We can also solve this question by applying some logic

Key concept #1: If we combine EQUAL volumes of two solutions, the concentration of the resulting solution will be the AVERAGE of the two original solutions
For example, if we combine 5 gallons of 20% solution with 5 gallons of 40% solution, then the resulting solution will have a concentration of 30%

Key concept #2: If we combine DIFFERENT volumes of two solutions, the concentration of the resulting solution will be the CLOSER to the concentration of the solution that we used MORE of
For example, if we combine 5 gallons of 20% solution with 6 gallons of 40% solution, then the resulting solution will have a concentration that's closer to 40% than it is to 20% (since we used MORE of the 40% solution)

GIVEN: 4 liters of 40% solution are combined with 5 liters of a different solution, and the resulting solution has a concentration of 50%
Concept #1 tells us that, if we combined 4 liters of 40% solution are combined with 4 liters of a 60% solution, the resulting solution would have a concentration of 50%.
Concept #2 tells us that, if we combined 4 liters of 40% solution are combined with 5 liters of a 60% solution, the concentration of the resulting solution will be GREATER THAN 50%.

This tells us that, the concentration of the second solution must be LESS THAN 60%
So, we can ELIMINATE D and E

IMPORTANT: We can also eliminate other choices A and B.
A) 28: If we combine 4 liters of 40% solution with 5 liters of 28% solution, then the resulting solution will be BETWEEN 28% and 40%.
In other words, it would be impossible to have a resulting solution that has a 50% concentration.

B) 38. The same logic applies.

So, by the process of elimination, the correct answer must be C

Cheers,
Brent

Solve it with weight average,

\(\frac{(0.4*4 + 5*X)}{9} = \frac{50}{100}\)
=> 1.6 + 5x = 4.5
=> 5x = 2.9
=> x = 5.8

Now, 5.8 * 100 = 58%

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.