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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.