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 year3/5 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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~fluke

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