M22-07

Question

If two different alcohol solutions with respective water to alcohol ratios of 3:1 and 2:3 by volume were combined in equal amounts, what would be the concentration of alcohol in the resulting solution?

A. 30.0%
B. 36.6%
C. 42.5%
D. 44.4%
E. 60.0%

Show Answer

Official Answer

C

A. 30.0%
B. 36.6%
C. 42.5%
D. 44.4%
E. 60.0%

Bunuel · Accepted Answer

Official Solution:

If two different alcohol solutions with respective water to alcohol ratios of 3:1 and 2:3 by volume were combined in equal amounts, what would be the concentration of alcohol in the resulting solution?

A. 30.0%
B. 36.6%
C. 42.5%
D. 44.4%
E. 60.0%

Show Answer

Official Answer

C

A. 30.0%
B. 36.6%
C. 42.5%
D. 44.4%
E. 60.0%

The concentration of alcohol in the first solution is  \frac{alcohol}{total}= \frac{1}{3 + 1} = 0.25  or 25%. The concentration of alcohol in the second solution is  \frac{alcohol}{total}= \frac{3}{2 + 3} = 0.60  or 60%. When the two solutions are mixed in  equal amounts , the resulting solution will have a concentration of alcohol of  \frac{60\% + 25\%}{2} = 42.5\% .

Answer: C

danjbon · Answer

I think this is a  high-quality  question and I agree with explanation. I like it! Another way of viewing this. If you are going to use 5 L of the 2:3 solution, you must use 5L of the 3:1 solution. Thus you will be adding 3.75:1.25 L to 2:3 L which results in a 10 L solution that has 5.75:4.25 ratio. You want to know what 4.25L is as a % of 10L, so just times 4.25 / 10 by 10 -> 42.5 / 100

Sallyzodiac · Answer

Bunuel's solution is pretty awesome, I didn't think one could solve it that simply. I took a different approach and worked with actual numbers:

1) We know that the ratio of water:alcohol in the first solution is  \frac{3}{1}  (which give 4 parts) and we know that the ratio of water:alcohol in the second solution is  \frac{2}{3}  (which give 5 parts).

2) 20 is the LCM of 4 and 5, so let's assume that both solutions have a volume of 20 units. From the first solution, we have that water is  \frac{3}{4}  of the solution (which we said had a volume of 20), which gives 15 units of water and thus 5 units of alcohol. From the second solution, we have that water is  \frac{2}{5}  of the solution, which gives 8 units of water and 12 units of alcohol.

3) Since we are mixing both solutions with an equal amount, 20 units, our new solution has a total volume of 40 units. From 2), combining the water and alcohol in both solutions, we get that our new solution has 17 units of alcohol (5 units from the first solution and 12 units from the second solution) and 23 units of water (15 units from the first solution and 8 units from the second solution). Thus, the amount of alcohol in the mixed solution is  \frac{17}{40}  = 42.5%.

PS: Time-wise I managed to do this slightly north of 2 minutes, but Bunuel's approach is of course much faster if one can identify the validity of that approach right off the bat.

/S

VSJ · Answer

my method is simple alligation

25% and 60% mix leading to x but the ratio of both original solutions in mix is 1:1. therefore:

x-25=60-x means 2x=85. finally x=42.5%

Spongebob02 · Answer

\frac{60\% + 25\%}{2} = 42.5\ how did you got equation ? Why you have divided by 2 ? @bunuel

Sent from my Redmi 3S using  GMAT Club Forum mobile app

Bunuel · Answer

Because we are told that the original solutions were mixed in EQUAL amounts. So, the percentage of alcohol in the resulting mixture would be the average of the percentages in two mixtures. Check other discussion here: https://gmatclub.com/forum/if-two-diffe ... 99529.html Hope it helps.

PrayasT · Answer

I think this is a  high-quality  question and I agree with explanation.

ffischer · Answer

I just summed up the sums of the solutions which yielded 9 ( (1+3) + (3+2) = 9) 
Afterwards I did the same with the alcohol solutions which yielded 4 (3 + 1) 
THe percentage of alcohol would be 4/9 = 0.4444 , Can you tell me what is wrong?

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.

Prasesh · Answer

Bunuel  I completely agree with your solution but I did the same thing as  ffischer  did so can you help resolve this

Bunuel · Answer

Your initial method combined the volumes of 4 parts and 5 parts directly, which is incorrect since the solutions are to be mixed in equal amounts, and 4 and 5 are not equal. To accurately determine the alcohol concentration in the mixed solution, you should first adjust the volumes to be equal. Multiply the 4 parts of the first solution by 1.25 to yield 5, thus matching the 5 parts of the second solution. This results in 1.25 parts alcohol for the first solution. When combining both solutions: 1.25 (from the first) + 3 (from the second) gives 4.25 parts alcohol out of a total of 10 parts, leading to a 42.5% alcohol concentration in the mixture.

Hope it's clear.

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