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weighted average.

by Aishwarya1204 » Sat Oct 20, 2012 11:15 pm
Last year all registered voters either voted for the Revolutionary party or the Status Quo party. This year the number of revolutionary voters increased by 10% and the Status Quo voters increased by 5%. No other votes were cast. If the number of total votes increased by 8%. What fraction of voters voted for the Revolutionary party this year.

Answer is [spoiler] 11/18 [/spoiler]

I did this with the weighted average formula and got :

a = people who voted for the Revolutionary party
b = people who voted for the Status Quo party

so,

10 a + 5 b/ a + b = 8

10 a + 5b = 8a + 8b

2a = 3b

a/b = 3/2

so revolutionary/total = 3/5

why is this wrong?
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by GMATGuruNY » Sun Oct 21, 2012 3:38 am
Aishwarya1204 wrote:Last year all registered voters either voted for the Revolutionary party or the Status Quo party. This year the number of revolutionary voters increased by 10% and the Status Quo voters increased by 5%. No other votes were cast. If the number of total votes increased by 8%. What fraction of voters voted for the Revolutionary party this year.

Answer is [spoiler] 11/18 [/spoiler]

I did this with the weighted average formula and got :

a = people who voted for the Revolutionary party
b = people who voted for the Status Quo party

so,

10 a + 5 b/ a + b = 8

10 a + 5b = 8a + 8b

2a = 3b

a/b = 3/2

so revolutionary/total = 3/5

why is this wrong?
Use alligation.
Let R = Revolutionary voters and S = Status Quo voters.

Step 1: Plot the 3 percentages on a number line, with the percentage increases for R and S (10% and 5%) on the ends and the percentage increase for the total (8%) in the middle.
R (10%)------------8%-------------------(5%) S

Step 2: Calculate the distances between the percentages.
R (10%)-----2-----8%----------3--------(5%) S

Step 3: Determine the ratio in the mixture.
R:S last year is equal to the RECIPROCAL of the distances in red.
Thus:
R:S last year = 3:2.

To determine R:S this year, we can plug in values for R and S.

Let R last year = 30 and S last year = 20.
This year:
R increased by 10% = (1.1)*30 = 33.
S increased by 5% = (1.05)*20 = 21.
R/(R+S) = 33/(33+21) = 33/54 = 11/18.
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