A certain city with a population of 132000, is divided into 11 voting districts, and no district is to have a population that is more than 10% greater than the population of any other district. What is the minimum possible population that the least populated district could have?
A) 10700
B) 10800
C) 10900
D) 11000
E) 11100
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- GMAT 2007
Total population = 132000 & no. of districts = 11.
If divided equally, the population of each district = 132000/11 = 12000
The condition to satisfy = no district can have the population > 10% of any other district.
For ex - assume district (A) has the least population, now the only way to get the min. population of (A) so that no other district can have population > 10% of (A) is to reduce the population of (A) to minimum and add the reduced amount equally into the rest 10 districts.
If you look at the answer choices the least possible population of (A) when no other district will have pop > 10% of A would be (11000)
If A = 11000 the reduced pop = 1000. so 1000 can be increased in rest of 10 districts, so the population of rest of the 10 district= 12100
10 % of (A's population) = 10% of 11000 = 1100. So rest of the districts have exactly 10% more population than (A)
Hence the answer is (D)
Hope it helps.
GMAT 2007
If divided equally, the population of each district = 132000/11 = 12000
The condition to satisfy = no district can have the population > 10% of any other district.
For ex - assume district (A) has the least population, now the only way to get the min. population of (A) so that no other district can have population > 10% of (A) is to reduce the population of (A) to minimum and add the reduced amount equally into the rest 10 districts.
If you look at the answer choices the least possible population of (A) when no other district will have pop > 10% of A would be (11000)
If A = 11000 the reduced pop = 1000. so 1000 can be increased in rest of 10 districts, so the population of rest of the 10 district= 12100
10 % of (A's population) = 10% of 11000 = 1100. So rest of the districts have exactly 10% more population than (A)
Hence the answer is (D)
Hope it helps.
GMAT 2007
- kouranjelika
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Re: A certain city with a population of 132000, is divided into
Ron, can you weigh in. No offense to the poster, but I'm super confused.
Thanks.
Thanks.
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Re: A certain city with a population of 132000, is divided into
Hang on, may be I got it. How about this...
Since minimum is basically the same as a solid number if all other districts are exactly 10% more, then can't we create a formula as follows:
x+1.1x*10=132,000
where x is the smallest population
So, then it becomes x = 11,000
Thoughts?
P.S. When I read the question I kept for some reason thinking that all the districts are different and no one can be 10% larger than the one smaller below it. Reading it now, makes absolutely no sense but for some reason I thought this was like uber mind bending because I could not understand how to create such a domino effect. Ron, if you recall the trees question in the OG where this gardener or whatever is planting trees for 4 years and he increases them by a fourth every year. And the question was what the original was given the final quantity of trees or something like that. This is what this question reads to me like at first sight.
Since minimum is basically the same as a solid number if all other districts are exactly 10% more, then can't we create a formula as follows:
x+1.1x*10=132,000
where x is the smallest population
So, then it becomes x = 11,000
Thoughts?
P.S. When I read the question I kept for some reason thinking that all the districts are different and no one can be 10% larger than the one smaller below it. Reading it now, makes absolutely no sense but for some reason I thought this was like uber mind bending because I could not understand how to create such a domino effect. Ron, if you recall the trees question in the OG where this gardener or whatever is planting trees for 4 years and he increases them by a fourth every year. And the question was what the original was given the final quantity of trees or something like that. This is what this question reads to me like at first sight.
"A creative man is motivated by the desire to achieve, not by the desire to beat others."
-Ayn Rand
-Ayn Rand
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Re: A certain city with a population of 132000, is divided into
kouranjelika Wrote:Hang on, may be I got it. How about this...
Since minimum is basically the same as a solid number if all other districts are exactly 10% more, then can't we create a formula as follows:
x+1.1x*10=132,000
where x is the smallest population
So, then it becomes x = 11,000
Exactly.
P.S. When I read the question I kept for some reason thinking that all the districts are different and no one can be 10% larger than the one smaller below it. Reading it now, makes absolutely no sense but for some reason I thought this was like uber mind bending because I could not understand how to create such a domino effect. Ron, if you recall the trees question in the OG where this gardener or whatever is planting trees for 4 years and he increases them by a fourth every year. And the question was what the original was given the final quantity of trees or something like that. This is what this question reads to me like at first sight.
If this kind of confusion occurs, the two most basic things you can do are...
- Slow down.
"- Try to explain the situation to an imaginary 10-year-old.
"Slow down" is perhaps the most important thing that can be said about word problems in general. Rushing and confusion go hand-in-hand, to a much greater degree than most people realize.
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Re: A certain city with a population of 132000, is divided into
Also, "slow down" is good advice to people who have trouble with timing on word problems, too.
Yes, I'm actually saying that people who are taking too long on word problems should slow down.
That probably sounds backward, but it's not. If you read a problem statement slowly and carefully"”taking the time to understand it enough to explain to your hypothetical 10-year-old"”then you shouldn't need to go through it more than once. If you rush through it, on the other hand, you'll almost certainly have to go through it several times.
"Several times faster" is slower than "one time slowly and carefully".
Yes, I'm actually saying that people who are taking too long on word problems should slow down.
That probably sounds backward, but it's not. If you read a problem statement slowly and carefully"”taking the time to understand it enough to explain to your hypothetical 10-year-old"”then you shouldn't need to go through it more than once. If you rush through it, on the other hand, you'll almost certainly have to go through it several times.
"Several times faster" is slower than "one time slowly and carefully".
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Re: A certain city with a population of 132000, is divided into
Words of wisdom. You won't believe, I just yesterday did another Gmat Prep test and got this question again...and *drumroll* was TOTALLY STUCK! I can't believe it. I usually am quite ok with work problems, but this one for some reason is a total pain in the ass for me. Ugh!
"A creative man is motivated by the desire to achieve, not by the desire to beat others."
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Re: A certain city with a population of 132000, is divided into
kouranjelika Wrote:Words of wisdom. You won't believe, I just yesterday did another Gmat Prep test and got this question again...and *drumroll* was TOTALLY STUCK! I can't believe it. I usually am quite ok with work problems, but this one for some reason is a total pain in the ass for me. Ugh!
These things happen sometimes.
(:
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