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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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Explanation

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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