Kamannia

[umaa.spk]

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?

I don't understand MGMAT strategy guide explanation. I used another formula and I got the answer 60%.

1.1R + 1.05 Q/(R+Q) = 1.08

[Ben Ku]

Please read (and follow!) the forum guidelines before posting.

Please state which edition of the Guide you're using (eg, 4th edition), the name of the book, and the page number on which the problem or question appears. This will help us to quickly find the problem you want us to respond to.

[bhumika.k.shah]

its from MGMAT fractions book ( 3rd edition) chapter # 3
page # 66

Kindly help me how to do it as per the alligation method.

Thanks

Bhumika

[Ben Ku]

its from MGMAT fractions book ( 3rd edition) chapter # 3
page # 66

Kindly help me how to do it as per the alligation method.

Thanks

Bhumika

What is the Alligator Method?

The approach given in the Strategy Guide's explanations uses the smart number 100 to represent last year's Revolutionary voters. Another algebraic approach is to assign R as the number of Revolutionary voters last year and T to be the total voters last year.

R = Revolutionary voters last year
T - R = Status Quo voters last year
T = Total voters last year

So for this year, the number of Revolutionary voters increased 10%, number of Status Quo voters increased 5%, and Total voters increased 8%. So

1.10 R = Revolutionary voters this year
1.05 (T - R) = Status Quo voters this year
1.08 T = Total voters this year.

Because the number of Revolutionary voters and Status Quo voters is equal to the total voters this year, we set up the following equation.

1.10R + 1.05(T - R) = 1.08 T
1.10R + 1.05T - 1.05R = 1.08T
0.05R = 0.03T
R/T = 3/5

We are looking for the fraction of Revolutionary voters this year, so we need the fraction 1.10R / 1.08T. We can do this by multiplying the ratio above by 1.10/1.08.

1.10R / 1.08T = (3/5)(1.10/1.08) = 11/18

Hope that makes sense.

[harsh170488]

I tried to solve the question using weighted average concept and got the answer as 60%

Status Quo voters : Revolutionary voters = (10-8)/(8-5) = 2/3

Now the Part:whole ratio is 3:5. What am i doing wrong here. Am i missing some concept here ?

There was a similar question in the FDP strategy guide , 5th edition as follows
Q. A company sells only pens and pencils. The revenue from pen sales in 2007 was up 5% from 2006, but the revenue from pencil sales declined 13% over the same period. If overall revenue was down 1% from 2006 to 2007, what was the ratio of pencil revenue to pen revenue in 2006?

i used the same weighted average concept here
Pencils : Pen = [5 - (-1)]/[ (-1) - (-13)] = 6/12 = 1/2.

But this answer is correct according to the book. What is the difference between the two questions ?

What if The current question was changed this way ?
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 last year?

[tim]

You've pinpointed the exact issue! It all has to do with whether we're calculating the ratio from last year or this year. Last year the ratio was indeed 60%, as you and the original poster calculated presumably using a method similar to that used in the pens and pencils problem. If you want to find the ratio for this year, you have to take the change into account and calculate the new ratio.

[adt29]

Q. A company sells only pens and pencils. The revenue from pen sales in 2007 was up 5% from 2006, but the revenue from pencil sales declined 13% over the same period. If overall revenue was down 1% from 2006 to 2007, what was the ratio of pencil revenue to pen revenue in 2006?

i used the same weighted average concept here
Pencils : Pen = [5 - (-1)]/[ (-1) - (-13)] = 6/12 = 1/2.

I would love to know the underlying logic in the above equation. Is this a formula that can be applied easily to all similar problems? It seems to take 20 seconds to solve in this case as opposed to creating tables and organizing the information first. Please advise. Thank you!

[RonPurewal]

Q. A company sells only pens and pencils. The revenue from pen sales in 2007 was up 5% from 2006, but the revenue from pencil sales declined 13% over the same period. If overall revenue was down 1% from 2006 to 2007, what was the ratio of pencil revenue to pen revenue in 2006?

i used the same weighted average concept here
Pencils : Pen = [5 - (-1)]/[ (-1) - (-13)] = 6/12 = 1/2.

I would love to know the underlying logic in the above equation. Is this a formula that can be applied easily to all similar problems? It seems to take 20 seconds to solve in this case as opposed to creating tables and organizing the information first. Please advise. Thank you!

When I look at that fraction, it takes me a really long time to see what's going on. But, that fraction is the math form of a "weighted average shortcut" that you can quickly visualize on a number line. (Don't memorize it as a formula; learn to draw it and look at it. Way easier.)

I did a session on this. Look for "weighted average shortcut" (or some similar title) in the archive on this page:
http://www.manhattangmat.com/thursdays-with-ron.cfm

[adt29]

Thanks very much, Ron. I viewed the video and subsequently enjoyed getting all the weighted average problems in the video as well as those in the strategy guide right. :)

[RonPurewal]

glad it helped

[aliag916]

Hello and thanks for directing me here. It is not clear to me why we have to multiply 3/5 by 110/108 to take the changes into account from last year to this year. I assumed that by using the number line like so, I'd already taken the changes into account:

105---------------108---------------110
Q---------3----------------2--------R

so i get fraction of R voters this year is 3/5


Thank u!

[RonPurewal]

Hello and thanks for directing me here. It is not clear to me why we have to multiply 3/5 by 110/108 to take the changes into account from last year to this year. I assumed that by using the number line like so, I'd already taken the changes into account:

105---------------108---------------110
Q---------3----------------2--------R

so i get fraction of R voters this year is 3/5


Thank u!

The problem with this approach is the same as the problem with the equation in the first post of this thread (1.1R + 1.05 Q/(R+Q) = 1.08).
Both of these approaches use "Q" and "R" to represent the original numbers of voters in each party.

In the equation, you can see that this is the case because we're writing 1.1R and 1.05Q. You don't multiply this year's totals by 1.1 and 1.05; you multiply last year's totals by those numbers to get this year's totals.

Same deal with using 105/108/110 in your number line concept. It works, but it gives you last year's totals. Nothing is 5%, 8%, or 10% of this year's totals, so you can't use the same number line directly.

So, you find out that 3/5 of last year's voters voted for xxxxxx party. But then you have to perform the increases described in the problem to get this year's figures.

[aliag916]

great explanation, v.clear and concise. Thanks much!

[RonPurewal]

You're welcome