Write out the first 10 or so in the series. Note the pattern
of odds and evens (O O E O O E O O E, etc.). This pattern will go
on for all integers in this sequence because the sum of 2 odds will always
be an even, the sum of 2 evens will always be an
even, and the sum of an odd and an even will always be odd.
If you look at this pattern, you can see that 2/3 of the integers are odd.
So out of the first 999 integers, 2 /3 or 666 of them will be odd.
You can figure then that the thousandth integer will also be odd because
of the pattern. So 666 + 1 = 667 integers are odd
(E).