x is the sum of an even number of consecutive numbers. (since y = 2z)

so x must be odd. (for example 1+2=3 2+3=5.......)
and y must be even.

so x/y cannot be an integer.


edit: sorry, x can be even. (1+2+3+4=10 for example)

however i still think the answer is c.
because x/y gives the number just in the middle. as there is no number in the middle (because there are even number of numbers?) it cannot be integer.

ok. the rule is

the sum of even number of consecutive integers is never divisible by the number of the integers.

e.g. 1+2 = 3 (not divisible by 2)
1+2+3+4 = 10 (not divisible by 4)
1+2+3+4+5+6 = 21 (not divisible by 6)

but for odd number of consecutive integer, this does not hold true. the sum of odd number of consecutive integers is divisible by the number of the integers.
e.g. 1+2+3= 6 (divisible by 3)
1+2+3+4+5= 15 (divisible by 5)
1+2+3+4+5+6+7 = 28 (divisible by 7)

here we are given that X is the sum of Y consecutive integers. So if Y is even then X/Y cannot be integer.
We are also given that Y = 2 * Z. therefore y is even
hence X/Y is not an integer.