Whenever we have a mixtures problem, we want to build a system of equations.
We know that 10% of X plus 18% of Y gives us 12% of the new solution, which is X plus Y. We can convert these percentages to decimals and write this as an equation:
0.1X + 0.18Y = 0.12(X+Y)
Simplifying gives:
0.1X + 0.18Y = 0.12X + 0.12Y
0.06Y = 0.02X
3Y = X
We want to find Y in liters.
Statement 1
This doesn't tell us anything about the number of liters in the solution. This means that while we may be able to find out information about the ratio of X to Y with this statement, we won't be able to put a concrete number of liters to it. So the statement will be insufficient.
If we weren't able to figure this out right off the bat, we can apply this statement by creating an equation. It tells us that X = 3/4(X + Y). Simplifying gives us:
X = 3/4X + 3/4Y
1/4X = 3/4Y
X = 3Y
This is exactly what we found before. So we actually don't learn anything new from this statement. Insufficient.
Statement 2
This tells us that X + Y = 16. Since we already know that 3Y = X, we have two distinct equations with two variables, meaning we should be able to solve for Y, making this statement sufficient. But let's go ahead and do that anyway, by plugging in 3Y for X:
3Y + Y = 16
4Y = 16
Y = 4
So there are 4 liters of Y in the final solution. Sufficient.
