Now, we turn our attention to the actual integer in question, 710. This is a power of 7, so we need to look for any pattern in the last two digits of the powers of 7. (We can assume that there must be such a pattern; otherwise, this question would not be realistically solvable on the GMAT.)
71 = 7
72 = 49
73 = 49 × 7 = 343. Note that we only need to pay attention to the last 2 digits (43), so we will write …43.
74 = …43 × 7 = …01.
75 = …01 × 7 = …07.
At this point, we see that the cycle is starting to repeat.
Well, I'm probably dumb (although I tend to believe I'm not), but how without trying 7^6 we can assume that there is some pattern here? I'm not sure that seeing at least one matching number should be supposed to be a pattern already. Other than that, good question to me knowledge base, I didn't make it right.