x, y, z are positive integers.
I. Given : x + y + z is even.
⇒x+y+z=2,4,6,8,10,12,14,16,....
Of these, only multiples of 14 are divisible by 7 while others are not.
∴ I alone is not sufficient.
II. Given :
x=4y−11 and
z=2y+4.
Adding the two we get,
x+z=6y−7⇒x+y+z=7y−7=7(y−1)Since 7 is a factor,
x+y+z is divisible by 7.
∴ II alone is sufficient.