x is the sum of y consecutive integers (manhattan gmat)

[ethankafka]

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:

1. x = w
2. x > w
3. x/y is an integer
4. w/z is an integer
5. x/z is an integer

Answer is 3

[sanjana]

Answer is C.

You just need to remember the below property :

1)The sum of an even number of consecutive integers is never a multiple of the number of terms.

2)The sum of an odd number of consecutive integers is alwys a multiple of the number of terms

Lets take examples.
Property 1

Say the sum of 1,2,3,4
4(even) consecutive integers,sum : 10 , which is not a multiple of 4.
Will hold for any such set of numbers

Property 2
5(odd) consecutive integers : 1,2,3,4,5,sum =15 which is a multiple of 5.

Hence in the question we have,
x which is the sum of an even number of consecutive integers since y=2y(will be even since 2 is even).
Hence
X/Y cannot be an integer.