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# Five gallons of a solution of vinegar and water with 8% vinegar is to

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Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink]

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15 Dec 2014, 01:58
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Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves
[Reveal] Spoiler: OA

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Re: Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink]

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15 Dec 2014, 03:33
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Its been given that there is 5 gallons of water and Vinegar with 8% of vinegar.
ie 8% of vinegar in 5 gallons is (8/100)*5 = 0.4 gallons of Vinegar and 4.6 gallons of water.

To make it 4% how many gallons of water should be added to the existing solution(5 g)

let us say it is x. i.e current Vinegar solution/(current soln in gallons + water to be added)=0.04
>> 0.4/(5+x)=4%

0.4/(5+x)=0.04 >> 5+x= 0.4/0.04=10

>>x=5

Ans B
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Re: Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink]

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23 Dec 2014, 10:32
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Hi rvc27,

In these types of mixture questions, if the answers are numbers, then it's likely that you can TEST THE ANSWERS to quickly get to the solution. Here's how:

First, we need to know about the original mixture of vinegar and water. We're told that a 5 gallon mixture is 8% vinegar....

(5 gallons)(.08) = 0.4 gallons vinegar
The rest = 4.6 gallons water

We're told to ADD WATER until the mixture goes from 8% vinegar to 4% vinegar.

Since the answer choices are numbers, we know that one of them will lead us to a 4% mix when added to the current mix. Changing 8% to 4% means that we have to add a significant amount of water (relative to what we started with), so I would TEST one of the bigger numbers first.

Let's TEST B

If 5 gallons of water were added, then we'd have....
0.4 gallons vinegar
9.6 gallons of water

0.4/10 = 4% vinegar. This is EXACTLY what we're looking for, so B MUST be the answer.

[Reveal] Spoiler:
B

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Kudos [?]: 3780 [3], given: 173 Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 432 Kudos [?]: 145 [0], given: 169 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Re: Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink] ### Show Tags 25 Dec 2014, 07:49 May I propose another approach here? That, because coming from a psychology background and pretty much learning math through my gmat practice, the more mathematical approaches are still sometimes difficult for me. So, as we said above, we have 5 gallons of solution, with 0.4 gallons of vinegar (8% of solution) and 4.6 gallons of water (92% of solution). Now, we can say that if the vinegar is the new solution is 4% of the total solution, then water must be 98%. Then, we can say: 4.6 gallons of water is 92% of the solution - x gallons are 98%? Or.. 4.6 ---> 92 x ---> 98 92x=4.6*98 92x=450.8 x=450.8/92 x= 4.9, so rounding up to 5. Kudos [?]: 145 [0], given: 169 SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1844 Kudos [?]: 2864 [0], given: 193 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink] ### Show Tags 25 Dec 2014, 23:06 Initial .................. Vinegar .................... Water ............... Total 8% Vinegar ............ $$\frac{40}{100}$$ ........................ $$\frac{460}{100}$$ .............. 5 "x" water added .... $$\frac{40}{100}$$ ....................... $$\frac{460}{100} + x$$ ......... 5+x Given that post addition of water, vinegar concentration should decrease to 4% $$\frac{4}{100} (5+x) = \frac{40}{100}$$ x = 5 Answer = B _________________ Kindly press "+1 Kudos" to appreciate Kudos [?]: 2864 [0], given: 193 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7868 Kudos [?]: 18494 [2], given: 237 Location: Pune, India Re: Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink] ### Show Tags 28 Dec 2014, 21:23 2 This post received KUDOS Expert's post rvc27 wrote: Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added? A. 10 B. 5 C. 4 D. 2 E. 1 This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated. Source: Bell Curves Yes, the question can be very easily solved by considering it a mixture problem where 8% vinegar solution is mixed with 0% vinegar solution (pure water) to make a 4% vinegar solution. Check out this post on weighted average: http://www.veritasprep.com/blog/2011/03 ... -averages/ The formula given in it will be very helpful to you in your GMAT journey. w1/w2 = (A2 - Aavg)/(Aavg - A1) = (0 - 4)/(4 - 8) = 1/1 So weights of both solutions should be same. We should put 5 gallons of water in 5 gallons of 8% vinegar solution. Answer (B) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink]

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29 Dec 2017, 10:05
rvc27 wrote:
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

let w=gallons of water to be added
.08*5=.04(5+w)
w=5 gallons
B

Last edited by gracie on 30 Dec 2017, 09:31, edited 1 time in total.

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Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink]

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29 Dec 2017, 10:46
rvc27 wrote:
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves

Let x = amount of water to be added
A = solution with 8% vinegar
B = water, which 0.0 percent vinegar

(% A)(Vol A) + (% B)(Vol B) = (% of A+B)(Vol A+B)

You do not need the 0x on LHS. It's a reminder that water IS being added, but that its concentration /percent vinegar has no weight.

$$.08(5) + 0.0(x) = .04(5 + x)$$
$$.40 + 0x = .20 + .04x$$
$$.20 = .04x$$
$$x = \frac{.20}{.04}=\frac{20}{5}=5$$

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Re: Five gallons of a solution of vinegar and water with 8% vinegar is to [#permalink]

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30 Dec 2017, 00:28
rvc27 wrote:
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10
B. 5
C. 4
D. 2
E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves

Initial vinegar content = 8%

Final vinegar content = 4%

Vinegar content in the additional water that is added = 0% (the water is 100% water and 0% vinegar)

Thus the ratio of the initial mixture and water that is added = (4-0) : (8 - 4) = 1 : 1

Thus in the 5 gallons of initial mixture, you will have to add another 5 gallons of water to get a 4% vinegar in the final mixture.

Note: The method that is used here is Alligation, which is similar to weighted averages, but faster to calculate.

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Re: Five gallons of a solution of vinegar and water with 8% vinegar is to   [#permalink] 30 Dec 2017, 00:28
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