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Algebra

by paresh_patil » Wed Mar 06, 2013 9:37 pm
Roderick mixes a martini that has a volume of n ounces that is 40% vermouth and 60% gin by volume. He wants to change this so that it 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

Answer C
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by vipulgoyal » Wed Mar 06, 2013 9:48 pm
40% V , 60% G
need 25% V 75% G

let x should be added

60+x/100+x=75/100=3/4
240+4x=300+3x
x=60
hence 60n/100=3n/5 ans
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by Anurag@Gurome » Wed Mar 06, 2013 10:07 pm
paresh_patil wrote:Roderick mixes a martini that has a volume of n ounces that is 40% vermouth and 60% gin by volume. He wants to change this so that it is 25% vermouth by volume. How many ounces of gin must he add?
Let us assume n = 100
Hence, there is 40 ounce of vermouth and 60 ounce of gin.
We have to make the ratio of vermouth to gin 25:75 by adding say x ounce of gin.

So, 40/(60 + x) = 25/75 = 1/3
--> 60 + x = 3*40 = 120
--> x = 120 - 60 = 60 = (60/100)*100 = (3/5)*100 = (3/5)*n

The correct answer is C.
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by GMATGuruNY » Thu Mar 07, 2013 3:10 am
paresh_patil wrote:Roderick mixes a martini that has a volume of n ounces that is 40% vermouth and 60% gin by volume. He wants to change this so that it 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

Answer C
Let n = 100 ounces.
Since the original solution is 40% vermouth, the amount of vermouth = 40 ounces.
After more gin is added, the amount of vermouth remains 40 ounces.
Since these 40 ounces must be 25% of the new total, the new total is 160 ounces.
Thus, the amount of gin added = new total - old total = 160-100 = 60 ounces. This is our target.

Now we plug n=100 into the answers to see which yield our target of 60.
Only C works:
3n/5 = (3*100)/5 = 60.

The correct answer is C.
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by Shalini Suresh » Thu Mar 07, 2013 4:38 am
Can the experts pls tell me what the difficulty level of this problem is ?

Is it 600s or 650+ ?
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by Brent@GMATPrepNow » Thu Mar 07, 2013 6:47 am
paresh_patil wrote:Roderick mixes a martini that has a volume of n ounces that is 40% vermouth and 60% gin by volume. He wants to change this so that it 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

Answer C
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 Brent@GMATPrepNow » Thu Mar 07, 2013 6:49 am
Shalini Suresh wrote:Can the experts pls tell me what the difficulty level of this problem is ?

Is it 600s or 650+ ?
I'm going to say that it's somewhere in the 650 zone (plus or minus 50)

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by GMATGuruNY » Thu Mar 07, 2013 7:18 am
paresh_patil wrote:Roderick mixes a martini that has a volume of n ounces that is 40% vermouth and 60% gin by volume. He wants to change this so that it 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

Answer C
Another approach -- one that is very fast.

In n, the percentage of vermouth = 40.
In the added gin, the percentage of vermouth = 0.
In the mixture, the percentage of vermouth = 25.

To determine the required ratio of n to gin, use ALLIGATION.

Step 1: Plot the 3 percentages on a number line, with the two starting percentages (40% and 0%) on the ends and the goal percentage (25%) in the middle.
n 40%----------25%----------0% g

Step 2: Calculate the distances between the percentages.
n 40%----15----25%----25----0% g

Step 3: Determine the ratio in the mixture.
The required ratio of n to g is the RECIPROCAL of the distances in red.
n/g = 25/15 = 5/3.

Cross-multiplying n/g = 5/3, we get:
5g = 3n
g = 3n/5.

The correct answer is C.

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https://www.beatthegmat.com/mixture-prob ... 90121.html
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by neeg » Fri Mar 08, 2013 6:19 pm
Anurag@Gurome wrote:
paresh_patil wrote:Roderick mixes a martini that has a volume of n ounces that is 40% vermouth and 60% gin by volume. He wants to change this so that it is 25% vermouth by volume. How many ounces of gin must he add?
Let us assume n = 100
Hence, there is 40 ounce of vermouth and 60 ounce of gin.
We have to make the ratio of vermouth to gin 25:75 by adding say x ounce of gin.

So, 40/(60 + x) = 25/75 = 1/3
--> 60 + x = 3*40 = 120
--> x = 120 - 60 = 60 = (60/100)*100 = (3/5)*100 = (3/5)*n

The correct answer is C.
Hi Anurag - Please could you expand on the last bit of the solution?
(60/100)*100 = (3/5)*100 = (3/5)*n--------why 60 divided by 100 & mutlipled by 100 as the 100 would simply cancel givign 60.

Thanks
Neeg
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