NandishSS wrote:
Bunuel wrote:
If there are 10 liters of a 20%-solution of alcohol, how much water should be added to reduce the concentration of alcohol in the solution by 75% ?
A. 25 liters
B. 27 liters
C. 30 liters
D. 32 liters
E. 35 liters
HI
GMATGuruNY ,
MentorTutoring ,
BrentGMATPrepNow,
Can you help me out on this problem? I tried to comprehend but missed it.
Hello again,
NandishSS. There are two separate components that you have to work through to solve the question. I often teach my students to stop whenever they encounter punctuation in a Quant problem, to take a moment to process what information was given. Too many students make the mistake of trying to read everything quickly and then jumping right into the problem, perhaps feeling overwhelmed because they do not know how to put all the pieces together. Anyway, how about we put this technique to use in this question?
Bunuel wrote:
there are 10 liters of a 20%-solution of alcohol
This information allows us to determine the
number of liters of alcohol in the solution: 0.2(10) = 2.
Bunuel wrote:
reduce the concentration of alcohol in the solution by 75%
To reduce the
concentration of alcohol, we have to reduce the 20% (concentration) of the original solution by 75%, or, in other words, we need to keep 1/4 of the original concentration: 1/4 * 20 = 5. The solution
after the addition of the water must have a 5% alcohol content.
Now we can put the two separate parts of the problem together. Since we are not adding any alcohol to the solution, but water only, we know that 2L of alcohol must be equivalent to the 5% concentration of alcohol in the final solution (which I will denote F).
2 = 0.05F or 2 = (5/100)F (if decimals cause you trouble, as they do for some people)
2 = (1/20)F
2 = F/20
40 = F
The final solution will be 40L in volume, of which 2L will be alcohol. Check your solution (if you were not in a time crunch):
2/40 = 1/20 = 5/100
Since 5/100 is 5%, we can now be sure about our solution. A good trap answer here would be 40 liters, since that is the volume of the final solution. But be careful and
make sure you are answering the question that is being asked. Here, at a barebones level (since we have already sorted out all the details), we have,
Bunuel wrote:
how much water should be added...?
If we started with 10L and we ended up with 40L, then we added 30L of water to the solution.
Choice (C) must be the answer.I hope that helps. Although, looking back on the official solution, I pretty much did the same thing as
Bunuel, perhaps the extra explanations will allow you to better understand how to break down such a problem. If not, just let me know.
- Andrew