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A certain city with a population of 132,000 is to be divided [#permalink]

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02 Dec 2006, 11:38

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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 reater 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

Population of one district = A
A will be minimum only when all other districtsâ€™ populations are more than 10% of A
So A + (110A/100)*10 = 132,000
A = 11,000

Ok, according to this: Let's say district A has the minimum, then a district B cannot be more than 10% of A. ie: A+10/100A= 110/100A. Now it's given that "no district is to have a population that is more than 10 percent greater than the population of any other district", so for A being a minimum, this can only be satisfied when all of the other 10 districts are 10% more than A (if they were any higher, then they would be more than 10% of A) . Thus the equation that Anindya came up with.

that's where I made a mistake also, the first time around. it's actually

1st district = 11,000 Multiplying each by 110/100 or 1.1
2nd = 11000* 1.1 = 12100
3rd = 11000 *1.1 = 12100 NOT (12100*1.1=13310)
4th = 11000 * 1.1 = 12100 NOT (13310*1.1)
etc

because think abt this, with your logic: 3rd district = 13310 which is greater than 10% of the 1st district. According to question, it cannot be more than 10% of any other district, including A. Thus, 3rd, or 4th or anything else can be a max of 110/100*A.

Dont worry - I've been misreading the question - I was looking at it as if it were a progression with a difference of 10% between districts ie. District 1 = x
District 2 = x+10%
District 3 = (x+10%)+10%

that's where I made a mistake also, the first time around. it's actually

1st district = 11,000 Multiplying each by 110/100 or 1.1 2nd = 11000* 1.1 = 12100 3rd = 11000 *1.1 = 12100 NOT (12100*1.1=13310) 4th = 11000 * 1.1 = 12100 NOT (13310*1.1) etc

because think abt this, with your logic: 3rd district = 13310 which is greater than 10% of the 1st district. According to question, it cannot be more than 10% of any other district, including A. Thus, 3rd, or 4th or anything else can be a max of 110/100*A.

Is this clearer?

I see you just posted before me - thank hsampath - I was tearing my hair out trying to see what was wrong with my working when I'd just read the question wrong. Will add that to error log!!!