Helen mixes a first solution, 4 liters of 40% concentrated sulfuric ac

Question

Helen mixes a first solution, 4 liters of 40% concentrated sulfuric acid solution, with a second solution, 5 liters of a sulfuric acid solution with a stronger concentration, and the resultant solution is 9 liters of 50% concentrated sulfuric acid solution. What was the concentration, as a percent, of the second solution?

(A) 28
(B) 38
(C) 58
(D) 68
(E) 78

(A) 28
(B) 38
(C) 58
(D) 68
(E) 78

BrentGMATPrepNow · Accepted Answer

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

RELATED VIDEO 
 https://www.youtube.com/watch?v=B7J6lr_qBG4

shameekv1989 · Answer

4 lts of 40% = 1.6 lts of acid
5 lts of x% =  \frac{x}{5}  ltrs of acid

Mixture = 9lts of 50% = 4.5 ltrs of acid

1.6+ \frac{x}{5}  = 4.5

x=58% - Answer - D

SaikatRoy · Answer

Going by relation of mixtures
We know that
4(0.40) + 5 (x%) = 9 (0.50)
or, 5(x%) = 9(0.50)-4(0.40)
or, x% =2.9/ 5 = 0.58
ie x= 58 %

Answer Is Option D

ScottTargetTestPrep · Answer

Solution:
 
Let x = the percent of the 5-liter solution that is a sulfuric acid. We can create the equation:

0.4(4) + x/100 * 5 = 0.5(9)

1.6 + x/20 = 4.5

x/20 = 2.9

x = 58

Answer: C

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Helen mixes a first solution, 4 liters of 40% concentrated sulfuric ac

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Helen mixes a first solution, 4 liters of 40% concentrated sulfuric ac

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