Dear friend the first statement is not clear to me....Anyway here is the solution.

Capacity of Tank 1 = z

Amount of water in Tank 1 after one minute = x-y (since in one minute x gallons are pumped into the and in the same one minute y gallons are emptied into Tank 2)

Given that capacity of Tank 2 = 2(x-y)

It is clear that Tank 1 is effectively filled at the rate of (x-y) gallons/minute and Tank 2 is filled at the rate of y gallons/minute

So time taken to fill Tank 1 = z/(x-y) and time taken to fill Tank 2 = 2(x-y)/y

Now the question: Is z/(x-y) < 2(x-y)/y

i.e Is zy < 2x^2 - 4xy + 2y^2.

So the first statement must be sufficient to answer this.

Statement 2(x-y) < z/2

i.e 4(x-y) < z

Clearly this is not sufficient to answer.