Algebra

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paresh_patil: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Thu Jan 03, 2013 10:30 pm; Thanked: 4 times

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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Source: Beat The GMAT — Problem Solving | Wed Mar 06, 2013 9:37 pm

vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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Shalini Suresh: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Dec 22, 2011 10:22 pmFollowed by: 1 member; Thanked: 4 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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.

More alligation problems:

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

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neeg: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Feb 26, 2013 8:12 am

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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