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

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Q50  V35
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Re: Method of Allegation in Percentages [#permalink]
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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]
Any response as to how to solve the problem using Allegation method would be useful.
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Re: Method of Allegation in Percentages [#permalink]
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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]
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

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)

Mathew
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Re: Method of Allegation in Percentages [#permalink]
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

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

Spoiler :

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

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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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]
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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

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

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

Spoiler :

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

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]
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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Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]
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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

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

Spoiler :

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 weighted averages formula, 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

Originally posted by KarishmaB on 19 Sep 2011, 03:29.
Last edited by KarishmaB on 11 Oct 2022, 00:46, edited 1 time in total.
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Re: Method of Allegation in Percentages [#permalink]
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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]
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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]
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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

Hope it helps!
Cheers!
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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]
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PROBLEM:
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

SOLUTION:

A quick way to calculate without any algebra is:

(Old - New)/(New)
i.e. (40-25)/(25) = 3/5
i.e. Martini should be diluted 3/5 times

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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]
Place n = 1 in the question as well as in OA & say "x" volume of Gin is added.

Equation setup would be as follows:

$$\frac{25}{100}(1+x) = \frac{40}{100}$$

$$x = \frac{3}{5}$$

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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]
HI Karishma

Is this approach also right (from one of your posts)?

Volume (initial) x concentration (initial) = Volume (final) x Concentration (final)
Since, the volume of Vermouth remains same (not Gin), this should be applied to Vermouth
Therefore, n x 40% = Volume (final) x 25%
Volume (final) = 8n/5

So, solution added = (8n/5) - n ==> 3n /5

VeritasPrepKarishma 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

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

Spoiler :

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 (https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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): https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... -mixtures/
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HI Karishma

Is this approach also right (from one of your posts)?

Volume (initial) x concentration (initial) = Volume (final) x Concentration (final)
Since, the volume of Vermouth remains same (not Gin), this should be applied to Vermouth
Therefore, n x 40% = Volume (final) x 25%
Volume (final) = 8n/5

So, solution added = (8n/5) - n ==> 3n /5

Yes, correct.
Since amount of Vermouth stays the same in the two cases, Volume of solution*Concentration of Vermouth should be equal in the two cases.
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Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]
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

This is how I did it. It took me 1m 10 S:
For simplicity, start by assuming the gin has a volume of 100 units.

Current amount of vermouth: 40 units

I rephrased the question to say:
With the numerator being 40, what should the denominator be, so that the fraction becomes 1/4 (25% Vermouth)?
For what value of x will the ratio 40/x become 1/4?

A quick mental math will tell you x should be 160 (since 40*4=160)

Thus, we have created a condition where the question's requirement is satisfied.

Thus the amount of gin in the new mix will be =160-40=120
Of this 120, 60 was already present.
Thus he needs to add another 60 units of gin to make the mixture 25% Vermouth

However, the answer choices are in terms of n, the volume of the whole mix.

So lets convert 60 to terms of n.
We had started by assuming that the mix had 100 units for simplicity.
So what % of 100 is 60? easy its 60%

60% in fraction is 3/5.
Thus the answer should be 3n/5
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