If there are 505 such asteroids, this is certainly an odd asteroid.
On the other hand, when they discover the next one, does the whole group become even asteroids, or do only half of them become even asteroids, and the other half stay odd asteroids?
If half of this group are already even asteroids, does that mean there are really 1010 earth-threatening asteroids total?
If you have 505-odd asteroids on a table, and 504 of them fall off, what do you have left? An odd or an even?