A certain painting job requires a mixture of yellow, green, and white paint

A certain painting job requires a mixture of yellow, green, and white paint. If 12 quarts of paint are needed for the job, how many quarts of green paint are needed?

  1. The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3.
  2. The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2.

Answer

To find the amount of green paint, you need to know either the amount of yellow and white paints, or the individual proportion of each colour in the total paint.

Statement 1: The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3.

Amount of green paint = 12 - (amount of yellow and white paint combined)

Amount of yellow and white paint combined = 12 - amount of green paint

Amount of green paint / (12 - amount of green paint) = 1/3

This is a linear equation with one variable. Therefore, from this equation, you can determine the amount of green paint. Hence, statement 1 is sufficient to answer the question.

Statement 2: The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2.

From this statement, you cannot find any information about the amount of white paint or the total amount of yellow and green paint. Hence, statement 2 is not sufficient to answer the question.

The correct option is A.