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

Question

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

Source: Bell Curves

kukr007 · Accepted Answer

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

EMPOWERgmatRichC · Answer

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.

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

pacifist85 · Answer

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.

PareshGmat · Answer

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

KarishmaB · Answer

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.

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)

gracie · Answer

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

generis · Answer

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

Answer B

EgmatQuantExpert · Answer

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

Regards, Saquib e-GMAT Quant Expert

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