sudai wrote:

Is the average (arithmetic mean) of a certain series of consecutive integers an integer?

(1) The number of terms in the series is even.

(2) The median of the terms in the series is not an integer.

statement 1:sum of series is given by: S = n/2[2a+(n-1).d]

hence arithmetic mean A.M.= S/n => 1/2[2a+(n-1)] as d=1( consecutive integer)

=> A.M.= a+(n-1)/2

now, since n is even so n-1 is odd hence (n-1)/2 will not be integer => hence A.M. will not be an integer ....suff.

2nd statement: as gurpreetsingh has mentioned ...suff.

hence both statements are sufficient to answer.