GMAT Focus EditionQuantitative ReasoningMedium
A chemist needs to mix a 60% acid solution with a 30% acid solution to produce 15 liters of a 40% acid solution. How many liters of the 60% acid solution are needed?
- A7.5 liters
- B5 liters
- C10 liters
- D12.5 liters
Show answer & explanationAnswer & explanation
Correct answer: B. 5 liters
Let x be the liters of 60% solution and y be the liters of 30% solution. We have two equations: x + y = 15 (total volume) and 0.60x + 0.30y = 0.40(15) (total acid). From the first, y = 15 - x. Substitute into the second: 0.60x + 0.30(15 - x) = 6. This simplifies to 0.60x + 4.5 - 0.30x = 6, so 0.30x = 1.5, and x = 5.
Why the other options are wrong
- A. Incorrect. This would mean equal parts, resulting in a 45% solution.
- C. Incorrect. This would result in a higher percentage acid solution.
- D. Incorrect. This would result in a much higher percentage acid solution.
Mixture Problems
Problems involving combining two or more quantities with different concentrations to form a mixture with a desired concentration.
- Often solved using a system of linear equations.
- One equation for total volume/quantity, another for total amount of substance.
- Concentration is substance amount / total volume.
Memory trick: Words to equations, variables in play, solve with logic, come what may.