If x,y belong to set of integers, is x^y even?

Wow there is something I didn’t see when I chose A. Can someone help me understand the question?

Thanks

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Hi,
Any explanation why it's not A and why it E.??


Regards,
Tamal

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Thanks for clarifying the question

sol-
1) take values-
2^2= 4
2^3= 8
0^0= 1 (not suff)

2) take values-
2^2= 4
3^2=9 (not suff)

combining 1 and 2
check if both x and y are even
2^2= 4
0^0 = 1 (not suff)

answer E

The first thing not to forget is that 0(zero) is even number too. And if the power of any number is 0, that number equals to 1, odd number.

If x,y € integers, is x^y even?

Statement1: x is even.
No info about y. y could be 1 or 2 or 0 or any number. If y=2, then x^2 will be even number. If y=0, then x^0 will be odd number,1. Insufffient.

Statement2: y is even.
No info about x. x could be even number or odd number. That’s why, we will get both odd and even number. Insufficient.

Taken together, it is also insufficient. Even if the power of the number and the base of the number are even numbers, we will get odd number in one condition.(if the power of the number equals to 0(zero).
Insufficient. Answer choice is E.

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