Will a 26x1.6 or 26x1.3 tire fit on a 26x1.5 rim?

Question

I would like to get the “Continental Sport Contact" tire for my mountain bike. Will a 26x1.6 or 26x1.3 tire fit on a 26x1.5 rim?

Alternatively, could you recommend a tire that is that is affordable and good for the road races?

Answer 1

No problem with those tires, but no matter what you do, you won't be competitive riding a mountain bike in a road race.  

Answer 2

You should never run a tire narrower than the rim. so the 1.3 tire is too narrow and the 1.6 should work OK.