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Help Needed..

by sanalnnair » Mon Sep 13, 2010 10:18 am
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 % greater than the population of any other district. What is the minimum population that the least populated district could have?

Source - GMAT Prep

1) 10,700

2) 10,800

3) 10,900

4) 11,000

5) 11,100



Ans [spoiler](C)
[/spoiler]



I had divided 132000 by 11 and got 12000. Then I had multiplied 12000 * 9 = 108,000.

Then I got 24000, subtracting 132000 - 108000. I tried allocating numbers like 10700 and subtracting remaining to get 13300.

Then I tried calculating the 10% of 10700 and added it to 10700, but now I am struck. Is this way of doing this problem correct?? Please help
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by sanalnnair » Mon Sep 13, 2010 10:19 am
A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

Source- GMAT Prep

1) PIE r`2

2) PIE r`2 + 10

3) PIE r`2 + (1/4) PIE`2 r`2

4) PIE r`2 + (40 - 2 PIE r)`2

5) PIE r`2 + (10 - (1/2) PIE r)`2


Answer is not given




I tried adding the areas of square and circle, and got PIE r`2 + (20-r)`2. But then I am
not able to get the answer.



I also tried adding the areas of circle (PIE r`2) and square( (20-r`2)) and equating
them to the area of wire(assuming it to be cylinder, and assuming h=1)

But then I am struck. Please help.
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by sanalnnair » Mon Sep 13, 2010 10:22 am
Source- GMAT Prep

Before being simplified, the instructions for computing income tax in country R were to add 2 % of one's annual income to the average(arithmetic mean) of 100 Units of country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is I?


1) 50 + I/200

2) 50 + 3I/100

3) 50 + I/40

4) 100 + I/50

5) 100 + 3I/100

Answer is not given


I did I/100 + 2I/100 + Avg(100 Units)

Now, how do I know the total of 100 Units?? Can anyone explain??
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by puneetdua » Mon Sep 13, 2010 10:36 am
For Q #1 , population one - iMO ans shd be D 11000 , coz if i take it 10900 to be least population - am not able to calculate the total population as 132000

taking 10900 -
suppose part 1 has 10900 populateion so no other part can have more than 10% of 10900 that is not more that (10900+1090) - > not more than 11990

suppose we take 11980 for one part so we can have 10 parts with same population ..

11980 * 10 - > 119800 + 10900 -> 130700

So it shd be 11000 , but OA is different ...:(

Expert please.
Thanks
Puneet
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by Brian@VeritasPrep » Mon Sep 13, 2010 10:40 am
Hey Sanalnnair

Good questions - you may want to even break these into individual posts so that people can devour each one thoroughly without confusion (I read your initial question, saw "pi" in the second post of this thread, and was completely lost).

Let me talk about that first one because I think it brings up a pretty good strategic point. When you're asked for the minimum of one city in this case, strategically you'll want to maximize everything else so that you can keep the district in question to a minimum.

With that in mind, let's see how we can minimize one district and maximize the others. We'd ideally want each of the other 10 districts to have the maximum allowable population which is 10% greater than (or 11/10 of) that of the smallest. That would mean that we have 10 districts of the maximum, and if we call the minimum population 'x', we could say that:

x (the smallest) + 10 districts * 11/10 * x = 132,000

x + 11x = 132,000
12x = 132,000
x = 11,000
Last edited by Brian@VeritasPrep on Mon Sep 13, 2010 12:05 pm, edited 1 time in total.
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by selango » Mon Sep 13, 2010 10:43 am
To have minimum population one has to be minimum and remaining population are same.

Let the minimum population be X.Remaining 10 populations are 10% greater than X.

X+10(x+10/100X)=132000

X+10(1.1X)=132000

12X=132000 or X=11000

Pick D
--Anand--
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by selango » Mon Sep 13, 2010 10:47 am
Income Tax=2/100*AI+(100R+1/100*AI)/2

Income Tax=2/100*I+(100+1/100*I)/2

=2I/100+(10000+I)/200

=4I+10000+I/200

=5I+10000/200=50+I/40

Pick C
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by selango » Mon Sep 13, 2010 10:52 am
2 wires of 20m length

Area of circle=Pi*r^2[this is common in all options]

Now Circumference of the square=40-circumference of circle

4a=40-2*pi*r

a=10-1/2*pi*r

Area of square=a^2=(10-1/2*pi*r)^2

Pi*r^2+(10-1/2*pi*r)^2

Pick E
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by goyalsau » Mon Sep 13, 2010 10:53 am
A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

Source- GMAT Prep

1) PIE r`2

2) PIE r`2 + 10

3) PIE r`2 + (1/4) PIE`2 r`2

4) PIE r`2 + (40 - 2 PIE r)`2

5) PIE r`2 + (10 - (1/2) PIE r)`2

I think answer is option 5.
area of circle is pie r'2 and area of square is 40 - circumference of circle.
we get 40-2pier/4 to get the desired side of square.
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by sanalnnair » Mon Sep 13, 2010 11:01 am
@ Selango, @ Saurabh,


Thanks a lot guys.. My brain stopped working.. I didn't read the question properly and thats why I didn't get the answer..
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by goyalsau » Mon Sep 13, 2010 11:03 am
Guys..... Good work but still confused.


Income Tax=2/100*AI+(100R+1/100*AI)/2

Income Tax=2/100*I+(100+1/100*I)/2

=2I/100+(10000+I)/200

=4I+10000+I/200

=5I+10000/200=50+I/40

Pick C



Before being simplified, the instructions for computing income tax in country R were to add 2 % of one's annual income to the average(arithmetic mean) of 100 Units of country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is I?

Can you please explain how you interpret It, I think that is the what required over here.... but i am confused
Before being simplified, the instructions for computing income tax in country R were to add 2 % of one's annual income
Till here its fine, then it said the average of 100 units .. what is this 100 units....... and then again 1 percent of one annual income.
What all i understand is that 3 % of total income. but i am sure that is not right. so what is being said over. if you can explain .. then that will be helpful for me and others as well

thanks
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by alivapriyada » Mon Sep 13, 2010 11:08 am
Brian@VeritasPrep wrote:Hey Sanalnnair

Good questions - you may want to even break these into individual posts so that people can devour each one thoroughly without confusion (I read your initial question, saw "pi" in the second post of this thread, and was completely lost).

Let me talk about that first one because I think it brings up a pretty good strategic point. When you're asked for the minimum of one city in this case, strategically you'll want to maximize everything else so that you can keep the district in question to a minimum.

With that in mind, let's see how we can minimize one district and maximize the others. We'd ideally want each of the other 10 districts to have the maximum allowable population which is 10% greater than (or 11/10 of) that of the smallest. That would mean that we have 10 districts of the maximum, and if we call the minimum population 'x', we could say that:

x (the smallest) + 10 districts * 11/10 * x = 132,000

x + 10x = 132,000
11x = 132,000
x = 11,000
wont that be X+11X=1,32,000
12X=1,32,000
X=11,000

M sorry if I'm mistaken.
Last edited by alivapriyada on Mon Sep 13, 2010 11:37 am, edited 1 time in total.
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by sanalnnair » Mon Sep 13, 2010 11:10 am
@ Saurabh,

the question says that income tax is equal to sum of 2 % of ones income and the average of 100 Units and 1 % of annual income.


That means income tax = 2/100 * I + (100 + 1/100 * I) / 2

if you solve it, you get

income tax = (4I + 10000 + I)/200

simplfiling it will give you, 5I/200 + 50,

then I/4 + 50, thats again is C.


Hope this helps
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by sanalnnair » Mon Sep 13, 2010 11:30 am
@ Brian,


Thanks for the wonderful explanation...
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by goyalsau » Mon Sep 13, 2010 11:47 am
Thanks Sanal,
i am not sure that next time when i see a problem like i will be able to solve it correctly,
very confusing wordings.....
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