GMAT Focus EditionQuantitative ReasoningHard
A chemist has two solutions: Solution X is 20% acid and Solution Y is 50% acid. How many liters of Solution X should be mixed with 10 liters of Solution Y to obtain a mixture that is 30% acid?
- A10 liters
- B20 liters
- C15 liters
- D25 liters
Show answer & explanationAnswer & explanation
Correct answer: B. 20 liters
Let 'x' be the liters of Solution X. The total amount of acid from Solution X is 0.20x. The total amount of acid from Solution Y is 0.50 * 10 = 5 liters. The total volume of the mixture is x + 10. The total acid in the mixture should be 0.30 * (x + 10). So, 0.20x + 5 = 0.30(x + 10). 0.20x + 5 = 0.30x + 3. 2 = 0.10x. x = 20 liters.
Why the other options are wrong
- A. This would result in a higher acid percentage than 30%.
- C. This would result in a slightly higher acid percentage than 30%.
- D. This would result in a lower acid percentage than 30%.
Mixture Problems (Algebraic)
Mixture problems involve combining two or more components with different concentrations to achieve a desired final concentration. They are typically solved using algebraic equations based on the total amount of a specific substance.
- Focus on the total quantity of the 'active ingredient' (e.g., acid, salt).
- Set up an equation where 'acid from X + acid from Y = acid in mixture'.
- Total volume of mixture is the sum of individual volumes.
Memory trick: Balance the pure stuff in each jar to get the right blend.