Last year, all registered voters in Kumannia voted either fo

Question

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?

Show Spoiler

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

Archived Topic

Hi there,

This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.

Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum

Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.

Thank you for understanding, and happy exploring!

gmat1220 · Answer

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

subhashghosh · Answer

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

GSDster · Answer

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

fluke · Answer

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
*******************************

amit2k9 · Answer

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.

amit2k9 · Answer

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.

varunmaheshwari · Answer

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

amjet12 · Answer

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.

KarishmaB · Answer

Weighted Average formula: w1/w2 = (A2 - Aavg)/(Avg - A1) wStatus/wRev = (10 - 8)/(8 - 5) = 2/3 Here is a link to this formula: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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

Bunuel · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Last year, all registered voters in Kumannia voted either fo

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards