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voters : another( word problem + weighted average)

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by bhumika.k.shah » Sat Feb 20, 2010 3:39 am
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?

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can we use the alligation method here ?
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by harsh.champ » Sat Feb 20, 2010 4:23 am
bhumika.k.shah 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?

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can we use the alligation method here ?
Let K be total voters
Let old Revolutionary Party voters be x.
Let new Revolutionary Party voters be y.
Similarly,K-x and P-y for old and new Status Que voters.
y=1.1x
P-y =0.95(K-x)
Also,
P=1.08K


Solving the 3 equations,u will get the answer.
I would advise that you go through advanced word translations problems.
Hope it helps.
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by thephoenix » Sat Feb 20, 2010 9:20 am
bhumika.k.shah 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?

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can we use the alligation method here ?
let the number of revolutionary voters last year=x--------> # of voters this year=1.1x
and # of Status Que voters last year =y------>this year=1.08 y

tot last year t1=x+y
tot this year t2=1.1x+1.05y

t2=1.08 of t1
---->1.1x+1.05y=1.08x+1.08y
solving
0.02x=0.03y

y=2/3 of x

tot this year=1.1x+1.05(2x/3)=1.8x

rev voters =1.1x

fraction=1.1x/1.8x=11/18
oa pls
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by shashank.ism » Sat Feb 20, 2010 11:19 pm
bhumika.k.shah 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?

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can we use the alligation method here ?
what does alligation method mean ...will u please explain. I don't know about it...
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by gmatmachoman » Sun Feb 21, 2010 12:29 am
bhumika.k.shah 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?

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can we use the alligation method here ?

Where are the options???

Is this a PS or ds???
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by harsh.champ » Sun Feb 21, 2010 2:39 am
shashank.ism wrote:
bhumika.k.shah 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?

Source MGMAT %

can we use the alligation method here ?
what does alligation method mean ...will u please explain. I don't know about it...
In short ,I would say :-
Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity. Alligation medial is merely a matter of finding a weighted mean.

If you want to look in further details you can check out this link:-
https://en.wikipedia.org/wiki/Alligation
and https://www.toomanymeds.com/pro/powerpoi ... gation.pps

Also,in MGMAT study guide the use of alligation method with examples is given.
For conceptual purposes,I would advise you to refer the Manhattan guide a in it only concepts related to GMAT are given.
Hope it helps.
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by harsh.champ » Sun Feb 21, 2010 2:43 am
gmatmachoman wrote:
bhumika.k.shah 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?

Source MGMAT %

can we use the alligation method here ?

Where are the options???

Is this a PS or ds???
Well,this is a PS question from MGMAT - gmatmachoman.
I guess the alligation method can be useful here -bhumika.
Also,I would rewuest you to kindly post the option choices also as it helps us to eliminate some of them and zeo in on our answer. Thanks!
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by firdaus117 » Sun Feb 21, 2010 9:57 am
Yes,you can use Alligation method here in this case,8% is actually the weighted mean of 10% and 5%.In fact we can also cross-check our answer by conventional method.
The alligation approach:
x ------ y
10% 5%
8%

3 : 2
fraction of voters voted Revolutionary this year=3/5=60%
The conventional method:
Let the number of revolutionary voters be x while the number of Status Que voters be y.
After respective increases,they become 1.1x and 1.05y.
Accd to question,
1.1x+1.05y=1.08(x+y)
or, 0.02 x = 0.03 y
or, x/y= 3/2
or, x/(x+y)=3/5=0.6=60%
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