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Rodrick mixes a martini that has a volume of 'n' ounces havi

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Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] New post 28 Dec 2009, 12:18
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Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5
[Reveal] Spoiler: OA
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Re: Method of Allegation in Percentages [#permalink] New post 28 Dec 2009, 12:25
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gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume.
He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must
he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C


Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:

0.4n=0.25(n+g) --> g=3n/5

Answer: C.
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Re: Method of Allegation in Percentages [#permalink] New post 28 Dec 2009, 14:35
Bunuel, thanks for the solution but as i said, i already know the "equations" method.
The problem is that I cant solve it using the Allegation method. Any help on that would be nice.
:)
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Re: Method of Allegation in Percentages [#permalink] New post 29 Dec 2009, 07:50
Any response as to how to solve the problem using Allegation method would be useful.
Please help!! :?
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Re: Method of Allegation in Percentages [#permalink] New post 01 Jan 2010, 19:25
Not sure if this is the method you're looking for but:

Verm Gin
40% 0%

25%

25 15

Which reduces to 5:3
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Re: Method of Allegation in Percentages [#permalink] New post 13 Jul 2010, 04:48
I want to respond to the following question appearing in this forum:
_____
Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume.
He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must
he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5
_____

The answer C) 3n/5 for Gin is obviously not correct for the following reason. Gin's concentration is 60% which is much higher than that of Vermouth (40%). Obviously, you need less of Gin than Vermouth to make n quantity of Martin. Consequently, the answer we should be looking for must be below 1/2 of the quantity of the total (n). The correct proportional volume of Gin is 3n/10 using the Alligation Method. Make a nine cell table like the one below (Unfortunately, I can't draw the table here. I have added starred lines to space the figures to create a Table image). Obtain diagonal differences and enter them as shown in top right and bottom right boxes(always positive numbers). Add right hand column (15+35=50). Calculate amount of Gin proportion as (n/50)*15 =3/10 n. Calculate amount of Vermouth proportion as (n/50)*35 =7/10 n

60(Gin)****************************15(40-25)
*******************25(Martin)
40(Vermouth)***********************35(60-25)


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Re: Method of Allegation in Percentages [#permalink] New post 22 Jul 2011, 04:02
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Dear Friends,

Using allegations we will view the action that Rodrick performs as below:

"He will Mix Martini [60 % gin by volume ] with Gin [ 100 % gin by volume] to yield a martini [75 % gin by volume]."

By the method of allegations :
If we have 2 quantities to mix ,one with higher percentage H and other with lower percentage L ,to get a desired solution R %we proceed as
Percentage of Lower in final Result = H-R
Percentage of Higher in final Result = R-L.


Therefore using the allegations method we have
%volume of Pure Gin required = 75 -60 = 15
%volume of Martini (60 % gin)required = 100 -75 =25

Which reduces to Pure Gin to Martini =3 :5.
Which can be inferred as for every 5 ml of martini if we should add 5 ml of pure gin to get a drink that is 75 % gin and 25 % Vermouth by volume.

So , we have :
For 5 ml Martini we need 3 ml Gin
For 1 ml martini we need 3/5 ml of Gin
For 'n' ml of martini we need 3n/5 ml of Gin.

I hope the solution helps as a good reference.

Cheers,
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Re: Method of Allegation in Percentages [#permalink] New post 18 Sep 2011, 00:45
Bunuel wrote:
gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume.
He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must
he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C


Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:

0.4n=0.25(n+g) --> g=3n/5

Answer: C.



Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).
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Re: Method of Allegation in Percentages [#permalink] New post 18 Sep 2011, 03:08
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petrifiedbutstanding wrote:
Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).

I will try.
Volume of martini given = n
Volume of vermouth in martini = 40% of n = 0.4n


Let "g" be the volume of gin we add.
New Volume of martini = n+g
Also, we did not add any vermouth.
New Volume of vermouth = 0.4n (still same as old)

New volume of vermouth= 25 % New martini (n+g)

0.4n=0.25(n+g)
n=3n/5

Pick number and see. It will be clear.
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Re: Method of Allegation in Percentages [#permalink] New post 18 Sep 2011, 08:02
total V G
1 ounce 0.4 0.6

n ounce 0.4n 0.6n -------------initial expression

lets say g ounces of gin is added to this mixture

n+g 0.4n 0.6n+g --------------final expression

given that after adding g ounces of gin , V should become 25% of the total volume.

=>Volume of V/total volume = 25/100

=> 0.4n /n+g = 1/4

=> 1.6n = n+g

=> g = 3n/5

Answer is C.













petrifiedbutstanding wrote:
Bunuel wrote:
gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume.
He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must
he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C


Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:

0.4n=0.25(n+g) --> g=3n/5

Answer: C.



Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).
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Re: Method of Allegation in Percentages [#permalink] New post 18 Sep 2011, 08:07
jamifahad wrote:
petrifiedbutstanding wrote:
Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).

I will try.
Volume of martini given = n
Volume of vermouth in martini = 40% of n = 0.4n


Let "g" be the volume of gin we add.
New Volume of martini = n+g
Also, we did not add any vermouth.
New Volume of vermouth = 0.4n (still same as old)

New volume of vermouth= 25 % New martini (n+g)

0.4n=0.25(n+g)
n=3n/5

Pick number and see. It will be clear.


Thanks! This does help!
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Re: Method of Allegation in Percentages [#permalink] New post 19 Sep 2011, 02:29
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gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume.
He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must
he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C


He wants to mix a martini of 60% Gin with a liquid that is 100% Gin to give a mixture with 75% Gin (because 25% is Vermouth)
Using the mixtures formula discussed here (http://www.veritasprep.com/blog/2011/03 ... -averages/),
we get,
w1/w2 = (100 - 75)/(75 - 60) = 5:3
Martini:Pure Gin must be added in the ratio 5:3. So if martini is n, pure gin must be (3/5)n

A very similar question is discussed in the 'Responses' of this post (at the bottom): http://www.veritasprep.com/blog/2011/04 ... -mixtures/
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Re: Method of Allegation in Percentages [#permalink] New post 20 Sep 2011, 03:56
mixture already has 60% gin, and we need 75%.

\frac{0.6n + x}{n + x} = 0.75

x = \frac{3}{5}n
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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] New post 09 Sep 2013, 00:30
gaurav05nov wrote:
Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5


Initially Martini = V : G = 4 : 6 = 2 : 3
Ratio required is = 25 : 75 = 1 : 3
Since V is same hence ratio should be 2 : 6
Hence 3 parts of gin should be added to the initial mixture i.e. same as what was in the initial mixture i.e. 60n/100 = 3n/5

The mixture related problems if dealt with ratios becomes much easier..
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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] New post 16 Dec 2013, 05:52
gaurav05nov wrote:
Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5


Way I did it

Smart Numbers

n=100

So we'll have 60+x/100+x=3/4
x=60

So 60/100 = 3/5n

Answer is C

Hope it helps!
Cheers!
J :)
Re: Rodrick mixes a martini that has a volume of 'n' ounces havi   [#permalink] 16 Dec 2013, 05:52
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