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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 [#permalink]

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28 Dec 2009, 13:18
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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
[Reveal] Spoiler: OA
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Re: Method of Allegation in Percentages [#permalink]

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28 Dec 2009, 13:25
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gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

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

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C

Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:

0.4n=0.25(n+g) --> g=3n/5

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Re: Method of Allegation in Percentages [#permalink]

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28 Dec 2009, 15:35
Bunuel, thanks for the solution but as i said, i already know the "equations" method.
The problem is that I cant solve it using the Allegation method. Any help on that would be nice.
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Re: Method of Allegation in Percentages [#permalink]

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29 Dec 2009, 08:50
Any response as to how to solve the problem using Allegation method would be useful.
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Re: Method of Allegation in Percentages [#permalink]

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01 Jan 2010, 20:25
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Not sure if this is the method you're looking for but:

Verm Gin
40% 0%

25%

25 15

Which reduces to 5:3
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Re: Method of Allegation in Percentages [#permalink]

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13 Jul 2010, 05:48
I want to respond to the following question appearing in this forum:
_____
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

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5
_____

The answer C) 3n/5 for Gin is obviously not correct for the following reason. Gin's concentration is 60% which is much higher than that of Vermouth (40%). Obviously, you need less of Gin than Vermouth to make n quantity of Martin. Consequently, the answer we should be looking for must be below 1/2 of the quantity of the total (n). The correct proportional volume of Gin is 3n/10 using the Alligation Method. Make a nine cell table like the one below (Unfortunately, I can't draw the table here. I have added starred lines to space the figures to create a Table image). Obtain diagonal differences and enter them as shown in top right and bottom right boxes(always positive numbers). Add right hand column (15+35=50). Calculate amount of Gin proportion as (n/50)*15 =3/10 n. Calculate amount of Vermouth proportion as (n/50)*35 =7/10 n

60(Gin)****************************15(40-25)
*******************25(Martin)
40(Vermouth)***********************35(60-25)

Mathew
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Re: Method of Allegation in Percentages [#permalink]

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22 Jul 2011, 05:02
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Dear Friends,

Using allegations we will view the action that Rodrick performs as below:

"He will Mix Martini [60 % gin by volume ] with Gin [ 100 % gin by volume] to yield a martini [75 % gin by volume]."

By the method of allegations :
If we have 2 quantities to mix ,one with higher percentage H and other with lower percentage L ,to get a desired solution R %we proceed as
Percentage of Lower in final Result = H-R
Percentage of Higher in final Result = R-L.

Therefore using the allegations method we have
%volume of Pure Gin required = 75 -60 = 15
%volume of Martini (60 % gin)required = 100 -75 =25

Which reduces to Pure Gin to Martini =3 :5.
Which can be inferred as for every 5 ml of martini if we should add 5 ml of pure gin to get a drink that is 75 % gin and 25 % Vermouth by volume.

So , we have :
For 5 ml Martini we need 3 ml Gin
For 1 ml martini we need 3/5 ml of Gin
For 'n' ml of martini we need 3n/5 ml of Gin.

I hope the solution helps as a good reference.

Cheers,
Rohan
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Re: Method of Allegation in Percentages [#permalink]

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18 Sep 2011, 01:45
Bunuel wrote:
gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

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

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C

Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:

0.4n=0.25(n+g) --> g=3n/5

Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).
_________________

petrifiedbutstanding

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Re: Method of Allegation in Percentages [#permalink]

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18 Sep 2011, 04:08
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petrifiedbutstanding wrote:
Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).

I will try.
Volume of martini given = n
Volume of vermouth in martini = 40% of n = 0.4n

Let "g" be the volume of gin we add.
New Volume of martini = n+g
Also, we did not add any vermouth.
New Volume of vermouth = 0.4n (still same as old)

New volume of vermouth= 25 % New martini (n+g)

0.4n=0.25(n+g)
n=3n/5

Pick number and see. It will be clear.
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Re: Method of Allegation in Percentages [#permalink]

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18 Sep 2011, 09:02
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total V G
1 ounce 0.4 0.6

n ounce 0.4n 0.6n -------------initial expression

lets say g ounces of gin is added to this mixture

n+g 0.4n 0.6n+g --------------final expression

given that after adding g ounces of gin , V should become 25% of the total volume.

=>Volume of V/total volume = 25/100

=> 0.4n /n+g = 1/4

=> 1.6n = n+g

=> g = 3n/5

petrifiedbutstanding wrote:
Bunuel wrote:
gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

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

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C

Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:

0.4n=0.25(n+g) --> g=3n/5

Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).
Senior Manager
Joined: 19 Oct 2010
Posts: 271
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
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Kudos [?]: 58 [0], given: 27

Re: Method of Allegation in Percentages [#permalink]

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18 Sep 2011, 09:07
petrifiedbutstanding wrote:
Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).

I will try.
Volume of martini given = n
Volume of vermouth in martini = 40% of n = 0.4n

Let "g" be the volume of gin we add.
New Volume of martini = n+g
Also, we did not add any vermouth.
New Volume of vermouth = 0.4n (still same as old)

New volume of vermouth= 25 % New martini (n+g)

0.4n=0.25(n+g)
n=3n/5

Pick number and see. It will be clear.

Thanks! This does help!
_________________

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Re: Method of Allegation in Percentages [#permalink]

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19 Sep 2011, 03:29
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gaurav05nov wrote:
Guys, please help me out. I want to know how to solve this question using the Allegation method.
I know the other way(using equations) but I need to understand the Allegation method.

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

A) n/6
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Spoiler :
[Reveal] Spoiler:
C

He wants to mix a martini of 60% Gin with a liquid that is 100% Gin to give a mixture with 75% Gin (because 25% is Vermouth)
Using the mixtures formula discussed here (http://www.veritasprep.com/blog/2011/03 ... -averages/),
we get,
w1/w2 = (100 - 75)/(75 - 60) = 5:3
Martini:Pure Gin must be added in the ratio 5:3. So if martini is n, pure gin must be (3/5)n

A very similar question is discussed in the 'Responses' of this post (at the bottom): http://www.veritasprep.com/blog/2011/04 ... -mixtures/
_________________

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Status: mba here i come! Joined: 07 Aug 2011 Posts: 270 Followers: 39 Kudos [?]: 936 [2] , given: 48 Re: Method of Allegation in Percentages [#permalink] ### Show Tags 20 Sep 2011, 04:56 2 This post received KUDOS 2 This post was BOOKMARKED mixture already has 60% gin, and we need 75%. $$\frac{0.6n + x}{n + x} = 0.75$$ $$x = \frac{3}{5}n$$ _________________ press +1 Kudos to appreciate posts Manager Joined: 29 Aug 2013 Posts: 78 Location: United States Concentration: Finance, International Business GMAT 1: 590 Q41 V29 GMAT 2: 540 Q44 V20 GPA: 3.5 WE: Programming (Computer Software) Followers: 0 Kudos [?]: 49 [1] , given: 24 Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] ### Show Tags 09 Sep 2013, 01:30 1 This post received KUDOS gaurav05nov 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 Initially Martini = V : G = 4 : 6 = 2 : 3 Ratio required is = 25 : 75 = 1 : 3 Since V is same hence ratio should be 2 : 6 Hence 3 parts of gin should be added to the initial mixture i.e. same as what was in the initial mixture i.e. 60n/100 = 3n/5 The mixture related problems if dealt with ratios becomes much easier.. Current Student Joined: 06 Sep 2013 Posts: 2035 Concentration: Finance GMAT 1: 770 Q0 V Followers: 43 Kudos [?]: 464 [1] , given: 355 Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] ### Show Tags 16 Dec 2013, 06:52 1 This post received KUDOS gaurav05nov 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 Way I did it Smart Numbers n=100 So we'll have 60+x/100+x=3/4 x=60 So 60/100 = 3/5n Answer is C Hope it helps! Cheers! J GMAT Club Legend Joined: 09 Sep 2013 Posts: 9697 Followers: 466 Kudos [?]: 120 [0], given: 0 Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] ### Show Tags 13 Jan 2015, 07:27 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 03 Jan 2015 Posts: 68 Concentration: Strategy, Marketing WE: Research (Pharmaceuticals and Biotech) Followers: 2 Kudos [?]: 22 [1] , given: 224 Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] ### Show Tags 13 Jan 2015, 07:50 1 This post received KUDOS 2 This post was BOOKMARKED PROBLEM: 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 SOLUTION: A quick way to calculate without any algebra is: (Old - New)/(New) i.e. (40-25)/(25) = 3/5 i.e. Martini should be diluted 3/5 times ANSWER: C SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 35 Kudos [?]: 1523 [0], given: 193 Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] ### Show Tags 15 Jan 2015, 02:35 Place n = 1 in the question as well as in OA & say "x" volume of Gin is added. Equation setup would be as follows: $$\frac{25}{100}(1+x) = \frac{40}{100}$$ $$x = \frac{3}{5}$$ Answer = C _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 04 Sep 2015 Posts: 36 Location: Germany Concentration: Operations, Finance WE: Project Management (Aerospace and Defense) Followers: 0 Kudos [?]: 11 [0], given: 14 Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] ### Show Tags 30 Dec 2015, 07:12 HI Karishma Is this approach also right (from one of your posts)? Volume (initial) x concentration (initial) = Volume (final) x Concentration (final) Since, the volume of Vermouth remains same (not Gin), this should be applied to Vermouth Therefore, n x 40% = Volume (final) x 25% Volume (final) = 8n/5 So, solution added = (8n/5) - n ==> 3n /5 VeritasPrepKarishma wrote: gaurav05nov wrote: Guys, please help me out. I want to know how to solve this question using the Allegation method. I know the other way(using equations) but I need to understand the Allegation method. 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 Spoiler : [Reveal] Spoiler: C He wants to mix a martini of 60% Gin with a liquid that is 100% Gin to give a mixture with 75% Gin (because 25% is Vermouth) Using the mixtures formula discussed here (http://www.veritasprep.com/blog/2011/03 ... -averages/), we get, w1/w2 = (100 - 75)/(75 - 60) = 5:3 Martini:Pure Gin must be added in the ratio 5:3. So if martini is n, pure gin must be (3/5)n A very similar question is discussed in the 'Responses' of this post (at the bottom): http://www.veritasprep.com/blog/2011/04 ... -mixtures/ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6584 Location: Pune, India Followers: 1795 Kudos [?]: 10802 [1] , given: 212 Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink] ### Show Tags 30 Dec 2015, 23:26 1 This post received KUDOS Expert's post madhusudhan237 wrote: HI Karishma Is this approach also right (from one of your posts)? Volume (initial) x concentration (initial) = Volume (final) x Concentration (final) Since, the volume of Vermouth remains same (not Gin), this should be applied to Vermouth Therefore, n x 40% = Volume (final) x 25% Volume (final) = 8n/5 So, solution added = (8n/5) - n ==> 3n /5 Yes, correct. Since amount of Vermouth stays the same in the two cases, Volume of solution*Concentration of Vermouth should be equal in the two cases. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi   [#permalink] 30 Dec 2015, 23:26

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