FDP Problem

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yuvarajait: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Mon Feb 28, 2011 4:16 pm

by yuvarajait » Sun Mar 13, 2011 4:57 pm

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 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 answer says 11/18. I couldn't catch the way its derived. Can someone help explaining this?

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sun Mar 13, 2011 5:54 pm

increase in the number of total voters --> 1.08x
increase in the number voted for Revolutionary --> 1.1y
increase in the number voted for Status Quo --> 1.05z

Question: find Revolutionary/total voters?

solution: 1.08x=1.1y+1.05z; last year x=y+z; 1.08x=1.08y+1.08z OR 1.08y+1.08z=1.1y+1.05z <> 0.03z=0.02y OR 3z=2y, z=2y/3. Now rewriting x=y+z OR x=y+2y/3, x=5y/3 AND 1.1y/1.08x --> 1.1y : ((5y/3)*1.08)= 11y/10 : (5.4y/3)=
=(11y/10) * (3/5.4y)= 33y/54y= 11/18

yuvarajait wrote: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 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 answer says 11/18. I couldn't catch the way its derived. Can someone help explaining this?

My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Mar 13, 2011 7:06 pm

yuvarajait wrote: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 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 answer says 11/18. I couldn't catch the way its derived. Can someone help explaining this?

Solution:
Let the number of revolutionary voters be 'r' and the number of Status Quo voters be 's'.
So, increase in the number of revolutionary voters is (10/100) * r = 0.1r.
Increase in number of Status Quo voters is (5/100) * s = 0.05s.
This is equal to (8/100) * (r+s) = 0.08(r+s).
So, (10/100) * r + (5/100) * s = (8/100) * (r+s).
Or, 10r + 5s = 8r + 8s.
2r = 3s.
Or s/r = 2/3.
Or r/(r+s) = 3/5.
We need to know 1.1r/{1.08(r+s)} which is (110/108) * r/(r+s) = (110/108) * 3/5 = 11/18.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Mar 13, 2011 7:38 pm

yuvarajait wrote: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 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 answer says 11/18. I couldn't catch the way its derived. Can someone help explaining this?

This is a weighted average question.
Let R = Revolutionary voters and S = Status Quo voters.

A 10% increase in R is being combined with a 5% increase in S to yield a mixture with an increase of 8%.

We can use alligation, which dictates the following:

The proportion of each element in the mixture is equal to the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the mixture.

Proportion of R = |percentage in S - percentage in mixture| = |5-8| = 3.
Proportion of S = |percentage in R - percentage in mixture| = |10-8| = 2.
Thus, last year R:S = 3:2.

To determine the ratio of R to S this year, we can plug in values for R and S.

Let R last year = 30 and S last year = 20.
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.

Last edited by GMATGuruNY on Sat Aug 13, 2011 6:36 pm, edited 2 times in total.

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kamalakarthi: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Jan 31, 2011 10:08 pmFollowed by: 2 members

by kamalakarthi » Sun Mar 13, 2011 9:06 pm

Mitch,

Thanks for the great idea. However I am still not able to understand this..

The proportion needed of R (10%) = 8-5 = 3.
The proportion needed of S (5%) = 10-8 = 2.

How did u get 8-5 , and same for 10-8...Can you please help us understand this better. Thanks in advance.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Mar 14, 2011 2:27 am

kamalakarthi wrote:Mitch,

Thanks for the great idea. However I am still not able to understand this..

The proportion needed of R (10%) = 8-5 = 3.
The proportion needed of S (5%) = 10-8 = 2.

How did u get 8-5 , and same for 10-8...Can you please help us understand this better. Thanks in advance.

The process is called alligation.

When an entity that is X% (a higher percentage) is combined with an entity that is Y% (a lower percentage) to form a mixture that is Z%:

The proportion needed of the X% entity = Z-Y (the distance between the other 2 percentages).
The proportion needed of the Y% entity = X-Z (the distance between the other 2 percentages).

The resulting values give the ratio of X:Y in the mixture.

In the problem above:
R = 10% is combined with S = 5%.
The resulting mixture = 8%.

Thus:
The proportion of R in the population = the distance between 8% and S = 8-5 = 3.
The proportion of S in the population = the distance between R and 8% = 10-8 = 2.
Thus, the ratio of R:S in the population = 3:2.

Here are a few other problems in which I used alligation:

https://www.beatthegmat.com/allegation-t69552.html
https://www.beatthegmat.com/problem-on-m ... 75453.html
https://www.beatthegmat.com/percentage-p ... 70078.html

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nadib002: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Mon Mar 02, 2009 6:27 pm

by nadib002 » Fri May 06, 2011 7:36 am

@Mitch

I used the "alligation" method as well to set up the proportions.

I was stuck after 3:2

Following was my line of thinking:

3 parts voted for R and 2 parts voted for S

Therefore 3/5 * Total number of voters voted for R and 2/5 * Total number of voters voted for S

But we do-not know the Total number of voters. Can I pick a number, say 30 or 100, for the Total number of voters? For example if i were to pick 100, then 3/5 * 100 = 60 voted for R, but if i do it the way i mention i do not get the correct value.

What I do-not understand is when you picked 30 and 20 for R and S, why did you do the 10% and 5% increase again. Didn't the 3/5 represent the 10% increase already?

What is the flaw in my logic?

Could you please help?

Thank you

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Tani: Legendary Member; Posts: 1255; Joined: Fri Nov 07, 2008 2:08 pmFollowed by: 90 members; Location: St. Louis; Thanked: 312 times

by Tani » Sat Aug 13, 2011 7:03 pm

Intriguing. I used to do that intuitively but never knew it had a name! Thanks!

Tani Wolff

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