If x and y are integers, then is x even? Statement I : x^2 y^2 is even. Statement II : 1 + x^2 + y^2 is odd.

If x and y are integers, then is x even? Statement I : x^2 y^2 is…

Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
Select this option if the question can be answered using either statement alone
Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
Select this option if the question cannot be answered even using any of the statements

Answer

Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone

Statement I: x^2y^2 is even, so at least one of x,y is even. x need not be even. Not sufficient.
Statement II: 1+x^2+y^2 is odd, so x^2+y^2 is even. Hence x and y have the same parity: both even or both odd. x need not be even. Not sufficient.
Together: at least one is even, and both have same parity. Therefore both must be even. So x is definitely even.

Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone

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