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ok guys, we are having short of problems. let us post some problems.......

if z1,z2,z3, ..................zn is a series of consequtive positive integers, is the sum of all the integers in this series odd?

(i) (z1+z2+z3+ ..................+zn)/n is an odd integer. (ii) n is an odd integer.

If n is even, then there's always even numbers of odd numbers and thus the sum would be even
If n is odd, however, depends on if the starting number is odd or even.
(i)S/n is odd
S=S/n*n if n is even, S is even; if n is odd, S is odd.
Insufficient
(II) n is odd
insufficient as it depends on the starting number

Combine together, we can determine that S is odd. Sufficient

I go for A, too. If the list had an even number of numbers, then the average would be a .5 (as in, if the list was 4,5,6,7, the average would be 5.5)

If it has an odd number of numbers, then the average is an integer, and if that integer is an odd number, then the sum must have been odd, too.

That's a good way to figure this one. Avg of even number of +ve consecutive integers is not an integer (rather .5) and for odd number of +ve consecutive integers it is an integer.