When a positive integer k is divided by 7, the remainder is 6. What is the remainder when k+2 is divided by?

It is 1.

If a positive integer k has a remainder 6 when it is divided by 7, it is of the form:

##k = 7n + 6##, where n is an integer.

Hence, k+2 would have such a form:

##k+2 = 7n + 6 + 2 = 7n + 8 = 7(n+1) + 1##

Here, (n+1) is again an integer, and the remainder would be 1.