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Re: DS: odd or even??????????? [#permalink]
26 Jan 2005, 23:48
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.
(II) n is odd
insufficient as it depends on the starting number
Combine together, we can determine that S is odd. Sufficient