Multiple choice

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.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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A Correct answer
Explanation

Statement 1 gives the ratio of green to (yellow + white) as 1:3. This means green paint is 1/4 of the total mixture (12 quarts), which is 3 quarts. Statement 2 only gives a ratio between yellow and green, which is insufficient to determine the total amount of green paint without knowing the total amount of yellow paint.

AI explanation

Statement 1 gives the ratio of green paint to the combined amount of yellow and white paint as 1 to 3. This means the total 12 quarts represent 4 total parts, making the 1 part of green paint exactly 3 quarts. Statement 2 only compares yellow to green without providing the total proportion of white paint, so the exact amount of green paint cannot be calculated. Therefore, statement 1 alone is sufficient, but statement 2 alone is not.

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