Amount = 1115.67, Interest = 1%
Using the above two values, we can calculate the month in which the Amount exceeded 1100 provided there was no addition or subtraction to the value in the account

St1: Not sufficient --> We do not know if there were any deposits or withdrawals
St2: Sufficient. (1115.67/1.01) gives the amount for previous month and so on. The exact month can be calculated if there are no deposits or withdrawals.

Answer: B

We're given the final amount, time period, type of interest, and rate of interest. Using these information, we can find the month in which the account first exceed $1,100 provided we can be sure of whether or not there were any other transactions involved during the course of time.

(1) Since we do not know whether there were any deposits or withdrawals, we can't find out answer.
Thus, not sufficient.

(2) 1000=(1115.67)/\((1.01)^t\)
From the above equation we can find the value of t.
Thus, sufficient.

Therefore, the answer is option B.
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I think it is 1100 instead of 1000 in your explanation for statement-2.