The question stem provides a fixed value for the amount of Chemical C (10 milliliters) but only a ratio for Chemicals A and B (3 to 7). A ratio is like a recipe; it tells you the baseline proportion needed, but you can increase the baseline recipe by multiplying each item in the recipe by the same number. For example, there could be 3 mL of ChemA to 7 mL of ChemB. There also could be 6 mL of ChemA to 14 mL of ChemB. And so on.
The question asks for the ratio of ChemA to ChemC (ChemA : ChemC). You know how much ChemC is in the mixture, so if you can figure out how much ChemA there is, then you can find the ratio A : C.
(1) SUFFICIENT: The mixture contains only these three chemicals, so before ChemC was added, the mixture must have contained only ChemA and ChemB. That is, the mixture contains 50 mL of ChemA and ChemB combined. You were also given the ratio (3 : 7), so it's possible to figure out how much ChemA is in the mixture and how much ChemB is in the mixture. If you know the exact amount of ChemA, then it's possible to find the ratio ChemA : ChemC.
If you're not sure, start to solve, but stop as soon as you can tell that you can solve. If there are 3 parts ChemA for every 7 parts ChemB, then there are 3 + 7 = 10 parts total of these two chemicals in the baseline recipe for the mixture. The mixture of ChemA and ChemB together is exactly 50 mL, or 5 times the baseline recipe, so multiply each ingredient by 5: There are (5)(3) = 15 mL of ChemA. [You can do the same calculation to find ChemB: (5)(7) = 35 mL. But don't in this case, since the question asks only about ChemA and ChemC.]
Since the solution has 15 mL of ChemA and 10 mL of Chem C, the ratio A : C is 15 : 10, which simplifies to 3 : 2. But don't solve this far on Data Sufficiency! Stop as soon as you can tell that it is (or is not) possible to solve.
(2) SUFFICIENT: If the total solution is 60 mL and ChemC is 10mL, then ChemA and ChemB combined are 50 mL of the solution. This information now matches what is given in Statement (1), so you can use the same solution process to show that this information is sufficient to find the ratio of ChemA to ChemC.
The correct answer is (D): Each statement by itself is sufficient to answer the question.
