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05 Oct 2021, 12:52
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B
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Difficulty:
5%
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Question Stats:
88% (01:57) correct
12%
(02:20)
wrong
based on 220
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The concentration of acid in solutions A, B and C are 4%, 2% and 2%, respectively. A new solution is created by combining 2 liters of solution A, 4 liters of solution B, and 2 liters of solution C. What percent of the new solution is acid?
A) 2.25
B) 2.5
C) 2.75
D) 3
E) 3.25
A) 2.25
B) 2.5
C) 2.75
D) 3
E) 3.25
05 Oct 2021, 16:24
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BrentGMATPrepNow
Since this question has no takers, here's my solution....
Useful property: If EQUAL VOLUMES of two solutions are combined, then the concentration of the resulting mixture will be equal to the AVERAGE of the two concentrations that were combined.
For example, if we combine 1 liter of 20% salt solution with 1 liter of 50% salt solution, the concentration of the resulting mixture will equal 35%, which is the average of 20% and 50%
We can apply that property here....
We'll start by combining 2 liters of solution A (4% acid) with 2 liters of solution C (2% acid).
Since we're combining EQUAL VOLUMES, the resulting mixture will be 3% acid (which is the average of 4% and 2%).
Note: The resulting mixture has 4 liters of solution (since we combined 2 liters of solution A with 2 liters of solution C)
From here, we'll combine the 4 liters of resulting solution (3% acid) with 4 liters of solution B (2% acid).
Once again, since we're combining EQUAL VOLUMES, the resulting mixture will be 2.5% acid (which is the average of 3% and 2%)
Answer: B
General Discussion
06 Oct 2021, 04:25
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Brent's solution is great and I like it better than my solution, but this is another way to do the problem: since B and C are both 2% solutions, we don't need to distinguish between them. We're mixing 2 liters of A, a 4% solution, with 6 liters of B+C combined, a 2% solution. Using weighted average principles, since the 2% and 4% components are in a 3 to 1 ratio, the answer should be "three times closer" to 2%, so it will be 2.5%.
