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Your reasoning is flawless IMO
possible sets
3,4,5,6,7,8,9,10,11,12,13
11,10,9,8,7,6,5,4,3,2,1
The average for first 9 terms for both is 7 so A) is insufficient and as you mentioned B) is also insufficient by the same reasoning.
Then from both statements togehter seems that only one set of numbers can be determined.
Good reasoning Ihotseface

My expln: (Assuming increasing order)
stmt 1: Since the nos are consecutive 7 is the 5th element. For 11 numbers, the average should be the 6th number. That is 8.

I concurr with RAO ... the defination of CONSECUTIVE INTEGER is the integers that follows in sequence,each number being one greater than the previous number ,represented by n,n+1,n+2 .....where n is any number ...