Multiple choice

A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint available to make the desired amount of the mixture? Exactly 20 quarts of the mixture are needed. Exactly 10 quarts of the yellow paint are available.

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

The given ratio of blue, yellow, and red is 2 to 3 to 1, meaning yellow paint makes up exactly half of the total mixture. Statement 1 alone is insufficient because the required amount of yellow paint cannot be determined without knowing the total mixture needed. Statement 2 alone is insufficient because it only provides the available amount of yellow paint without stating how much mixture is required. Using both statements together, the required mixture is 20 quarts, meaning 10 quarts of yellow paint are needed, which exactly matches the 10 available quarts, proving they are sufficient together.

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