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

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Intern
Joined: 11 Nov 2014
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Rodrick mixes a martini that has a volume of 'n' ounces havi  [#permalink]

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14 Jan 2016, 23:10
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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Joined: 31 Mar 2015
Posts: 35
Location: United States (IL)
Concentration: Marketing, General Management
Schools: Sauder '20
GMAT 1: 640 Q46 V32
GPA: 2.75
WE: Engineering (Computer Software)
Re: Rodrick mixes a martini that has a volume of 'n' ounces havi  [#permalink]

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18 Mar 2016, 23:47
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

I solved it like this,

Give n = 40% Vermouth + 60% Gin
I assume n=10, So, 10=4(Vermouth) + 6(Gin)

What we need is to add gin(Not Vermouth) to make Vermouth 25% of solution..

4/10+x =1/4 , Here X is the ounce we are adding to make Vermouth 25% of solution.

X=6. Substitue n=10 in answer choices and watch for '6' as the answer-----> C

It looks little long when u jot it down step by step, but it solves almost all the Mixture and allegation Question with out any doubt.
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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi  [#permalink]

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19 Mar 2016, 00:20
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

Let n is 100 ounces. Therefore, 40 ounces Vermouth and 60 ounces Gin
Now, 40 ounces are 25%; 160 ounces are 100%
Implies 40 Vermouth and 120 Gin
When n is 100, 3*n/5 is 60
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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi  [#permalink]

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25 Sep 2016, 09:36
(60/100) n + (1-n) = 75/100

-40/100 (n) = -25/100

n = 5/8 --> Gin needed is 1 - n = 3/8

Multiply n to answer choices --> C is the only one that gives you 3/8
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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi  [#permalink]

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19 Jul 2017, 14:52
Let's test values!

Let n = 10; that means that V = 4 ounces and G = 6 ounces
In order for V to be 25% of the new total (T), the new total volume would need to be:
4 = 0.25T = 1/4 * T
T = 16 ounces

The new volume of 16 ounces is 6 more than the old volume, which means 6 ounces of G is added.
Test the answer choices, plugging in n = 10, and see which answer choice gives you 6.

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

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17 Jan 2020, 11:39
We need to make a portion of Vermouth to 40 by adding a certain amount of Vermouth.
Suppose n=100 and add X to 40
40+X/100+X=25%
160+4X=100+X
X=20
Now, we need to find an option which gives us 20.
C is the correct one ( 100*3/5=20)
Re: Rodrick mixes a martini that has a volume of 'n' ounces havi   [#permalink] 17 Jan 2020, 11:39

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