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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paresh_patil
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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
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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Let us assume n = 100paresh_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?
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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Let n = 100 ounces.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
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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For mixture questions, I find it helpful to draw the mixtures with their components separated.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
This will allow you to visualize the question, and it makes it easy to add individual components.
Cheers,
Brent
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I'm going to say that it's somewhere in the 650 zone (plus or minus 50)Shalini Suresh wrote:Can the experts pls tell me what the difficulty level of this problem is ?
Is it 600s or 650+ ?
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Another approach -- one that is very fast.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
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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Hi Anurag - Please could you expand on the last bit of the solution?Anurag@Gurome wrote:Let us assume n = 100paresh_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?
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.
(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
