How many families have a dog?
Total families = 60
Families with cats = 38
Families with no pets = x
Families with cats only = 38 - x
Families with cats and dogs = y
Families with dogs = d
Families with dogs only = d - y
Number of families with a dog = ?

Statement 1 : 28 of the families in the neighborhood have a cat but not a dog.
This means families with cat only = 28
28 = 38 - x
x = 38 - 28
x =10 families with no pets.
Information in statement 1 is not sufficient enough to find the number of families with a dog.
Hence statement 1 is NOT SUFFICIENT.

Statement 2 : The number of families in the neighborhood who have a dog and cat is the same as number of families who have neither a cat nor dog.
Remember that number of families with no pets = x
No. of families with cats only = 38 - x
Total NO. of families without dogs = 38 - x+ x
= 38
Total number of families with a dog = Total NO. of families - Total NO. of families without dogs
= 60 - 38
= 22
Hence, statement 2 is SUFFICIENT.
Option B is CORRECT.