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GMAT PREP Question (Population)

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Re: GMAT PREP Question (Population)

by Vemuri » Mon Mar 09, 2009 4:30 am
I answered 10,800. Please help me understand where I went wrong

I avg the total number which came to 12,000 people per voting district. From this, I subtracted 10% (1,200) to get 10,800. I thought this is the lowest number.
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by Ian Stewart » Mon Mar 09, 2009 6:34 am
bluementor wrote:Experts, I need some help here.

I agree with durgesh's solution above. However, when I attempted this question, I setup the equation as follows:

0.9x + 10x = 132,000
x = 10,900.

What's wrong with the equation that I've setup. I'm quite sure there's a fundamental concept that I'm just not seeing here. Could someone please explain this? Thanks.
It's the '0.9x' which isn't quite right. If one number is 10% larger than another, then the smaller number is not equal to 90% of the larger number. If one number is 90% of another number, then the larger number is actually 10/90 = 11.1% greater than the smaller number, as you can see by using the numbers 90 and 100.

I find Durgesh's approach more natural here, but it would certainly be possible to modify your approach to get the right answer. If x is the population of the larger districts, we want to know the population S of the smallest district:

S + 0.1S = x
S = (1/1.1)*x
S = (10/11)*x

That is, the population S is 90.909... % of x.

Now plug that into your equation in place of '0.9x':

(10/11)*x + 10x = 132,000
(120/11)*x = 132,000
x = 12,100

and S = 11,000.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by bluementor » Mon Mar 09, 2009 8:03 am
Ah, I see it now. It's the way percentages work:

When I add 10% to 90 I will get 99. But taking off 10% from 99 does not bring me back to 90.

Thanks Ian. As always, this is very helpful.

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by bluementor » Mon Mar 09, 2009 8:08 am
mals24 wrote:
bluementor wrote: 0.9x + 10x = 132,000
How did you come up with this equation, as in whats the logic behind it.

What Durgesh has done is that in order to minimize one variable you maximize all the other variables.

So the minimum value = x
population of the other 10 districts < 10% greater than x (1.1x)
since we need the maximum value, we'll take the population of the other 10 districts as = 1.1x

Equation should be x+ 1.1x*10 = 132,000
How did you get 0.9 and 10?
mals24,

Instead of assigning x to the minimum value (as what durgesh did), I have assigned to the maximum value. As Ian pointed out, I will need to use 10/11 instead of 0.9 if I wanted to use my equation, which is of course much more cumbersome.

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by mmslf75 » Sat Dec 26, 2009 7:23 am
dferm wrote: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. 10,700
B. 10,800
C. 10,900
D. 11,000
E. 11,100

Can someone give a little light to this problem?

Thanks.
What kinda language is this ?
I fail to undersatnd watis being asked ?

that is more than 10 percent greater than the population of any other district
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by valleeny » Sat Dec 26, 2009 10:01 pm
durgesh79 wrote: for x to be min, all other will have the same population equal to 1.1x
I cannot readily see this concept in a blink when it comes to this kind of question. Is there a concept or explanation that I have to understand for this?
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by Stacey Koprince » Thu Jan 14, 2010 10:36 am
You can try this article to see if it helps:

https://www.beatthegmat.com/mba/2009/11/ ... -problems
(The second problem discussed in the article is the voting districts problem above.)
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by TheUT » Wed Dec 05, 2012 8:15 am
1.1 Min >= Max
For Min to be lowest
1.1 Min = Max

Min + 10 Max = 132000
12 Min = 132000
Min = 11K
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by SaraLotfy » Sat Oct 12, 2013 4:18 am
Can experts pleaaasseee confirm OA. Thx
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