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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

In an 8-gram solution of water and alcohol, the ratio by mass of water to alcohol is 3 to 1. If 12 grams of a solution consisting of 2 grams water for each gram of alcohol is added to the 8-gram solution, what fraction by mass of the new solution is alcohol?

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To find what fraction by mass of the new solution is alcohol, you can find how many grams of alcohol are in the final solution of 20 grams. Since the 8-gram solution is 1 part alcohol to 3 parts water, it is 1 over 4 alcohol. So it contains 2 grams of alcohol. Similarly, the 12-gram solution is 1 over 3 alcohol by mass, so it contains 4 grams of alcohol. Thus, the final 20-gram solution contains 6 grams of alcohol, so 6 over 20, or 3 over 10, of it is alcohol.

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