Problem Solving - 41

If eleven consecutive integers are listed from least to greatest, what is the average (arithmetic mean) of the eleven integers?

(1) The average of the first nine integers is 7.
(2) The average of the last nine integers is 9.

Answer: D

Let the numbers be a, b, c, d, e, f, g, h , i, j, k

i) For odd number of consecutive integers median = mean
ii)We also know that the median is the "middle" number in a group (when arranged in ascending or descending order) consisting of an odd number of numbers

We have to find f

From statement (1): It is given that average of first nine numbers = 7
Hence this implies e = 7 ..since it is given numbers are consecutive hence f = 8
Thus sufficient

From statement (2): It is given that average of last nine numbers = 9
Hence this implies g = 9..since it is given numbers are consecutive hence f = 8
Thus sufficient