Consecutive Integers

[heshamelaziry]

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w

x > w

x/y is an integer

w/z is an integer

x/z is an integer

OA C [spoiler]Although I learned new concept today about consecutive integers and understand why the answer is indeed correct, I can't refute the other options when I choose variables for each integers in this form: a + a+1+a+2....
for example, to prove a is wrong, the OE simply picked any number of integer, but why when I pick variables it does not work ?[/spoiler]

[palvarez]

x = sum of 2z consecutive integers.

x = (2z)*average, here the average is not integer, because the list size is even.
x/y = x/2z = not an integer.

could be true except = must be false. Look for something obvious like the above to zero-in on

[heshamelaziry]

New rule I learned today:

The summ od odd numebr of terms in a set IS a multiple of the number of terms. The sum of an even number of term is NEVER the the multiple of the NUmber of trems. Y + 2Z means y is an even number of terms and consequently x / y is not an integer.