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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

by rakeshd347 » Sun Oct 06, 2013 6:29 pm
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

OA is C

Can someone please explain me this. I always have issues with mixture problems. What do you think is the difficulty level of this question.
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by GMATGuruNY » Sun Oct 06, 2013 7:11 pm
rakeshd347 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

OA is C
Let V = vermouth and G = gin.

Original solution:
V:G = 40:60 = 2:3.
Let V = 2 ounces and G = 3 ounces.
Thus, n = 2+3 = 5 ounces.

New solution:
After more gin is added, the amount of vermouth -- 2 ounces -- must be 1/4 of the new volume.
Since 2 is 1/4 of 8, the new volume must be 8 ounces.
Thus, the amount of added gin = new volume - old volume = 8-5 = 3 ounces. This is our target.

Now plug n=5 into the answers to see which yields our target of 3.
Only C works:
3n/5 = (3*5)/5 = 3.

The correct answer is C.
Last edited by GMATGuruNY on Mon Oct 07, 2013 5:15 am, edited 1 time in total.
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by rakeshd347 » Sun Oct 06, 2013 7:31 pm
GMATGuruNY wrote:
rakeshd347 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

OA is C
Let V = vermouth and G = gin.

Original solution:
V:G = 40:60 = 2:3.
Let V = 2 ounces and G = 3 ounces.
Thus, n = 2+3 = 5 ounces.

New solution:
After more gin is added, the amount of vermouth -- 2 ounces -- must be 1/4 of the new volume.
Since 2 is 1/4 of 8, the new volume must be 8 ounces.
Thus, the amount of added gin = new volume - old volume = 8-5 = 3 ounces. This is our target.

Now plug n=5 into the answer to see which yields our target of 3.
Only C works:
3n/5 = (3*5)/5 = 3.

The correct answer is C.
Mitch when you solved a question it looks like 500 level difficulty when I solved it, then it looks like 700 difficulty.
You must have done some PHD and R& D in gmat question mate.

Thanks for that mate my headache is gone now :)
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by Brent@GMATPrepNow » Sun Oct 06, 2013 9:09 pm
rakeshd347 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
For mixture questions, I find it helpful to draw the mixtures with their components separated.
This will allow you to visualize the question, and it makes it easy to add individual components.
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by theCodeToGMAT » Sun Oct 06, 2013 9:22 pm
Let n = 100
Vermouth = 40
Gin = 60

Gin is added 60+x to make percentage 75%
60+x/100+x = 3/4
x = 60

3n/5 = 60
Answer [spoiler]{C}[/spoiler]
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