consecutive integers are integers that occur one after another. eg. 2,3, 4 are consecutive integers.
here they say x, y and z are consecutive integers.

i) x= 11 implies y= 12 and z= 13.

average = (11+12+13)/3.

sufficient

ii) y+z/2 = 12.5

y+z = 25

the only consecutive numbers whose sum results in 25 are 12 and 13.
so y= 12
z= 13
x= 11

again the average can be found out.

Sufficient.

therefor and is D

Hope this helps!