M07-08

Question

If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a three-percent vinegar solution, what was the concentration of the original solution?

A. 19.3%
B. 17%
C. 16.67%
D. 15.5%
E. 12.5%

Bunuel · Accepted Answer

Official Solution:

If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a three-percent vinegar solution, what was the concentration of the original solution?

A. 19.3%
B. 17%
C. 16.67%
D. 15.5%
E. 12.5%

Let's assume that the original solution has a concentration of  x\%  vinegar.
 
The amount of vinegar in the original solution is therefore,  12*\frac{x}{100}  ounces. 
 
The amount of vinegar in  50+12=62  ounces of the final solution is  \frac{3}{100}*62 . 
 
Since only water was added to the original solution, we can equate the amount of vinegar in the final solution to that in the original solution:
 
 12*\frac{x}{100}=\frac{3}{100}*62  
 
 12x=3*62 
 
 x=15.5 
 
Therefore, the original solution had a concentration of 15.5% vinegar.

Answer: D

ARIEN3228 · Answer

C1xV1=C2xV2

C1= initial concentration
V1= initial volume= 12 oz

C2=final concentration= 3%
v2=final voulne= (12+50)= 62 oz

C1x12=3%x62

C1=15.5%

DJ1986 · Answer

Vinegar+Stuff = 12
Water+Vinegar+Stuff = 62
3% of 62 = 1.86 = Vinegar
1.86/12 
I changed the fraction to 3.1/20 which is close to 15%

TheNightKing · Answer

Water has 0 vinegar.

12 ounces had some % of vinegar.

The result is what we know. 3% of 62 ounces is vinegar. That's 1.86 ounces but that came only from the original solution of 12ounces.

So 1.86/12 should give us the % of vinegar in original solution. That's around 1.2+0.6=1.8 about 15%. Option D

AndrewN · Answer

Another approach : There is actually no need to get too specific here, provided you have a decent grasp of how to work with percentages. Yes, as has been pointed out already, you will need to figure out a way to derive 3 percent of (12 + 50) ounces, but you can do this using mental math quite easily.

1) 10 percent of any number is that number with the decimal pushed one place to the left (e.g., 10 percent of 62 is 6.2)

2) 5 percent of any number is half the value of ten percent of that number (e.g., 5 percent of 62 is 6.2/2, or 3.1)

3) 1 percent of any number is that number with the decimal pushed two places to the left (e.g., 1 percent of 62 is 0.62)

Since we know we are dealing with 3 percent, we can just triple the value for 1 percent:

3(0.62)=1.86

We know there  must  be 1.86 oz. of vinegar in the solution. Since water contains no vinegar, these 1.86 oz. have to come from the original 12 oz. of vinegar. Just work your way to the target value of 1.86 oz.

1) 10 percent of 12 oz. is 1.2 oz. (too low, but more than halfway to the target number)

2) 5 percent of 12 oz. is 1.2/2, or 0.6 oz.

1.2+0.6=1.8

We have added up 15 percent of the 12-oz. solution, and we need just six one-hundredths of an ounce more. But rather than derive the exact value, we can simply test what would happen if we added 1 percent to what we have:

3) 1 percent of 12 oz. is 0.12 oz.

1.8+0.12>1.86

The answer cannot be 16 percent or greater, and since we know we need more than a 15-percent concentration of vinegar in the original solution,  the answer must be (D) . Not that I necessarily encourage it, but I completed this problem entirely in my head. (It took about a minute, and I am guessing that many aspirants are just as good at math(s) as I.)

Good luck with your studies.

- Andrew

ScottTargetTestPrep · Answer

Solution:

Let the amount of pure vinegar in the original solution be x. After adding 50 ounces of water to the original solution, there are still x ounces of pure vinegar in the solution, but now the solution is 12 + 50 = 62 ounces. We are told that the concentration of this new solution is 3%, thus:

x/62 = 3/100

x = 186/100 ounces

Since there are 186/100 ounces in the original solution, the concentration of the original solution is   x 100 = 15.5%.

Answer: D

yanyas · Answer

Is there an approximation/estimation way to solve the fraction 1.86/12 ?
To save time I took 1.86 ~ 2 ==> so 2/12 = 1/6 = 16.67%

Can someone please suggest how should I have tackled this question and not fallen for this trap? Or am I expected to actually solve the fraction?

Posted from my mobile device

AndrewN · Answer

Hello,  yanyas . I worked out the quotient using mental math, the kind I sometimes fall back on in a pinch. (This time, I tried it as a challenge.) How? Just ignore the decimal for the time being. If the numerator were 186, how would you approach solving the quotient? In my case, I thought of 144 as the product of 12 and 12. Then, the difference between 144 and 186 was 42. Finally, 12 fit into 42  exactly  3 and a half times: 12 * 3 + 6. Putting everything together, we can determine that the quotient is 12 (from twelve 12s) + 3 (from three 12s) + 0.5 (from half of 12), or 15.5.

I hope that helps. You do not have to take everything at face value. (Decimal manipulation is fine as long as you remember to adjust later on, as necessary.)

Good luck with your studies.

- Andrew

joe123x · Answer

I got to~ 1.8/12. but how do I do this accurately ? I was like 1.8 is close to 2, 2/12 = 1/6, so it can't be bigger than 1/6

Bunuel · Answer

It's actually not hard do get an exact answer. Calculate 186/12 and divide by 100:

\frac{186}{12} =\frac{180}{12} +\frac{6}{12} =15+0.5=15.5  .

Dividing by 100 gives 0.155.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Aishyk97 · Answer

Hi,

Using allegation made this problem easy.

0%----3%------x%

\frac{x-3}{3-0}=\frac{50}{12}

Solve for x.

x = 15.5

hazeljj · Answer

Same here i did the same as you did! Took me a while to get the proportions right though because it isn't as intuitive as the usual weighted average questions

Pranay6110 · Answer

Here is the simple approach:
Concentration of vinegar = 12
Concentration of vinegar (when added water) = 0
Take this senerio into the allegation:

12-3:3-0 = 3:1
Now, as per the question value of vinegar and water is- 3+1= 4.
Now, the value of 4 is 62, hence the value of 1 is 15.5

Posted from my mobile device

ritik156 · Answer

Can you please share similar questions (easy, medium hard) to understand this concept fully?

Bunuel · Answer

Mixture Problems

Theory: 
 
  Weighted Average and Mixture Problems on the GMAT  
  Tips and Tricks: Mixtures

Questions: 
 
  DS Questions  
  PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Adit_ · Answer

We are mixing 12 ounces of something with 50 ounces of pure water.

x% 0%

3%

3 x-3

We thus see that they are mixed in proportions of 3/3-x
What is 3/3-x it is 12/50 and 12 parts of 1st is mixed with 50 parts of next.

12/50 = 3/3-x => x = 15.5%

Answer:  Option D

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