The thing that takes longest about this problem is the writing part. If you have seen enough of these problem types, you wouldn't even need to do that, as you would know what you need to get the answer. However:

n + (n + 1) + (n + 2) + (n + 3) ...... + (n + 10) =

11n + 55

1) Average of first nine is 7:

9n + 36/9 = 7 sufficient

2) Average of last nine is 9:

9n + 54/9 = 9 sufficient

Choose D.

explain how you got 36/9 and how are u doing ur calculation.

Okay, my friend. You better appreciate my typing this out for you!

n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5) + (n + 6) + (n + 7) + (n + 8 ) + (n + 9) + (n + 10).

I hope you see this represents 11 consecutive integers, just count the n and the expressions in the parantheses.

Now, the first statement tells you that the FIRST NINE average to 7 so you add the "n"s and the numbers in the parentheses of the first nine terms and put that number over 9 and equate it to the average, 7. You will get 9n + 36 all over 9, not just the 36 part [you know, the way you do averages].

Do the same for the second statement, just count the LAST NINE terms, starting with n + 2 expression up to the n + 10 expression. When you add the "n"s and the numbers, you end up with 9n + 54, once again, all over 9 and equate it to 9, the average.

Once you solve for n in each statement - though you don't have to - you will see that you can get the average of any of the expressions, because all you will have to do is just take the desired number of expressions (say the middle three) and plug in the answer of n for n and just add them all up divide them by the number of expressions and you will get the average. Also, if the statement told you that the average of the first 2 is blah and the average of the last 4 is blah, you would still be able to answer the question. As long as you can figure out n, you can answer the question.

One important part of DS problems that Aleksandr demonstrates in the first post and then mentions in the second post is that there is NO POINT and it is even a detriment to actually using the sufficient statements to solve for what the consecutive integers are.

I see the "need to solve rather than simply determine sufficiency" a lot in students; as soon as you know you can solve for the value in the question stem based on the information given in the statement/s, mark your answer choice and move on.

The statements each and independently yield an equation that can be solved. At that point, move along and use those precious seconds somewhere else to get your rockin' score.