A certain mixture of paint requires blue, yellow, and red paints in ratios 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?
(1) Exactly 20 quarts of the mixture are needed.
(2) Exactly 10 quarts of the yellow paint are available.
Rephrase: We need to know the “desired amount.” Insert a ratio multiplier – B : Y : R = 2k : 3k : k. The total – i.e. the desired amount – is 6k. The yellow paint is 3k. FINAL rephrase: “do we have 3k quarts of yellow paint?”
Clue (1): The desired amount is 20. So, we know 6k = 20. Therefore, we can find k and 3k, but we still don’t know how much yellow paint we have. INSUFFICIENT. A and D are out.
Clue (2): We now know how much yellow paint we have, but we no longer know how much we need. INSUFFICIENT. B is out.
Clues (1) and (2): We know we need 3k quarts of yellow paint, and we have 10 quarts available. Because we can deduce k from (1), we have everything we need. SUFFICIENT.
The correct answer is C.
Note that I never bothered to find the actual value of k – once I know that I can find it, that’s enough information to determine sufficiency.