Algebra

Question

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

vipulgoyal · Answer

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

Anurag@Gurome · Answer

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.

GMATGuruNY · Answer

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.

More alligation problems:

https://www.beatthegmat.com/mixture-prob ... 90121.html

Shalini Suresh · Answer

Can the experts pls tell me what the difficulty level of this problem is ? Is it 600s or 650+ ?

Brent@GMATPrepNow · Answer

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.

Brent@GMATPrepNow · Answer

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)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

GMATGuruNY · Answer

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.

More alligation problems:

https://www.beatthegmat.com/mixture-prob ... 90121.html

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neeg · Answer

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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