but in this case statement A contradicts to statement B. A states that x is an integer and B states that it is not.
Not so, taken together x can be zero which is an integer.
If we need to indicate that x is an integer, shouldn't the answer be C?
Statement 1 alone: Insufficient.
Statement 2 alone:
|-1-6| = 7. True.
|1-6| = 5. False 5 is not larger than 5. Also insufficient.
Both statement together:
If say we take zero as an integer we need statement 1 to indicate that x is in fact an integer.
|0-6| = 6. True