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Last year, all registered voters in Kumannia voted either fo

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Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post Updated on: 27 Jun 2014, 02:44
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Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

The way they solve the problem uses a weighted average percent change table. However, I approached the question using the algebraic weighted averages formula. Accordingly, I did the following:

0.1x + 0.05(1-x) = 0.08
0.1x + 0.05 - 0.05x = 0.08
0.05x = 0.03
x = 3/5

This answer is incorrect. The actual answer is 11/18. I can arrive at the correct answer using the suggested table, but I'm hoping someone can please explain to me why my method does not work. Thanks in advance!


OPEN DISCUSSION OF THIS QUESTION IS HERE: weighted-average-126519.html

Originally posted by GSDster on 18 Apr 2011, 19:22.
Last edited by Bunuel on 27 Jun 2014, 02:44, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 18 Apr 2011, 21:32
Your method is correct. But you didn't complete the solution.
If R is the revolutionary and S is the Status_ you got R/(R+S)=3/5

But we want the value of 1.10R/1.08(R+S)=11/18

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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 18 Apr 2011, 21:56
2
x - Revolutionary Party

y - Status Quo Party


1.1x + 1.05y = 1.08x + 1.08y

0.02x = 0.03y

x/y = 3/2

1.1x/(1.08x + 1.08y)

= 1.1x/(1.08x + 1.08 * 2x/3)

= 1.1x/(1.08x + 0.72x)

= 1.1x/1.80x

= 11x/18
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 19 Apr 2011, 11:28
gmat1220 wrote:
Your method is correct. But you didn't complete the solution.
If R is the revolutionary and S is the Status_ you got R/(R+S)=3/5

But we want the value of 1.10R/1.08(R+S)=11/18

Posted from my mobile device


Thank you! I'm still having some trouble understanding this. Can you please explain the reasoning? Does 3/5 only represent the change?
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 19 Apr 2011, 11:52
1
GSDster wrote:
This question is from the Manhattan GMAT.

Last year, all registered voters in Kummania voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of Revolutionary voters increase 10%, while the number of Status Quo voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

The way they solve the problem uses a weighted average percent change table. However, I approached the question using the algebraic weighted averages formula. Accordingly, I did the following:

0.1x + 0.05(1-x) = 0.08
0.1x + 0.05 - 0.05x = 0.08
0.05x = 0.03
x = 3/5

This answer is incorrect. The actual answer is 11/18. I can arrive at the correct answer using the suggested table, but I'm hoping someone can please explain to me why my method does not work. Thanks in advance!


Your approach is this:

Total number of voters last year= 1
Let "x" be the number of voters voted for RP last year
"1-x" voters voted for SQP last year

0.1x + 0.05(1-x) = 0.08
0.1x + 0.05 - 0.05x = 0.08
0.05x = 0.03
x = 3/5

x is found; x=the number of voters for RP last year=3/5.

Question asked:
what fraction of voters voted Revolutionary THIS year

3/5 voters voted for RP last year.
Thus, with an increase of 10%; 3/5*1.1 voters voted for RP THIS year = 3.3/5=0.66

(1-3/5)=2/5 voters voted for SQP last year.
Thus, with an increase of 5%; 2/5*1.05 voters voted for SQP this year = 0.42

Total voters voted this year = 0.66+0.42=1.08, which is 8% more than the last year's total number as already mentioned in the question.

Thus; fraction of RP voters out of Total voters this year:
0.66/1.08 = 66/108 = 11/18
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 20 Apr 2011, 23:17
GSDster wrote:


Thank you! I'm still having some trouble understanding this. Can you please explain the reasoning? Does 3/5 only represent the change?


In your solution x represents the fraction of votes cast in favor or Rev party.
Meaning x = (3/5)th of total votes cast before the respective increments.

Hence, the answer should be x(incremental) = (1.1/1.08) * (3/5)
where 1.1 = increment 0f 10% for Rev party
and 1.08= increment of 8% in total votes cast.

Thus, answer is 11/18.
thank you.
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 20 Apr 2011, 23:18
GSDster wrote:


Thank you! I'm still having some trouble understanding this. Can you please explain the reasoning? Does 3/5 only represent the change?


In your solution x represents the fraction of votes cast in favor or Rev party.
Meaning x = (3/5)th of total votes cast before the respective increments.

Hence, the answer should be x(incremental) = (1.1/1.08) * (3/5)
where 1.1 = increment 0f 10% for Rev party
and 1.08= increment of 8% in total votes cast.

Thus, answer is 11/18.
thank you.
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 20 Apr 2011, 23:41
Let Revolutionary Party (RP) votes for last year = x and the Status Quo Party(SP) votes for last year = 100 – x

Inc in votes for RP = (1/10)x ----- 1
Inc in votes for SP = 5(100 - x)/100 ------ 2
Inc in total votes for RP = (8*100)/100 ----- 3

Add 1 and 2 and equating it to 3
(0.1)x + (100 – x) / 20 = 8

Solving for x we get x =60

Total vote for x this year = 66.
Total no of votes for this year = 108

Fraction of voters voted Revolutionary this year = 66 / 108 = 11 / 18
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 26 Jun 2014, 21:37
subhashghosh wrote:
x - Revolutionary Party

y - Status Quo Party


1.1x + 1.05y = 1.08x + 1.08y

0.02x = 0.03y

x/y = 3/2


1.1x/(1.08x + 1.08y)

= 1.1x/(1.08x + 1.08 * 2x/3)

= 1.1x/(1.08x + 0.72x)

= 1.1x/1.80x

= 11x/18


I know that this post is 3 years old but I was trying to understand weighted avearge and percent problems from MGMAT's book and couldn't understand there table method. From reading this post I was able to understand and get the answer. Could you explain the logic behind the weighted average formula or is there a link to it somewhere so that I can really understand it for when I come across a problem like this again? Thanks so much and kudos to you! Really cleared up the mechanics issue I was having just need to learn the logic now.
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 26 Jun 2014, 23:15
2
1
amjet12 wrote:
I know that this post is 3 years old but I was trying to understand weighted avearge and percent problems from MGMAT's book and couldn't understand there table method. From reading this post I was able to understand and get the answer. Could you explain the logic behind the weighted average formula or is there a link to it somewhere so that I can really understand it for when I come across a problem like this again? Thanks so much and kudos to you! Really cleared up the mechanics issue I was having just need to learn the logic now.


Weighted Average formula:

w1/w2 = (A2 - Aavg)/(Avg - A1)
wStatus/wRev = (10 - 8)/(8 - 5) = 2/3

Here is a link to this formula: http://www.veritasprep.com/blog/2011/03 ... -averages/

Last year, 2/5th people voted Status Quo and 3/5th voted Revolutionary. If there were 5 voters last year, there are 5*(1.08) voters this year.

This year, Revolutionary voters have increased by 10% i.e. if there were 3 voters last year, this year there are 3.3 voters.

Fraction of voters who voted revolutionary = 3.3/5*(1.08) = 33*2/108 = 11/18
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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New post 27 Jun 2014, 02:45
GSDster wrote:
Last year, all registered voters in Kumannia voted either for the Revolutionary Party or for the Status Quo Party. This year, the number of revolutionary voters increased 10%, while the number of Status Que voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

The way they solve the problem uses a weighted average percent change table. However, I approached the question using the algebraic weighted averages formula. Accordingly, I did the following:

0.1x + 0.05(1-x) = 0.08
0.1x + 0.05 - 0.05x = 0.08
0.05x = 0.03
x = 3/5

This answer is incorrect. The actual answer is 11/18. I can arrive at the correct answer using the suggested table, but I'm hoping someone can please explain to me why my method does not work. Thanks in advance!


Set the equation for the number of total voters this year: \(1.1R+1.05S=1.08(R+S)\) --> \(2R=3S\)

The question is \(\frac{1.1R}{1.1R+1.05S}=?\) --> \(\frac{1.1R}{1.1R+1.05S}=\frac{110R}{110R+105S}\). Now, as \(2R=3S\) then \(70R=105S\) (multiplying by 35) --> substitute 105S by 70R: \(\frac{110R}{110R+105S}=\frac{110R}{110R+70R}=\frac{11}{18}\)

OPEN DISCUSSION OF THIS QUESTION IS HERE: weighted-average-126519.html
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Re: Last year, all registered voters in Kumannia voted either fo  [#permalink]

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Re: Last year, all registered voters in Kumannia voted either fo   [#permalink] 01 Jan 2019, 09:22
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