re: Population of a city PS GMAT prep [#permalink]

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30 May 2011, 20:46

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I attempted in GMAT prep test and couldn't figure out , how to solve it. Important part was to understand , what question is asking. Later on during review, I realised that question is asking the minimum value so all other values have to be maximum with one condition that they are not beyond 10% of minimum value , hence

Re: Population of a city PS GMAT prep [#permalink]

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24 Mar 2009, 15:28

It is E =11,100

Say all districts are same size >> 132000/11 = 12,000 people per district

(A) 10,700: If one district has 10,700 people that means that the minimum possible difference would be achieved if the 1,300 people (12,000-10,700) would be split equal across the remaining 10 districts. Thus each remaining district has 12,130 people. 12,130/10,700 > 1.10 --> cannot be

(B) 10,800: thus 1200/10 = 120 in each remaining district. 12,120/10,800 >1.10 --> cannot be

Re: Population of a city PS GMAT prep [#permalink]

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24 Mar 2009, 17:45

Many thanks, one follow up question: In equation: nx + (11 - n) (1.1x) = 132000 , are you assuming the following: n=number of districts having minimum value (11-n)= number of districts not having mimimum values, DOES this mean all other districts have maxium values since you are multiplying it by 1.1x

If all other districts have maximum values then it means that we can solve it by using equations. Let y be maximum value and x be mimimum value: x+10y=132,000 y=1.1 x then x+10*1.1x=132,000 12x=132,000 or x=11,000

Re: Population of a city PS GMAT prep [#permalink]

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09 Jan 2012, 12:27

T and E

a) Max population of district is 11 770. If we have 10 districts at 11 770 then population of 10 districts is 117 700. Therefore 117 700 + 10700 = 128 400. This does not equal 132 000

d) Max population of district is 12 100. If we have 10 districts at 12 100 then population of 10 districts is 121 000 Therefore 121 000+ 11 000 = 132 000. This does equal 132 000. (ANSWER)!

Re: Population of a city PS GMAT prep [#permalink]

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09 Jan 2012, 14:39

Say, we equally divided the population among 11 districts, we can have 12000 each, which is not minimum. Lets try 11000 each with some distribution such that the distribution is < 10% when any two districts are picked.

We assigned 11000 to each district, so now we are left with 11000. Say one district stays at 11000 and the remaining 10 distribute 11000. So for those 10 districts, we will have individual distribution of 1100. This violates the 10% rule. Therefore, the minimum must be >11000.

Answer E it is. _________________

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