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Please Crack the Math (PS) Question! Anyone! Thanks ;)

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Please Crack the Math (PS) Question! Anyone! Thanks ;) [#permalink]

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New post 21 Jul 2009, 21:07
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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 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



It was from the GMAT Prep. Thanks!

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Re: Please Crack the Math (PS) Question! Anyone! Thanks ;) [#permalink]

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New post 21 Jul 2009, 21:20
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Out of 11 districts, one district can have least population when the remaining 10 have the maximum possible population.
Let x be the average population of the 11 districts. Since a maximum deviation of 10% is allowed, the population for the 10 districts is (110/100)*10*x = 11x

Population of the least populated district = x
Total population = 11x + x = 132000
12x = 132000
x = 11000

So least populated district can have min population of 11000

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Re: Please Crack the Math (PS) Question! Anyone! Thanks ;) [#permalink]

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New post 21 Jul 2009, 21:49
Thanks! You are the absolute best.

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Re: Please Crack the Math (PS) Question! Anyone! Thanks ;) [#permalink]

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New post 21 Jul 2009, 22:15
Another method is by substituting the options.
Tip: The numerical options in GMAT are sorted in increasing order.

Start with the middle option C, i.e. 10900
Min Population = 10900
Population in other cities = (132000 - 10900) / 10 = 12110
Difference between min populated and other cities= 12110 - 10900 = 1211 ..(i)
10% of min population = 10% of 10900 = 1090 ..(ii)

As (i) is greater than (ii), hence invalid option.

Now try substituting option D (remember, now you don't need to substitute A or B, as these values are even smaller then C, and will lead to greater difference)
Min Population = 11000
Population in other cities = (132000 - 11000) / 10 = 12100
Difference between min populated and other cities= 12100 - 11000 = 1100 ..(i)
10% of min population = 10% of 11000= 1100 ..(ii)

As (i) is equal to (ii), hence valid option. Answer D.
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Re: Please Crack the Math (PS) Question! Anyone! Thanks ;) [#permalink]

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New post 21 Jul 2009, 22:27
bigoyal wrote:
Another method is by substituting the options.
Tip: The numerical options in GMAT are sorted in increasing order.

Start with the middle option C, i.e. 10900
Min Population = 10900
Population in other cities = (132000 - 10900) / 10 = 12110
Difference between min populated and other cities= 12110 - 10900 = 1211 ..(i)
10% of min population = 10% of 10900 = 1090 ..(ii)

As (i) is greater than (ii), hence invalid option.

Now try substituting option D (remember, now you don't need to substitute A or B, as these values are even smaller then C, and will lead to greater difference)
Min Population = 11000
Population in other cities = (132000 - 11000) / 10 = 12100
Difference between min populated and other cities= 12100 - 11000 = 1100 ..(i)
10% of min population = 10% of 11000= 1100 ..(ii)

As (i) is equal to (ii), hence valid option. Answer D.

Nice explaination with PITA(plug in the answer tech)
I started off with the same bt shifted to my instincts :D

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Re: Please Crack the Math (PS) Question! Anyone! Thanks ;)   [#permalink] 21 Jul 2009, 22:27
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Please Crack the Math (PS) Question! Anyone! Thanks ;)

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