Use the property that the arithmetic mean of a set of consecutive integers is the same as the median. For example, average of 1,2,3 is 2 and average of 2,3,4,5 is 3.5. Finding the average of 11 consecutive integers is the same as finding the median, which would be the 6th number.

Statement 1: the average of the first 9 integers is 7 tells us that 7 is the median of these 9 integers, so the first 9 must be 3,4,5,6,7,8,9,10,11. This tells us that the 6th overall number is 8, so the average of the 11 consecutive integers is 8. SUFFICIENT.

Statement 2: Same idea. The average of the last 9 integers is 9, so the last 9 integers is 5,6,7,8,9,10,11,12,13. This means the 11th integer is 13. Counting backwards we again get that the 6th integer is 8. SUFFICIENT

Ans: D