A chemist has 200 grams of a saltwater solution that is 30%... | SAT Percentages Question, Answer Explained

Math · Problem-Solving and Data AnalysisHard

A chemist has $200$ grams of a saltwater solution that is $30\%$ salt by mass. How many grams of pure water must be added so that the resulting solution is $24\%$ salt by mass?

$12$

$50$

$60$

$250$

Show answer and explanation

Answer: B

The solution contains $0.30 \times 200 = 60$ grams of salt, and adding water doesn't change that amount. If the new solution has total mass $T$ grams, then $0.24T = 60$ , so $T = 250$ . The amount of water added is $250 - 200 = 50$ grams.

Choice D is the total mass of the new solution, not the amount of water added to the original $200$ grams.

Why the other choices are wrong

A. This takes 6% of 200, the drop in percentage points, but the salt stays at 60 grams while the total grows.
C. 60 grams is the amount of salt in the solution, not the water added.
D. 250 grams is the total mass of the new solution. Subtract the original 200 grams.

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