x gallon 40% alcohol solution is mixed with another y gallon10% alcoho

1. For x^2 > y^2, the necessary condition is that x>y.
If x is greater than y, there will be more gallons of 40% alcohol solution than 10% alcohol solution.
Case 1: x = 20, y = 10
First solution will have 8 gallons of alcohol and the second solution will have 1 gallon of alcohol.
When we mix these solutions, we will get 9 gallons of alcohol out of 30 gallons solution. p = 30%

Case 2: x = 1.1, y = 1
First solution will have 0.44 gallons of alcohol and second solution will have 0.1 gallons. On mixing
these solutions, we would have 0.54 gallons of 2.1 gallons which is slightly over 25%
In both these cases, the percentage of alcohol is greater than 25%(Sufficient)

2. z > p
Case 1: x = 10, y = 20
First solution will have 4 gallons of alcohol and the second solution will have 2 gallon of alcohol.
When we mix these solutions, we will get 6 gallons of alcohol out of the 30 gallons, which is 20%
Here z=30 and p=20% (z > p and p is not greater than 25%)

Case 2: x = 50, y = 10
First solution will have 20 gallons of alcohol and the second solution will have 1 gallon of alcohol.
When we mix these solutions, we would have 21 gallons of alcohol out of 60 gallons which is 35%.
Here z=60 and p=35(a > p and p is greater than 25%)
Since we have contradicting cases for p>25%, this statement is not sufficient. (Insufficient) (Option A)