Hi All,
This is a 'Weighted Average' question, so it can be solved in a number of different ways. For most Test Takers, setting up the Weighted Average formula and doing the necessary algebra is a straight-forward way to get to the solution, but there ARE alternatives. Since the question asks for the number of milliliters of Solution Y that are needed, and the answer choices are NUMBERS, we can TEST THE ANSWERS.
From the prompt, we are told to mix 200 milliliters of a 10% alcohol solution with an unknown number of milliliters of a 30% alcohol solution to get a 25% total alcohol solution.
IF....we mixed 200 milliliters with another 200 milliliters, then we'd end up with a 20% mixture (since the average of 10% and 30% is 20%). That result would be TOO LOW, so we clearly need a lot MORE milliliters of the 30% solution. From this, we can eliminate Answers A and B from consideration.
Let's TEST Answer D....
IF...we have 480 milliliters of Solution Y, we have....
Does [.1(200) + .3(480)]/680 = .25?
Does 20 + 144 = .25(680)?
Does 164 = 170?
No it doesn't, so Answer D is NOT the answer. We likely need to add MORE of the 30% solution to get the two 'sides' to match, but we can confirm this by TESTing Answer E.
IF....we have 600 milliliters of Solution Y, we have...
Does [.1(200) + .3(600)]/800 = .25?
Does 20 + 180 = .25(800)?
Does 200 = 200?
Yes it does, so this MUST be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich