A certain painting job requires a mixture of yellow, green,

[AbeNeedsAnswers]

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.

A

Source: Official Guide 2020

[Ian Stewart]

From Statement 1, 1/4 of the mixture is green paint, and since we know we have 12 quarts of paint in total, we must have 3 quarts of green paint. So Statement 1 is sufficient.

Statement 2 is not sufficient because we have no information about what fraction of the mixture is white paint.

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Hi All,

We're told that a certain painting job requires a mixture of yellow, green, and white paint and that 12 quarts of paint are needed for the job. We're asked for the number of quarts of GREEN paint that are needed. This question can be answered with ratio-based math and TESTing VALUES.

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

With the information in Fact 1, we have the following relationship:
(Green) : (Yellow + White) = 1 : 3

This means that for every 1 quart of green paint, we have a total of 3 quarts of yellow and white paint, so we can think of this ratio in terms of '4 quart blocks'. With 12 total quarts, we would have 3 of those blocks - meaning that we have 3 quarts of green paint and 9 quarts of yellow+white paint. The actual amounts of yellow and white paint don't matter though, since we're asked for the amount of GREEN paint and we now know that the answer must be 3.
Fact 1 is SUFFICIENT

(2) The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2.

Fact 2 gives us a different ratio, but not enough to determine the exact amount of green paint....
IF....
Yellow = 3 quarts, Green = 2 quarts and White = 7 quarts, then the answer to the question is 2.
Yellow = 6 quarts, Green = 4 quarts and White = 2 quarts, then the answer to the question is 4.
Fact 2 is INSUFFICIENT

Final Answer: A

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