Hi AbeNeedsAnswers,

We're told that K is an INTEGER and that 56 < K < 66. We're asked for the value of k. This question can be solved by TESTing VALUES.

1) If K were divided by 2, the remainder would be 1.

Based on the information in Fact 1, K could be 57, 59, 61, 63 or 65.
Fact 1 is INSUFFICIENT

2) If (K+1) were divided by 3, the remainder would be 0.

Based on the information in Fact 1, K could be 57, 60, or 63.
Fact 2 is INSUFFICIENT

Combined, we can see that there are 2 possibilities that 'fit' both Facts: 57 and 63.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich