GIven X and Y are integers
We need to find if Y is an even integer
Statement 1\(2y - x = x^{2}-y^{2}\)
=> \(2y = x^{2}-y^{2} + x\)
The left hand side of above equation is always even
=> \(x^{2}-y^{2} + x\) is even
Lets see the result for different combinations of X and Y
X | Y | \(x^{2}-y^{2} + x\)
Even | Even | EvenOdd | Even | EvenOdd | Odd | Odd
Even | Odd | Odd
We can see that Y is an even integer whenever \(x^{2}-y^{2} + x\) is even
Statement 1 is sufficientStatement 2X is an odd integer => doesn't tell anything about Y
Statement 2 not sufficientAnalysis of statement 1 and 2 together is not required
Hence
option A
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